Fashion during the Elizabethan Era

Keeping Up With the Fashion Field â€Å"Clothing and fashion during the Elizabethan Era was complex, complicated, and too dramatic† (Bloom). The Elizabethan Era, was a time period from 1558-1603 when Queen Elizabeth I reigned, and was a period when people expressed who they were through creativity and originality (Black and Garland 16). Some may say that the Era was important, as it was the Golden Age in English history. Fashion during the Elizabethan Era was very extravagant and â€Å"over the top†. Fashion and style were competitive, varied by gender, and also depended on one's social class.Keep up† is a phrase to describe the attitudes toward fashion during the Elizabethan Era. There was always pressure to be up to date. People's attempts to stay in fashion cost them a lot of money (Lace). Land owners felt obligated to entertain the rulers such as the king and queen when they traveled, so they would arrange big parties, and they and their families wore the most expensive clothes. Even the royal court wanted to show off and out-dress everyone. When the royal court traveled, they often made the nobles go broke trying to keep up with their standard of display (Lace).All types of people from land owners to the royal court felt the pressure to keep up. Fashion and style were different for men and women who were not rich. It varied by gender. Women and men both had fashion rules to follow. Men had to wear cheap materials which included sheepskin and wool (Elizabethan Era). They had to wear dull colors such as brown, dull blue and beige. Men wore low, flat hats. They also wore cheap breeches made out of rough materials. Women wore material from sheepskin and wool like men. They also had to wear dull colors. Women wore aprons and bodices. The bodice fronts were often laced up.They did not wear Jewelry or any other accessory. Men and women of working class both had restrictions on clothes, however, the clothes varied by gender. No matter how rich a man or woman was, no one could wear what they pleased. Clothing during the Elizabethan Era was controlled by sumptuous laws. These laws were put in place to keep the class structure strict (Renaissance Clothing for Kids). Clothes defined who a person was and what class they belonged to. Upper classes wore bright colors. Their clothes were made from expensive materials such as velvet, satin, silk, taffeta and lace.They also wore costly Jewelry such as pearls. The upper class women would wear clothes that included several different layers of material, while others women wore thin materials. Typical people such as the working class wore simple clothes as described above. During the Elizabethan Era clothing was associated with rank. There were a variety of colors and choices one could pick from if they were in a high class or had a high rank (Sixteenth- Century Clothing). No one could wear whatever they chose because people's clothing was controlled by laws.In conclusion, the Elizabet han Era as a time period when Queen Elizabeth I reigned, between 1558 and 1603. During the Era, many fields such as poetry and literature grew and flourished. An area that flowered included style and fashion. Some may say that the era was a time when people had the opportunity to express themselves. Others feel that fashion and style during this time was restricted. In today's world, fashion is not as restricted as it was during the Elizabethan Era and both men and women are free to wear whatever they want. Works Cited Black, Anderson J. , and Mange, Garland.

Competition Between Private and Public Schools, Vouchers, and Peer-Group Effects

t American Economic Association Competition between Private and Public Schools, Vouchers, and Peer-Group Effects Author(s): Dennis Epple and Richard E. Romano Source: The American Economic Review, Vol. 88, No. 1 (Mar. , 1998), pp. 33-62 Published by: American Economic Association Stable URL: http://www. jstor. org/stable/116817 . Accessed: 01/02/2011 12:55 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at . http://www. jstor. org/page/info/about/policies/terms. jsp.JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at . http://www. jstor. org/action/showPublisher? publisherCode=aea. . Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email  protected] org. American Economic Association is collaborating with JSTOR to digitize, preserve and extend access to The American Economic Review. http://www. jstor. org CompetitionBetween Privateand Public Schools, Vouchers, and Peer-GroupEffectsBy DENNIS EPPLE AND RICHARD E. ROMANO* A theoretical and computational model with tax-financed, tuition-free public schools and competitive, tuition-financedprivate schools is developed. Students differ by ability and income. Achievement depends on own ability and on peers' abili ties. Equilibrium has a strict hierarchy of school qualities and twodimensional student sorting with stratification by ability and income. In private schools, high-ability, low-income students receive tuition discounts, while lowability, high-income students pay tuition premia.Tuition vouchers increase the relative size of the private sector and the extent of student sorting, and benefit high-ability students relative to low-ability students. (JEL H42, 128) Discontent in the United States with the primary and secondary educational system has become the norm. The decline in SAT scores in the 1970's, embarrassinginternationalcomparisons of student achievement, slow growth in productivity measures, and increasing disparity in earnings all call into question the quality of the educational system. ‘ Education policy figured prominently in recenit presidential elections.The debate has centered on issues of school choice, including voucher systems (Karen De Witt, 1992). Typical vouch er proposals provide students attending private schools a tax-financed, school-redeemable voucher of fixed amount toward (or possibly covering) tuition. Although a 1993 California referendumfor vouchers was defeated, policy change at state and local levels abounds, as does change in the private educational sector. The state of Minnesota and school districts in 30 states allow residents to choose the public school their children attend. 2The city of Milwaukee introduced a voucher system in the 1989-1990 school year.A -number f private o school and private-public school initiatives are developing (see e. g. , John F. Witte et al. , 1993; Steve Forbes, 1994; Steven Glazerman and RobertH. Meyer, 1994; Joe Nathan, 1994; Newsweek, 1994; Wall Street Journal, 1994; Steven Baker, 1995; Jay P. Green et al. , 1996). Educational reform emphasizing increased school competition with an increased * Epple: GraduateSchool of IndustrialAdministration, Carnegie Mellon University, Pittsburgh, PA 15213; Romano: Department of Economics, University of Florida, Gainesville, FL 32611.We greatly appreciate the comments of Linda Argote, Richard Arnott, Lawrence Kenny, Tracy Lewis, David Sappington, Suzanne Scotchmer, and three anonymous referees, in addition to workshop participants at Carnegie Mellon University, Florida State University, Indiana University, Northwestern University, Princeton University, the University of Chicago, the University of Colorado, the University of Florida, the University of Illinois, the University of Kansas, the University of Virginia, Yale University, the 1993 Public Choice meetings, and the 1994 American Economic Association meetings.We thank the National Science Foundation, and Romano thanks the Public Policy Research Center at the University of Florida for financial support. Epple acknowledges the supportof Northwestern University, where some of this research was conducted. Anv errors are ours. 2 Public funding of nonsecular schools and considerable fre edom of school choice has been practicedfor years in England (Daphne Johnson, 1990) and much of Canada (Nick Kach and Kas Mazurek, 1986). These choice systems support horizontal differentiation in schooling and safeguards exist to limit vertical (quality) differentiation.Our analysis is concerned primarily with the effects of a voucher system on vertical differentiation. ‘The provocatively titled report of the National Commission on Excellence in Education (1983), A Nation at Risk, details the decline of performance of U. S. students in the 1970's. More recent data can be found in Daniel M. Koretz ( 1987). Modest gains in performanceon standardized achievement tests, followed by a leveling off, well below peak scores of the early 1960's, characterizes the late 1980's and 1990's. 33 34 THE AMERICANECONOMICREVIEW role of the private sector is at the forefront of he policy debate and recent policy initiatives. The modern economic case for vouchers and increased educational choice was made by Milton Friedman (1962). The academic educational and political-science professions have since considered the pros and cons of voucher systems and educational choice (John E. Coons and Stephen D. Sugarman, 1978; Myron Liberman, 1989; John Chubb and Terry Moe, 1990). Economic analysis of the interaction between public and private schools, and of related policy instrumentslike vouchers, is only beginning to emerge. This paper continues the study of the â€Å"market† for ducation by developing a model that focuses on the interactionbetween the public and private educational sectors and also examines the consequences of vouchers. We describe the equilibrium characteristics of the market for education with an open-enrollmentpublic sector and a competitive private sector. Our model embodies two key elements of the educational process. First, students differ in their abilities. Higher ability is assumed to increase a student's educational achievement and that of peers in the school attended. Second, households differ in their incomes, with higher income increasing the demand for educational achievement.A studentin our model is then characterizedby an ability and a household income, a draw from a continuous bivariate distribution. A school's quality is determined by the mean ability of the student body, reflecting the model's peer-groupeffect. We characterizethe equilibriumdistributionof studenttypes across public and private schools and examine the tuition structure of private schools, assuming that student types are verifiable. We develop a theoretical and computational model in parallel, with the latter calibrated to existing estimates of parameter values. Equilibria are simulated for a range of voucher values.Key characteristicsof an equilibriumare the following. A hierarchyof school qualities will be present, with the set of (homogeneous) public schools having the lowest-ability peer group and a strict ability-groupranking of private schools. T he equilibrium student bodies of schools correspond to a partition of the ability-income-type space of students with MARCH 1998 stratification by income and, in many cases, stratificationby ability. As Figure 1 from our computational model illustrates, type space is then carved into diagonal slices with each higher slice making up a private school's student body and with the bottom lice comprising the public sector. The normality of demand for a good peer group leads relatively high-income studentsto cross subsidize the schooling of relatively high-ability students, producing the latter partition. Private schools attract high-ability, low-income students by offering them tuition discounts, sometimes fellowships. Even with free entry, schools price discriminate by income against students who are not on the margin between switching schools. The equilibrium differentiation of schools and economies of scale in education preclude perfect competition for every type of student.Nevertheless , this price discriminationdoes not disrupt the internalization of the peer-group externality by private schools. An equilibrium without a public sector is Paretoefficient given the equilibrium number of schools. Because free public schools do not price the peer-group externality, an equilibriumwith public schools is Pareto inefficient. In the computational model, we employ a Cobb-Douglas specification of utility and educational achievement which incorporatesthe peer-group effect. The parameters are calibrated to U. S. data from various sources. We compute approximate equilibria for voucher alues ranging from $0 to $4,200 per student ($4,222 equals the expenditure per student in public schools in 1988). ‘ With no vouchers, the predicted percentage of students in the public sector is 90 percent (the actual value for the United States is 88 percent). As the voucher is increased, the size of and mean ability in the public sector decrease. With a $2,000 voucher, for example, the p ercentage of students remaining in the public sector equals 70 percent, and the mean ability declines by 15. 8 percent. 3 The integer number of private schools in our model precludes existence of competitive equilibrium except in special cases.This integer problem and our approximation approachare discussed later in the paper. VOL. 88 NO. 1 EPPLE AND ROMANO:PRIVATE-PUBLIC SCHOOLS COMPETITION The entry of private schools and consequent more efficient sorting of students across schools caused by vouchers increases average welfare (and achievement) only a little in our computational model, while having larger distributional effects. As we discuss in detail later, the magnitude of the aggregate effect depends on the extent of complementarity of peer ability and own ability in the educational production function. There is little empirical evidence to guide assessment of the extent of uch complementarity. The voucher increases the premium to ability in private schools. The largest proport ionate gains from the voucher then accrue to low-income, high-ability students. For example, a household with income of $10,000 and student with ability at the 95th percentile has a welfare gain of about 7. 5 percent of income from a $2,000 voucher. Students of low income and low ability who remain in the public sector when a $2,000 dollar voucher is available experience small welfare losses but make up a majority. It bears emphasizing that our model takes public and private schools to be equally effective providers of education, however.Some argue that private schools are more productive and that the competitive effect of a voucher program will increase public-school effectiveness. 4 For example, Hoxby (1996) concludes from her empirical investigation that competition-induced performance improvement would increase public-school achievement by more than enough to offset 4 Caroline M. Hoxby (1994, 1996) provides evidence thatprivate-school competition increasespublic-school effective ness. William N. Evans and Robert M. Schwab (1995) find that Catholic private schools are more effective in inducing studentsto complete high school and also to attend college.These studies take on the challenge of finding instrumentsthat predict well private-school attendance while being independent of unobserved determinants of educational achievement. Controversy exists concerning the quality of the instruments used. See Thomas J. Kane ( 1996) for a discussion of Hoxby's methodology. David N. Figlio and Joe A. Stone ( 1997) employ a different set of instrumentsthan Evans and Schwab and find that, at currentinput levels, religious private schools are less effective than public schools in producing achievement on standardizedexams in math and science but nonreligious private schools are more effective). See Witte (1996) and Figlio and Stone (1997) for references to other studies. 35 losses of the magnitude thiatemerge due to reduced peer quality in our computational model. Our anal ysis delineates the allocative effects of vouchers and demonstrates a potential for significant redistribution. A theoretical-economics literature on education is beginning to emerge. Charles A. M. de Bartolome ( 1990) develops a twoneighborhoodmodel of the provision of public educational inputs (quality) with two ability types and peer-group externalities. He shows hat the voting/locational equilibrium is inefficient because the median voter does not internalize the consequences of migration on peer groups in choosing the input level. No independent income variability characterizes students in his model. Raquel Fernandez and Richard Rogerson (1996) introduce income differences in a two-neighborhood model of the provision of inputs but abstractfrom peergroup effects. They examine the effects of redistributive policies and direct controls on inputs. Neither model has a private sector. Our analysis is differentiated by its consideration of a private sector and its two-dimensional, ont inuous type space. In a nolrnativeanalysis of student groupings in the presence of peergroup effects, RichardArnott and John Rowse ( 1987) show how a social plannerwould maximize the sum of achievements in allocating students of various abilities across classrooms. We analyze equilibrium outcomes, and most of our analysis is positive. Joseph E. Stiglitz ( 1974), Norman J. Ireland (1990), Ben Eden (1992), Charles F. Manski (1992), Michael Rothschild and Lawrence J. White (1995), Epple and Romano (1996), and GerhardGlomm and B. Ravikumar(1998) consider the consequences of a private sector for education. Stiglitz,Glomm and Ravikumnar, and Epple and Romano are concerned with the existence and properties of voting equilibria over taxfinanced, public-school expenditure in the presence of a private alternative. Ireland analyzes the effects of vouchers on utilities and the quality of the public alternative,taking the tax rate as exogenous. Individuals differ only by income, and the private alternative can be purchased continuously in all these analyses. Hence, the private sector is relatively passive, and issues of financial aid and differences in 36 MARCH 1998 THE AMERICANECONOMICREVIEW studentability across schools do not arise.Our model is distinguished by having differences in ability and related peer-group effects, and by providing an active role for private-sector schools. Eden ( 1992) analyzes vouchers in a purely private market system of provision of education having two ability types and peergroup effects. A voucher equal to the difference between the social and private benefit of education to each ability type is shown to induce socially optimal provision of education. Key differences in our analysis include our consideration of the interaction between the public and private sectors, our exploration of the implications of continuous ifferences in ability and income, and our attention to positive issues. Manski ( 1992) pursues a computational analysis of vouc hers that also considers peer-group effects among other aspects of education (especially various objectives of public-school decision makers). Our models differ in a number of ways. Most importantly, we permit private schools to discriminate in their tuition policies, with many consequences. Rothschild and White ( 1995) analyze a competitive model with consumers also inputs to production (a peer-group effect), using higher education as their primary example.We share a concern for market pricing in the presence of an externality. Differences in our model, among others, are the presence of a public sector, a more detailed specification of peer effects and demand for education, and student variation in both ability and household income. Our attention to the implications for pricing, profitability, and school qualities of a peer-group effect deriving from student abilities, the allocation of students according to ability and household income and the related distribution of educational b enefits, and the effects of vouchers are not concerns in Rothschild and White.Private schools are cases of clubs with nonanonymous crowding due to the abilitydependent externality and schools' power to price it. Suzanne Scotchmer (1994) provides an excellent synthesis of this literature. We follow this literaturein our competitive specification of private schools as further discussed below. The next section presents the model. Section II develops the theoretical results. The computational results comprise Section III. Concluding remarks follow. An Appendix contains some of the detail. I. The Model Household income is denoted y, and each household has a student of ability b. The joint arginal distributionof ability and income in the population is denoted f(b, y) and is assunmedto be continuous and positive on its . (0, bmax X (0, Ymax]All students ] support, S attend a school since we assume that free public schooling is preferredto no schooling. The household decision maker's utilit y function, U( ), is increasing in numeraireconsumption and the educational achievement of the household's student, and it is continuous and twice differentiable in both arguments. Achievement, a = a (0, b), is a continuous and increasing function of the student's ability and the mean ability of the student body in the school attended,O. Let Ytdenote after-taxincome and ‘ The influence of ability on own educational achievement is well documented and not controversial. Eric Hanushek( 1986) provides an excellent survey. In the economics literature, Anita A. Summers and Barbara L. Wolfe (1977) and Vernon Henderson et al. (1978) find significant peer-group effects. Evans et al. (1992) adjust for selection bias in the formationof peer groups and show that it eliminates the significance of the peer group in explaining teenage pregnancy and dropping out of school. They are careful to point out that their results should not be interpretedas suggesting that peer-groupeffects do not xis t, but as demonstrating that scientific proof of those effects is inadequate. Note, too, that their work supports the notion that peer-group variables enter the utility function since a selection process does take place. The psychology literatureon peer-group effects in education also contains some controversy. In their survey paper, Richard L. Moreland and John M. Levine (1992) conclude: The fact that good students benefit from ability grouping, whereas poor students are harmedby it, suggests that the mean level of ability among classmates, as well as variability in their ability levels, could be an importantfactor.The results from several recent studies . . supportthis notion. This squares with our reading of the literature(Summers e and Wolfe, 1977; Henderson. t al. , 1978; Chen-Lin Kulik and James A. Kulik, 1982, 1984; Aage B. Sorensen, 1984; VOL. 88 NO. I EPPLE AND ROMANO:PRIVATE-PUBLIC SCHOOLS COMPETITION p tuition expenditure, the latter equal to zero if a public school is at tended. Thus, U = U(Y, – p, a(O, b)), with U1, U2, a,, and a2 all positive. The achievement function captures the peer-group effect in our model, discussed further below. To maintain simplicity and highlight the role of peer groups, a chool's quality is determined exclusively by the mean ability of its peer group. 6In ongoing work we are extending the model to include variation in educational inputs. U is also assumed to satisfy everywhere the â€Å"single-crossing† condition (SCI): (1) 0a OU/0 J yt > ?. Preferences for school quality might also depend on ability. We say preferences satisfy weak single crossing in ability if a Sorensen and MaureenT. Hallinan, 1986; Adam Gamoran and Mark Berends, 1987; Jennie Oakes, 1987; Gamoran, 1992). However, there are alternative interpretations (Robert E. Slavin, 1987, 1990). For simplicity, the possibility that dispersion in peer ability also affects achievement is not built into our model. Roland Benabou (1996b) explores the con sequences for economic growth of dispersion in human capital. 7 We believe this to be uncontroversial. hile we know W of no empirical studies that use direct measures of educational quality, a substantial empirical literature on the demand for educationalexpenditureexists. Although considerable diversity in magnitudes of estimates of the income elasticity of demand for educational spending are present, estimates using a variety of approaches find the ncome elasticity to be positive (Daniel Rubinfeld and Perry Shapiro, 1989). 8 Households may consider education a consumption good, an investment good, or a combination of the two. Our formulation can be interpretedto accommodate any of these motives. However, for households not subject to borrowing constraints, a pure investment motive would imply a zero income elasticity of demand. For such households, this in turn would imply that the SCI condition in (1) would be only weakly satisfied. In light of the empir- OU/00 / Ob t OUIOyt whic h implies a weakly positive ability elasticity of demandfor quality.However, because the pertinent empirical evidence is mixed and scarce, we postpone restricting preferences in this regard until necessary. 9 In our computational model and to illustrateour more general theoretical results, we adopt a Cobb-Douglas specification of the utility function: (2) Hence, for students of the same ability, any indifference curve in the (0, p)-plane of a higher-income household cuts any indifference curve of a lower-income household from below. This condition corresponds to an income elasticity of demand for educational quality that is positive at all qualities for all types. One set of sufficient conditions on U for SCI is U11 0 and U12 2 0, with at least I one having strict inequality. 8 37 U = (yt-p)a(O, a(O, b) b) = 0Yb'6 g ; O y ; O. While(2) satisfiesSCI,it embodies he â€Å"neut tral† assumption of zero ability elasticity of demand: at O? /0 9b 0. Our computational results are not driven by own-ability effects on the demand for education. Keep in mind, too, that the theoretical results do not assume specification (2). A school's costs depend only on the number of students it enrolls, since inputs vary only with size. All schools, public and private,have the simple cost function: (3)C(k) = V(k) + F V' ;0 V†>o ical evidence suggesting the income elasticity to be positive, we conserve space in the development that follows by assuming that SCI is strict for all households. 9 Henderson et al. (1978) find no interaction between own ability and the benefits to an improved peer group, corresponding to 2IU/00&b= 0 in our model. Summers and Wolfe ( 1977) find some supportfor higherpeer-group benefits to lower-ability students, that is, 02U/la6ab < 0. Thus the literatureprovides limited evidence from which to draw conclusions. 38 THE AMERICANECONOMICREVIEW where k denotes the number of attendingstudents.Technical differencesamong schools are not an element of our model (for simplicity). Hence, vouchers cannot drive technically inefficient schools from the market,an effect predicted by some proponents of vouchers (see footnote4). Let k* denotethe â€Å"efficientscale,† (4) k* ARGMIN[C(k)/k]. The presumptionof some economies of scale in education is realistic (Lawrence Kenny, 1982) and important. Otherwise, the private market would produce an infinite number of schools containing infinitely refined peer groups. Our model's equilibriumwill be consistent with the fact thatthe numberof types of studentsgreatlyexceeds the numberof schools.Public-sector schools offer free admission to all students. This open-enrollment policy leads to homogeneous public schools in equilibrium because we assume no frictions in public-school choice are present. Without equalization of 0's in public-sector schools, students would migrate to higher-0 schools to reap the benefits of a better peer group. With equalized 0's, no incentives for switching schools wit hin the public sector remain. We study the alternative of neighborhood school systems that impose residence requirementsin Epple and Romano (1995). Since all public schools will have the same , one can think of the public sector as consisting of one (possibly large) school. Publicsector schooling is financed by a proportional income tax, t, paid by all households, whether or not the household's child attends school in the public sector. Thus, Yt= (1 – t)y. The public sector chooses the (integer) number of schools and their sizes to minimize the total cost of providing schooling subjectto (3). The tax rate adjuststo balance the budget. Because households are atomistic, there is no tax consequence to a household's decision about school attendance. The public finance of chooling can then be largely suppressedin the analysis until the consideration of vouchers. The public sector is passive in this model for simplicity. Public-sector schools do not segment students by ability (tra ck), increase educational inputs to compete more effectively with the private sector, or behave strategically MARCH 1998 in any way. More realistic alternativesare importanttopics for research, some of which are discussed in the final section. Private-sectorschools maximize profits, and there is free entry anidexit. 10Modeling private schools as choosing an admission policy and uitionpolicy is convenient andinvolves no loss of generality. Student types are observable, implying that tuition and admission can be conditioned on ability and income as competition permits. 1 Private schools are an example of clubs with â€Å"non-anonymous crowding† (Scotchmer and Myrna H. Wooders, 1987; Scotchmer, 1997) because of the peer-groupeffect, and we model private-schoolbehaviorfollowing the literature on competitive club economies. In particular,private schools maximize profits as utility tak-ers(see Scotchmer, 1994), a generalization of price-taking when consumers (types) and productsdif fer. Private chools believe they can attract any studenttype by offering admission at a tuition yielding at least the maximum utility the student could obtain elsewhere. Let an i subscript, i = 1, 2, .. n, indicate a value for the ith private school. A zero subscript does the same for â€Å"the† public school. Let pi (b, y) denote the tuition necessary to enter school i, with po(b, y) = 0 V (b, y). Let ai (b, y) C [0, 1] denote the proportionof type (b, y) in the population that school i admits, 10Consideration of alternative objective functions to profitmaximization is reasonable,especially given the significant proportion of nonprofit schools.Some private pursuethe objective of quality schools might, for exa-mnple, maximization. Quality maximization, like profit maximization, is a member of a set of objective functions that are utility independent in the sense that they place no weight on offering any student types higher utility than the student's (equilibrium) reservation utility. Our preliminary analysis of this issue suggests that equilibtia where some private schools pursue objectives from this set other than profit maximization must also be competitive equilibria. Roughly, the failure of any school to maximize profits would permit ently by a profit-maximizingschool. The notion is that abilities can be determinedthrough testing, and required financial disclosures permit determination of household income. At least in the case of Cobb-Douglas utility, equation (2), students will have no incentive to underperformon exams, since tuition will be nonincreasing in ability in equilibrium (proved in Epple and Romano [1993]). Incentive compatibility in the reporting of income is more complex. EPPLE AND ROMANO:PRIVATE-PUBLIC SCHOOLS COMPETITION VOL. 88 NO. I with any ao(b, y) E [0, 1] â€Å"optimal† for the public school as determinedby the residualdemand for public education.A private school's profit-maximizationproblem can be written as (5) MAX rri Oj,kj,pj(b,y),aj(b,y) [pi(b, y)ai (b, y) f – s X f(b, y) db dy]-V(ki) –F subject to ai (b, y) E [0, 1] V (b, y); (5a) (5b) (b, y)a(Oi, U(y,-pi MAX 2 j b) ) p1(b, y), a(0j, b)) j * i; aj(b,y) > O is in the optimal set of j U(yt I0,1, †¦ ,n that (5b) hold for all (b, y) as we have specified (i. e. , including for nonadmitted students). Tuition charged to students for whom ai (b, y) = 0 is school i's only optimal choice (i. e. , nonadmittedstudents) is irrelevant. Note, too, that tuition such that (5b) holds with strict quality will be optimal. Private schools enter so long as they expect to make positive profits as utility takers. Because incumbent private schools maximize profitsas utility takers,entryresults if and only if wri> 0 for some incumbent school. The public-sector/private-sectorequilibriumis described by the following five conditions in addition to the government balanced-budget condition presented below in Section II, subsection C, for the more general case with vouchers. Condition UM: U*(b, y) – MAX U(y,-pi(b, V (b, y); 39 ie E 0,1,†¦ ,nI ai(b,y) y), a(0i, b)) > O is in the optimal set of i}V (b, y). (5c) (b, y)f(b, y) db dy; ki =fai Condition VIM: s [Oi, ki, pi(b, y), ai (b, y) ] satisfy (5), (Sd) O kjfbai(b, y)f(b, y) db dy. s Constraints(5c) and (5d) define, respectively, the size of the school's student body and the mean ability. Constraint (5a) precludes a school from admitting a negative number of a type or more of a type than exits in the population. â€Å"2Constraint(5b) imposes the utilitytaking assumption. Students' alternatives are limited to schools where they are admitted. Students always have the option of attending the public school. It is innocuous to require i= 1,2,†¦ ,n.Condition ZfH: 7ri = 0 i = 1, 2, †¦ , n. Conditions PSP: po(b, y) = V (b, y) ao(b, y) E [0, 1] V (b, y) 12 One might object to the presumptionthat â€Å"competitive schools† recognize the limit to demand. The presum ption is analogous to a monopolistically competitive firm's recognition of a limit on its demand curve. Dropping the presumptionwould lead to schools admitting infinite densities of some types. See Scotchmer (1994) for the analogue in the literatureon club goods. ao(b, y)f (b, y) db dy ko= s Go =-Af ko bao(b, y)f (b, y) db dy. s THE AMERICANECONOMICREVIEW 40 Condition MC: n xai (b,y)=1 V(b,y). i=OCondition UM summarizes household utility maximization. Households choose a mostpreferred private or public school, taking admission/tuition policies, school qualities, and taxes as given. Profit maximization of private schools (VIM) and the public-sector policies (PSP) have been discussed. While the entry assumption above is formally part of the definition of equilibrium, it is convenient to substitute the implication that private schools must earn zero profits (ZH). The last condition is market clearance, which uses the simplifying assumption above that free public schooling is preferredt o no schooling.II. Theoretical esults R A. Solution to the Private School's Problem Using UM, the first-order conditions for problem (5) can be written as follows: U(yt- pi , a(Oi, b)) (6a) =U*(b, ai (b, y) (6b) piC as f (6c) We now turn to the properties of equilibrium, assuming one exists. Existence issues are discussed below. Heuristic argumentshave been substituted for formal proofs when reasonable. The first result concerns the qualities of schools. b0,db [ (b, si) L sho0 V'(ki) yd 0 +io (Oi b) = n7i- – X PROPOSITION 1: A strict hierarchy of school qualities results, with the public sector V (b y); i i J ith equality combined with the equilibrium condition UM; pe () is student-type (b, y)'s reservation price for attending school of quality 0i. Condition (6b) characterizes optimal admission policies. † The term 77i0i – b) may ( be thoughtof as the marginalcost of admission operating via the peer-group externality in school i. From (6c), 77i[the Lagrangianmult iplier on (5d) ] equals the per-studentrevenue change in school i deriving from a change in 0i. The appropriatelyscaled change in 0i due to admitting student of ability b equals (b t 0k); its negative is then multiplied by rqj o obtain the peer-externalitycost.The peer cost of admitting students with ability below the school's mean is positive because the resulting quality decline dictates reduced tuition to all students, while the peer â€Å"cost† of admitting above-mean-ability students is negative. Let ( MCi (b) V'(ki ) + r7i 0 – b), which we term effective marginal cost. Types with reservation prices below MCi (b) are not willing to pay enough to cover their effective marginal cost and are not admitted. The school admits all of a type that has a reservationprice above effective marginal cost, and any ai E [0, 1] is optimal if pi* = MCi. 1 B. Properties of EquilibriumV (b, y); y) MARCH 1998 ai(b y) f(b y) db dy] Condition ( 6a) describes sclhooli' s optimnalut ition function, Pi* (b, y, Oi) and is just (5b) ‘3 Results (6b) and (6c) are found by substituting p* from (6a) into (5), and then forming a Lagrangianfunction to take account of (Sc) aind(Sd). Result (6b) is then derived by pointwise optimization over ai while taking account of the constraint (Sa). ‘4 In the upper and lower lines of (6b), the solution for ai is at a corner, and the first-orderconditions are also sufficient for a local maximum. In the middle line of (6b), where p * MCI and any ac (b, y) E [0, 11 satisfies the irst-orderconditions, V† sufficiently large implies local maximization. VOL. 88 NO. 1 EPPLE AND ROMANO:PRIVATE-PUBLIC SCHOOLS COMPETITION having the lowest-ability peer group: 0,, fJn-I > .. > > fJI > 00. Formal proof is in the Appendix. Here an economic interpretationis provided. All private schools must be of higher peer quality than schools in the public sector. Otherwise, no students would be willing to pay to attend any private school. Why mus t a strict hierarchy of private schools characterize equilibrium? If two private schools were of the same quality, then they would compete perfectly for students.Consequently, they would have the same effective marginal costs of admitting all types, and their tuitions (to all admitted students) would equal effective marginal costs. An opportunity to increase profits would exist by varying admissions/tuitions in such a way to either: (a) increase quality and admit a student body that values quality by more, or (b) decrease quality and admit a student body that values quality by less. In either case, the school differentiates itself in quality, at the same time attractinga student body that permits profitable price discrimination over the quality change.We sketch the example of a profitablequality improvement, beginning with schools having identical student bodies (the proof shows that this is without loss of generality). Let one school admit the same numberof (b2, Y2) types as it exp els of (bl, yl) types, where b2 > b, and Y2> Yl, implying an increase in 0 but no change in production costs, V(k) + F. Further, choose the types (which is always feasible) such that Y2 – YI > b2 – bi by enough that, using SCI, the (b2, Y2)-types value increased quality by more than the (bl, Yi)types, even though their abilities differ.This permits the school to charge the newly admitted students tuitions higher than their effective marginal costs because they are selected to value quality increases by more than the expelled students. The profit increase occurs because the new student body values the quality increase by more than would the original student body; 0 and rl rise in the school. It would not increase profits to substitute students in such a way that 0 rises without also changing the student body's average value of quality improvements, because tuitions equal 41 ffective marginal costs in the initially nondifferentiated schools. ‘5 This example assumes that a school substitutes students to increase quality, but alternativeprofitablesubstitutions exist that decrease quality, roughly, by also creating a lower-income studentbody. In either case, the argumentdepends on SCI. It also identifies the model's force for â€Å"diagonal stratification† (see the examples in Figure 1). As developed more fully below, this stratification results because students having relatively high income and low ability within a school cross subsidize relatively lowincome, high-ability students.The strict hierarchy of Proposition 1 supports the equity-relatedconcerns of some that private schools operate to the detriment of public schools by siphoning off higher-ability students. Whethera strict hierarchyis efficient is analyzed below. First we develop furtherthe positive properties of equilibrium. Proposition 2 describes equilibriumpricing, and Proposition 3 describes the resulting partition of types. Some definitions are useful. Let { (b, y) E SIai ( b, y) > 0 is optimal} denote the admission space of school i, i = 0, 1, †¦ , n (see Figure 1, for example). A locus of points (b,y) E A. n Aj, i ]j, assuming t exists, is referredto as a boundary locus between i and]. (Boundary loci have zero measure in S, as proved in Epple and Romano [1993]. ) Since any household prefers free public schooling to no schooling, the entire type space S is partitioned into admission spaces. Last, to avoid tedious qualification of statements for public-sector schools, we specify that MCo -0 for all (b, y). This notation is convenient since students see a zero cost of public education. PROPOSITION 2: (i) On a boundary locus between school i and j, pi MCi(b) and pj = MCj(b); pricing on boundary loci is strictly according to ability in private schools. ii) pi (b, y) > MCi (b) for off-boundarystudents who attend private school i; pricing off- ‘† Mathematically,beginning with equal O's,first-order effects on profits of varying admissions va nish, but the profit function is convex in some directions in [a(b, y), p(b, y)] -space, allowing a profit increase. 42 THE AMERICANECONOMICREVIEW boundary loci depends on income in private schools. (iii) Every student attends a school that would maximize utility if all schools instead set pi equal to equilibrium MCi Jor all students. The allocation is as though effective marginal cost pricing prevails in private schools. 16See Epple and Romano (1993) for proof. Competition between private schools that share a boundary locus forces prices to effective marginalcosts for student-typeson the locus. These students are indifferentto attending the schools sharing the locus. Private schools then have no power to price discriminatewith respect to income on boundaryloci. Prices are, however, adjusted to differing abilities because private schools internalize the peergroup effect. Tuition to private school i decreases with ability at rate rRialong its boundary loci, reflecting the value of pe ergroup improvements of the school's student body.Moving inside a boundarylocus in a private school's admission space, students' preferences change in such a way that they would strictly prefer the school attended if it practiced effective marginal-cost pricing. Part (ii) of Proposition 2 establishes that private schools exploit this by increasing price. These students are also indifferent between the private school attended or their best alternative by (6a), but this is a result of discriminatory pricing. Generally, then, price depends both on ability and income within admission spaces. â€Å"7 Part (iii) of Proposition 2 follows because it is profitable for a private school to be sure o attractany student whose reservation price 16 The statementsregard the equilibriumeffective marginal cost. Income effects would cause these costs to change if tuition equaled effective marginal cost for all students. This has distributional (but not efficiency) implications. ‘7 While there a re no published studies of the allocation of financial aid by income and ability among private elementary and secondary schools, there is evidence on the allocation of financial aid by colleges and universities. There the evidence is that both ability and family income are significant determinantsof whether and how much financial aid is received (J.Brad Schwartz, 1986; Sandra R. Baum and Saul Schwartz, 1988; Charles T. Clotfelter, 1991). MARCH 1998 exceeds the school's effective marginal cost. The student allocation's link to effective marginal costs, and hence abilities, will be shown to be efficient (except for the public sector). The income-related price discrimination that occurs does not disrupt the allocation consistent with effective marginal-cost pricing; rather,it is purely redistributive. While this income-related price discrimination is of the first degree (a la Pigou), its magnitude is limited by competition for students among the differentiatedschools.Near a boundaryin a school's admission space, a student's preference for the school attended would be slight under effective marginal-cost pricing, so that the admitting school can capture little rent. The numberand sizes of private schools then determine their powier to price discriminate over income. All private schools have student bodies less than k* by a similar argumentto that in more standardmonopolistically competitive equilibria. â€Å"8Here school i's marginal-revenuecurve can be constructed by ordering from highest to lowest students' reservation prices minus peer costs [i. e. , p* + rbi(b – Of)], and thus the associated ownward-slopingaverage revenue curve may be derived. Zero profits then implies a scale below k*. If we let k* decline, then private schools become more numerous and less differentiated (have closer 0's), and incomerelated price discriminationdeclines. Now consider the partition of types into schools. We say stratificationby income (SBI) holds if, for any two househ olds having students of the same ability, one household's choice of a higher-O school implies it has a weakly higher income than the other household. Analogously, stratification by ability (SBA) is present if, holding income fixed, the household that chooses a higher-Oschool must ave a student of weakly higher ability. The combination of SBI and SBA implies a diagonalized partitionas, for example, in Figure 1. PROPOSITION 3: (i) SBI characterizes equilibrium. (ii) If preferences satisfy weak c single crossing in ability (W-SCB) and m7, 18 The points made here are proved in Epple and Romano (1993). EPPLE AND ROMANO:PRIVATE-PUBLIC SCHOOLS COMPETITION VOL. 88 NO. I ?72 ? ‘- ? 71, then SBA also characterizes equilibrium. ‘9 To confirm part (i), consider two households with students of the same ability but dif- feringincomes y2 ; yI. In the (0, p) -plane, indifference curves of a household are upward loping. For the same ability, SCI implies that any indifference curve of y2 cuts any indifference curve of yl from below. Allocations are as if tuitions equal effective marginal costs [part (iii) of Proposition 2]. Thus, the choice between schools i andj may be representedin the ( 0, p ) -plane as a choice between ( Oi, MCi (b)) and (0j, MCj(b)). If Oj; Oi, it must be that MCj(b) ; MCi (b) if either type chooses i. A standard single-crossing argument then applies to complete the proof. Part (ii) is proved in the Appendix; here we provide some intuition. Assume first that the demand for quality is independent of ability (e. . , as in the Cobb-Douglas specification) and that all private schools give the same discount to ability along their boundary loci (i. e. , schools' 7's are the same). Holding nominal household income fixed, real income would rise with student ability due to tuition discounts at all private schools. SBA would then result by the same logic explaining SBI. Hence, the combination of a positive income elasticity (SCI) and discounts to ability alone would cause both SBI and SBA, the diagonalized partition as in Figure 1. Relatively high-income and lowability students cross subsidize relatively low-income and high-ability students in rivate schools. The argument holds more strongly if the 7's strictly ascend or if WSCB holds strictly. However, neither condition is necessary for SBA, nor do any of our other results require these conditions or SBA. It may be possible absent these conditions to get cases having nonmonotonic boundary loci in the (b, y) -plane. 20 9 We thank an anonymous referee for encouraging us to investigate bid-rentfunctions (see e. g. , MasahisaFujita, 1989), which ultimately led to part (ii) of Proposition 3. 20 The alternativeto W-SCB implies that lower-ability types are willing to pay more for a better peer group, and he alternativeto weakly ascending q's implies that lower- 43 We now turnto normativeresults which are quite intuitive. Again, see Epple and Romano (1993) for the formal analysis. Pareto efficiency requires: (i) a student allocation that internalizes the peer-group externality given the nmtmberf schools, and (ii) entry as long o as aggregate household net willingness to pay for an allocation with one more school exceeds the change in all schools' costs. An equilibrium without a public sector would satisfy condition (i) but not condition (ii). Effective marginal cost includes the marginal value of he peer group externality, implying that MCi (b) equals the social marginal cost of attendance at school i by a student of ability b. A purely private-school equilibrium then satisfies efficiency condition (i) by part (iii) of Proposition 2. However, entry to the point of zero profits entails externalities so that efficient entry [condition (ii)] fails to hold in a fully private equilibrium. An entrantcapturesthe full value of its product to the studentbody it admits but ignores utility changes of nonadmitted students and profit changes of other schools resulting from the r eallocation. ‘ Fixed costs, quality schools give bigger discounts to ability. Either would tend to work against pure ability stratification, though Proposition I implies that some degree of ability stratificationwould be present. It is desirable to demonstrate SBA without assuming ascending q's, since these values are endogenous. However, providing general primitive conditions for SBA independentof assumptionsconcerning the equilibrium q's is difficult, because their equilibrium values depend on the entire distribution of types in the population. For the Cobb-Douglas case and ssuming independence of income and ability in the population, we (Epple and Romano, 1993) have shown SBA without assuming weakly ascending 7's. 21 The comparison of the equilibrium number of schools in a fully private equilibrium to the Paretoefficient number entails a trade-off. The entrant ignores the lost revenues and cost savings to other schools from the students that; t admits. Since almost every st udent ati tracted away from incumbent schools is inframarginal (i. e. , tuition exceeds effective marginal cost), the net effect here of entry is negative, tending to cause too much entry.Opposing this is the entrant's failure to capture the full returnsfrom increased varie-tyof school qualities that results. Altlhoughthe entrant fully price discriminates to the students it admits, it cannot tax other students for the adjustments in the incumbent schools' qualities. A net benefit to other students is likely to result because the incumbent schools will better accommodate preferences. 44 THE AMERICANECONOMICREVIEW hence the finite size of an entrant,underlie the entry externalities as in many models of monopolistic competition. Introductionof the free public sector implies eviations from both efficiency conditions. In general, the public sector displaces multiple differentiatedprivate schools, substitutingthe equivalent of one â€Å"large† homogeneous school. This effective red uction in the number of schools is without attention to costs and benefits, generally implying a deviation from efficiency condition (ii). Holding fixed the number of schools in the public-private equilibrium (and counting the public sector as one school), zero pricing of public schooling violates condition (i). By just reallocating students between the public sector and private school 1 near their shared oundary locus, Paretian gains are feasible. Reference to the upper panel of Figure 1 from our computational equilibrium may help clarify the argument. Gains would result from shifting into private school I relatively lowerability students below but near the boundary locus, students for whom the marginal social cost in the public sector is positive. These students are nearly indifferent between the two schools when facing the social cost of attending the private school but a tuition (zero) below the social cost of attending the public school. Students near the boundary locus and tte nding the private school may also be of sufficiently high ability that the social â€Å"cost† of attending the public school is negative. Gains from shifting such studentsinto the public sector are then also feasible. Such students exist in our computational model, the rough prescriptionbeing to rotatethe boundarylocus counterclockwise at the point of ability having zero social marginal cost in the public school. Collecting these results, we have the following proposition. efficient. (ii) The public-private-sector equilibrium has neither an efficient number of schools, nor an efficient student allocation iven the number of schools. When fixed costs of schooling are small, the departure from efficiency in a fully private equilibrium will be correspondingly small. Part (i) of Proposition 4 can then be interpreted as making a case for private schooling and the vouchers we study. However, we have some reservations concerning this efficiency result. First, we are sympathetic to th e view of many that access to a quality education is a right and serves as a means to limit historical inequities. Second, longer-run externalities from education not considered by private schools, like reduced crime, may be present.For these reasons, we explore the consequences of vouchers on all types instead of just providing aggregate measures. A somewhat distinct concern arises because exact equilibrium exists only in special cases. The interpretationof the efficiency results in the approximateequilibriumwe study is discussed in subsection D, below. C. Vouchers We examine tax-financedcash awardsto all those attending private school. 22 No role for vouchers is present in the tuition-free public t sector. Refo-rmulate he model by everywhere adding the amount of the voucher, v, to yt for households that choose a private school.The government's budget constraintis: tyf (b, y) db dy (7) s This positive externality will tend to cause too little entry. We believe that too many or too few private schools are possible, but we have not proved this. vf(b,y)dbdy fJ – PROPOSITION 4: (i) The allocation in a fuilly private equilibrium is (Pareto) efficient given the number of schools; the equilibrium number of schools is not, however, generally MARCH 1998 . U AlU UA2U . +sr[s N U . +r , / B 7(k 22 Our model permits households to retain as income any excess of the voucher amount over the tuition paid to he private school of choice, thereby avoiding considerable complication. VOL. 88 NO. 1 45 EPPLE AND ROMANO:PRIVATE-PUBLIC SCHOOLS COMPETITION where N and k denote, respectively, the costminimizing number and size of schools in the public sector that satisfy demandfor public education. Vouchers lower the real price of private education and increase the demand for it. We examine the effects of vouchers in our computationalmodel. the results will provide at least suggestive evidence about the impact of policy interventions. However, scant empirical evidence exists on some important parameters of the odel. D. Existence of Equilibriumand an ApproximateEquilibrium We require specifications for the density of income and ability, the utility and achievement functions, and the cost function for education. As we discuss in the Appendix, exact equilibrium generally fails to exist due to the integer number of private schools. We examine an approximate equilibrium in our computational analysis. Our â€Å"epsilon-competitive equilibrium' requires that no (utility-taking) private school, incumbentor entrant,could increase profitsby more than s. Let 7rax and .. min denote the maximum and minimum profits arned by incumbent schools [which maximize profits overp(b, y) and a (b, y) locally], and replace Zfl in the definitionof equilibrium with MAX [irmax, Xrmax -lrmin – rminl c Here lrmax equals the maximum potential profits to an entrant,and the maximum of the second two terms in the brackets equals the largest feasible profit increase by an incumbent s chool. The revised definition of equilibrium continues to require UM, PSP, MC, and local profit maximization by incumbent private schools [i. e. , (6a) – (6c)]. Last, the number of private schools is the minimum number satisfying these requirements.The epsilon equilibriumretains all the positive propertiesof an exact equilibriumexcept that private schools could gain s in profits via global adjustments. The allocation of students in a fully private equilibriumwould then continue to satisfy efficiency condition (i). M III. Computational quilibrium odeland E R Illustrative esults We develop a computationalmodel to illustrate our results, to examine vouchers, and to explore issues for which comparative-static analysis may yield ambiguous results. We calibrate it to existing empirical evidence so that A. Specification and CalibrationWe assume that [n (b) is distributedbivar- iate normal with mean LbJand covariance matrix 2 01b P UbUy P bUy aY J To calibratethe distributionof incom e, we use mean ($36,250) and median ($28,906) income for households from U. S. census datafor 1989. With units of income in thousands of dollars, these imply that ,uy = 3. 36 and ay = 0. 68. We adopt specification (2) for the combined utility-achievement function. To calibrate the ability distribution we presume that educational achievement determines futureearnings and that the benchmarkeconomy is in a steady state. First, define normed achievement, aN, s our achievement function raised to the power 1/3 and multiplied by a constant, aN Y Ka â€Å"‘ = KO l'b. 23 Then, a studentwith ability b attending a school with a peer quality of 0 is presumedto have futureannualearnings (E) given by ln E = ln aN= In K + (y/o/)ln 0 + ln b. This normalization is such that a percentage change in ability leads to the same percentage change in dollars earned. Henderson et al. ( 1978) reportthe change in achievement percentile that results from moving students from classes stratified by ability to mixed 23 The constant of proportionality, K, is arbitrary. A onvenient scaling is to set K = E[ b -‘. This scaling has the propertythat, if all students in the populationwere to attend the same school (i. e. , 0 = E[b]), then normed achievement would equal ability (i. e. , aN = b). 46 THE AMERICANECONOMICREVIEW classes. An elasticity of achievement with respect to peer ability that is 30 percent as large as the elasticity with respect to own ability is representative of the results they report. We adopt the somewhat conservativevalue of y/l 0. 2. To complete the calibration of the distribution of ability, we then assume that the observed household-income distributionis the ncome distribution that emerges in a steadystate equilibrium in our benchmark model. 24 This yields Ilb = 2. 42 and b = 0. 61. Thus, mean and median ability are 13. 6 and 11. 3, respectively, and the standard deviation of ability is 9. 1. 25 GarySolon (1992) and David J. Zimmerman (1992) provide evidence on the correlationbea tween father's income and son's incomrre,nd they both find that the best point estimate of this correlationis approximrately. 4. Intergen0 erationalcorrelationin income arises from two sources:correlationbetween householdincome nd student ability and, for given ability, correlation between income and quality of school attended. Hence, SBI suggests that the intergenerationalcorrelationin incomes is an upper bound on the correlationbetween parent's income and child's ability. For purposes of sensitivity analysis, we then assume that p E [0, 0. 4]. For our benchmarkcase, we set p = 0, More precisely, we let the distribution of ability be lognormal, and we approximateby assuming that this generates a lognormal distributionof earnings. We set the first two moments of the distribution of earnings equal to the irst two moments of the distribution of income. That is, a we choose 11h nd cb such that our benchmarkequilibrium has E[aN] = E[y]lm and Var[aN] = Var[y]/m2. T he constantm is the ratio of employed workersper household to the number of students per household (m = 2. 6 in 1990). The distribution of earnings will not be exactly lognormal because of the discrete difference in schools attended, even though the distribution of ability is presumed to be lognormal. If every student attended public school in the benchmarkmodel, and hence faced the same 0, earnings would be exactly lognormal.The approximation is a good one because 90 percent of the students do attend public schools as we will see. 25 Ability can be related to IQ. Using IQ – X(100, 256), one obtains In b = -1. 38 + 0. 038(IQ). In our novoucher steady state, this implies that a workerwith an IQ of 100 has expected income of $22,074, and a 10-point increase in his IQ increases expected income to $32,510. See the discussion in what follows relatingto Figure 6 and the calculation of expected steady-state income conditional on ability. 24 MARCH 1998 which is particularly onvenient for our steadyc state calibrationof the model.This completes the calibrationof f(b, y). We now complete the calibration of preferences. The Cobb-Douglas specification implies unitary price and income elasticities for school quality, 0. Given the absence of empirical evidence on the demand for quality, these are plausible focal values and are consistent with estimates of demand for school expenditure (see e. g. , Theodore Bergstrom et al. , 1982). This function also implies thatthe marginal rate of substitutionbetween school quality and the numeraire is invariant to own ability. Empirical evidence is mixed about whether an improvementin peer group is more eneficial to high- or low-ability students. Hence, our model's assumption that the effect of peer group is not biased toward either highor low-ability types seems an appropriate choice for a baseline model. If school quality could be purchasedat a constant price per unit of quality, each household's expenditure on education relativ e to total expenditureon other goods would be y/( 1 + -y). The existing share of aggregate disposable personal income in the United States that is spent on education is approximately 0. 056. Hence, we set y = 0. 06. Using y/P = 0. 2 from above, the calibrated tility-achievement function is then U = (Yt – P)0006b0. 30. We chose a cost function that is quadratic in the percentage of students (or households) a school serves: F + V(k) = 12 + 1,300k + 13,333k2, with parameters set as follows. Expenditure per student in public schools in 1988 was $4,222 (Statistical Abstract, 1991 p. 434) and there was 1/2studentper household (Statistical Abstract, 1992 pp. 46, 139). We specified our benchmark case to have four private schools and chose parametervalues such that average cost in equilibriumwas approximately$4,200 per pupil. 26 Experimentation indicated that 6 We have presented the cost function in terms of the percentage of students served or, equivalently, the per- VOL. 88 NO. I EP PLE AND ROMANO:PRIVATE-PUBLIC SCHOOLS COMPETITION equilibriumpropertiesare not very sensitive to the benchmark number of schools, but rather are sensitive to the minimum of the average cost of schooling. We set e = 4. 2. This is the minimum value sufficient to assure existence of epsilon equilibrium for voucher values varying from zero to $4,200 per student. 27 B. Results For our benchmark equilibrium with no voucher, the public sector has 90 percent of the student population, and the four private chools combined serve the remainder. The actual U. S. percentage of students enrolled in public schools during this period equaled 88 percent. Increasing p from 0 to 0. 4 reduces public-sector attendance to 88 percent. Effects on other variables of so changing p are also small, and the results that follow are for p = 0. centage of households served, k. In terms of k, average cost reaches a minimum at $2,100, with k* = 0. 03; $2,100 can then be interpretedas the average cost per household. There are twice as many households as students in the United States. Letting s denote the numberof studentsand ubstituting s = k/2, one sees that the minimum of the average cost per student is $4,200. In our presentation,we focus on per-student measures of tuition and costs; the related per-household measures are simply half those of the per-studentvalues. 27 This value is about 7 percent of the cost of a school operating at a scale that minimizes cost per student. Relative to fixed cost, ? is approximately 35 percent. Of course, a minimal E, however measured, is desirable. We have studied how the minimum e varies as we vary efficient school scale, k*, while holding average cost constant.We find that the requisite e to support equilibrium varies approximatelyproportionatelywith k* if fixed cost is varied proportionately with k*. This suggests, as we would expect, that e can be made as small as desired if k * is made sufficiently small. We have also investigated increasing fixed cost while holding k* and minimum average cost constant. This tends to reduce the ratio of e to fixed cost but increases the absolute magnitude of e required to sustain equilibrium. Our investigation reveals that substantive findings from the computational model re not sensitive to the choice of k* or the relative magnitude of fixed to variable cost. Rather, the key aspect of costs is the value of average cost at the minimum, and as discussed in the text, this value is based on observed school costs. The problem with pursuinga calibrationthat further lowers e is that it leads to a computationally unmanageable number of schools for large vouchers. 47 Othercomputationalresults are presentedin Figures 1-6. The upperpanel of Figure 1 presents the boundary loci and admission sets in type space, in addition to the equilibrium O's nd k's. Here and in some other figures, both absolute and percentile ability scales are provided for perspective. The lower panel displays the allocation for a vouch er of $1,800. The linear boundary loci derive from the Cobb-Douglas specification. For results we present, intersections of boundaryloci, if any, occur very near the bounds of the support of type space. S

Analyse How Moliere Uses Comedy as a Dramatic Technique in Le Tartuffe

Set in the 17th century, Moliere’s Drama, Le Tartuffe is a satirical representation of religious hypocrisy. Its comedy drives the play in a direction where the audience can not only be entertained but understand the morals which are portrayed. It is important to realise the historical context that influenced Moliere’s work of Le Tartuffe in order to understand the construction of the characters and comedy portrayed. Commedia dell’arte were a group of traveling players in Italy who specialised in improvised theatre, creating stock characters for every performance for the audience to identify with and understand their representation in a comic way. Some of these features have been known to have inspired Moliere’s construction of the plot and characters such as Clever talking Dorine shedding light on the truth. In that way, Dorine almost acts as a comedic dramatic tool to highlight the truths and themes of the play. This is particularly evident in her dialogue towards Madame Pernelle, ‘Il passe pour un saint dans votre fantaisie:/Tout son fait, croyez-moi, n’est rein qu’hypocrisie’(Moliere: 1. 1. 69) In supporting this idea, Peter Hampshire Nurse writes that Dorine has ‘brilliant wit with which she ridicules hypocrisy’ (1991:85). Although the majority of modern audience’s would find the witty servant humorous, Paula Alekson noted that ‘Moliere became a master of â€Å"Le ridicule†, so much so that in the process of making the audiences laugh, he made a multitude of serious enemies’(2007:ll 15-16). Away from the controversy that the themes created, Moliere generates much more of the comedy in terms of language, structure and pace of the play. For example in the exposition, when Madame Pernelle talks to the rest of the characters, we are able to see the desire of power towards the daughters as they try to speak by saying, ‘Mais†¦. Je crois†¦mais ma mere’ (Moliere:1. 1)but are cut off every time. Furthermore, repetition is used when Orgon says, ‘Et Tartuffe? / Le pauvre home! (Moliere:1. 4) This conveys Orgons constant obsessive nature over Tartuffe which provokes laughter. Of course when being performed the proxemics and movement of the character along with the dialogue would emphasise the comedy and complete farce that Moliere had stylized the play with. Overall, we are able to conclude that Moliere uses a variety of different techniques, and themes to make the comedy work for the play. We realise that it is not just a form of entertainment but to aid the audience in following the events in the play; to understand the central themes. Andrew Calder noted that Moliere does this in both his plays, Le Tartuffe (1664) and Don Jaun (1665). Calder states that they go ‘beyond the comic stage, and both reflect a lively interest in some of the most topical, moral and theological issues of the time. ’ (1973:153). [Wordcount:457] Bibliography Moliere, 2006. Le Tartuffe. Paris: Larousse. Alekson, Paula. 2007. Dramatic and Theatrical Style a la Moliere: Le ridicule, le naturel, and â€Å"The comic war†. [online] Available at: http://www. mccarter. org/Education/tartuffe/html/4. html Calder, Andrew. 1973. Moliere: The Theory and Practice of Comedy. London:Athlone Nurse, Peter Hampshire,1991. Moliere and The Comic Spirit. Geneve:Libraire Droz

Accounting ASC Research Paper Example | Topics and Well Written Essays - 750 words

Accounting ASC - Research Paper Example An example of these guidelines are those provided by Accounting Standards Codification (ASC) that has within it two methods to recognize revenue for online retailers. One of these methods is the gross method and the other is the net method. Two online retailers that have been used in the examination of these two methods are Amazon and Overstock. ASC guidelines The ASC guidelines recognize two basic accounting methods in the case where one is recognizing revenues. These are the gross method and the net method. The gross method seeks to recognize the total amount of sales that have been made from which any discounts that occur within the time frame opened for discounts are then recorded. These discounts may be accrued in periods. This is where they have occurred in periods that are greater than two accounting periods and where the likely period of payment is not certain. The net method on the other hand records revenue in terms of the net sales that have been made on the product. In th e case where later on the customer decides not to take advantage of any discounts that have been offered then this is recorded as income. Gross method of accounting is one that considers the discounts that may be taken and majorly relies on how good a client is in honoring their obligations to pay. The net method on the other hand looks at the discounts that the customer has not taken advantage of and also on how ineffective the customer may be in honoring their obligations to pay. Amazon Amazon recognizes revenue on its books based on the satisfaction of four factors. The recognition is also dependent on the source of the revenue; this is as to whether it is from direct sales or commissions earned. The four factors considered are that there should be considerable evidence that there is the intent of conducting business. The next is that the goods have been delivered or the service has been rendered. The selling price also has to be determinable and fixed. Finally that the collectio n of the amount is to a certain extent assured. In cases where the price is not easy to determine and Amazon is the primary source of the goods then the net revenue is charged. Subscription fees are recognized as revenues over the life of the subscription. In cases where gift cards have been purchased, they are recognized as revenues when they are used by the customer or when they expire. Amazon is a company that utilizes the net method of revenue recognition. This is evident from the fact that the company recognizes the total revenue that is estimated to stem from any of the transactions that they make netting any promotional discounts that the products may have. This also nets the rebates that the products may attract and the allowance for any costs that may be involved in returning the goods. The recognition of this revenue is also limited to the point where the risk of loss and the title of any product sold have been transferred to the client. Overstock Overstock on the other ha nd has different revenue recognition procedures. They have a customer loyalty program whose revenue is allocated ratably over the period of ownership of the membership card. The revenue from rewards intended for those who are members are recognized when they take advantage of these rewards, when the rewards expires which is usually ninety days after the expiry of membership and when there is a breakage (when the redemption by the customer of rewards is highly unlikely). There have not been any instances of breakage. The revenues from gift cards are also recognized when they are redeemed or when redemption is highly unlikely from experience. It can be seen

Waste Management Reseach Paper Research Example | Topics and Well Written Essays - 750 words - 1

Waste Management Reseach - Research Paper Example Sampling is concerned with selecting a section of the population (sample) to carry out research, in order to find out certain characteristic of a population. The objective of carrying out the sampling exercise will be to determine if there is any connection between operating street sweepers and contraction of chronic diseases. Random sampling method will be used. The sample population will consist of one hundred street sweeper operators and the same number of city staff who work in the office. Confidentiality of the informants will be paramount and no one will be required to give their names or any other personal information. They will have to give their consent before the experiment begins. The questionnaires will be administered to the two groups separately, together with focus group discussions. This method will be used because it is cheap and not time consuming. A set of questions will be administered to the target audience. The type of questions will include the number of years that they have been doing the street sweeper operator job, their medical history and other socio-demographic factors. The two groups of respondents will be required to fill in the questionnaires. The medical history will look at respiratory diseases such as bronchitis and asthma. End results will be presented in the form of graphs for analysis. If from the medical history, the street operators are proved to have acquired new infections, then, more studies will need to be conducted into the issue. The work environment of the street sweepers will therefore, be a hazard, requiring to be controlled or eliminated (Ericson, 2005). 2) What is the pel of the substances that you might detect? Permissible exposure limits are enforced to protect workers from the negative effects of being exposed to substances that are a hazard to their health. They are divided into two according to the United States Environmental Protection Agency; PM 10, basically are particulates with a diameter of less than ten microns in diameter. The other is PM 2.5, which are particulates with a diameter of less than 2.5 microns. Particulates with a diameter of less diameter are inhaled and easily absorbed into the cells of the body and consequently to the bloodstream. Consistent exposure to the particles will lead to contraction of respiratory diseases. The waste removed by the street sweeps is mainly composed of sulphates and nitrates from wearing out of roads and rubber form vehicle tires and gasoline combustion. Dust is also a crucial component, composed mainly of silica and metal. The following permissible exposure limits are established by the Occupational Safety and Health Administration (OSHA). Sand has a permissible exposure limit of is 0.1mg/m3 , whose overexposure can lead to pulmonary diseases such as silicosis. The pel of dust, on the other hand is 15mg/m3 ,can also damage the respiratory system. 3) What are your recommendations? Occupational health and safety should be available to th e operators, which should among others include regular medical examination. Through these processes, infections will be able to be detected earlier on and treated. Other occupational health steps to reduce infections in the work place will include provision of protective gears such as masks (Sullivan, 2010); through such a process, infections will

THE PHYSICS OF SPORTS BIOMECHANICS AND ITS SCIENTIFIC FOUNDATION IN Essay

THE PHYSICS OF SPORTS BIOMECHANICS AND ITS SCIENTIFIC FOUNDATION IN THE PHYSICAL EDUCATION CURRICULLUM - Essay Example On the other hand, the Oxford Dictionary (2005) defines curriculum as the "subjects included in a course of study.† This purports the idea that every discipline needs a defined means of in depth study and, therefore, physical education curriculum is essential as a right approach to sports program. A methodical, scientific study approach will help in removing the anomalies like injuries and other mishaps. The right education leads to establishing good health and the right sport programs for students will be instrumental for future generations as the core for improved health and fitness. Mechanics is a branch of physics that relates to the description of motion and how forces create motion, as well as other physical laws, which are essential for movements. Within mechanics are two sub-fields of studies: statics, which is the study of systems that are in a state of constant motion either at rest or at motion; and dynamics, which is the study of systems in motion in which acceleration is present, which may involve kinematics. In addition, correlation between physics and sport biomechanics is a concept of work through mechanical energy for the creation of a motion. Physics, through physical education, takes part in the educational system as a planned, sequential K-12 curriculum that provides cognitive content and learning experiences in a variety of activity areas. These include basic movement skills; physical fitness; rhythm and dance; games; team, dual, and individual sports; tumbling and gymnastics. Besides a variety of planned physical activities, each student need s to be trained with optimum physical, mental, emotional, and social development and should promote activities and sports that all students not only enjoy but can also pursue throughout their lives (Stilwell, 2005). Biomechanics takes part in kinesiology for a precise description and a qualitative analysis of human movement, as well as the study of the cases of human movement, which is relevant

The couses of increasing the crime in the UK (just in the UK) Essay

The couses of increasing the crime in the UK (just in the UK) - Essay Example It differs from simply citing poverty or racism as the cause of crime because it includes almost all social components including the family, social institutions such as school, the community, peer groups and home life. The concept of being "socially excluded" can also take into account economic and political exclusion, such as unemployment and immigration status, as well as lack of access to medical care, housing, policing and security. (Young, J, 'Crime and Social Exclusion'). The effect of social exclusion on crime is evident. Richard Garside (2008) reports in the Guardian that there were no homicides in 2007 in more prosperous areas of London, whereas other more impoverished areas accounted for 46 alone. The Londoners who are socially included are safer, whereas "those living in the capital's poorer neighbourhood's appear to be at much greater risk of homicide than those living in its leafier, richer suburbs." To look at the causes of crime this way makes it a social problem rather than an individual problem; in other words, it is viewed as a symptom of the society we live in rather than the situation of an isolated individual. But those who research crime in the U.K. differ in how they interpret the cause of social exclusion. Some assert that people are self-excluded; that is, the fault lies within themselves and their lack of motivation can be traced to their dependency on the welfare state. Under this scenario, even if there were jobs available, they wouldn't take them. Another theory is that the individual doesn't lose the motivation to work but doesn't have the capacity to look for work due to lack of positive role models. Then there's the third theory that may best explain the increase in crime: that economic decline over the last few decades has been so extreme and jarring that it thrust many in the category of social exclusion. It used to be that one could count on a lifetime employment with a good company and a sense of security. Now, due to downsizing, outsourcing and widespread unemployment, work is much more temporary and contractual. This adds a great deal of insecurity and creates a larger underclass of the stigmatized unemployed who are often paraded in the media as drug dealing criminals separate from those in the "leafier, richer suburbs". That dichotomy of exclusion/inclusion combined with media amplification led to one of the most famous and effective enunciation of crime policy by any politician, former Prime Minister Tony Blair's slogan, "Tough on crime, tough on the causes of crime." (King 2008, p. 137). It ushered in the Labour Party after a string of defeats. It emulated that of the United States with its emphasis on enforcement as opposed to rehabilitation. The implication was that the government would take a two-pronged attack on crime: enforcement and prevention. The framework of social exclusion, prevention and enforcement led the Home Office department of the government to pursue sweeping solutions to a myriad of interrelated causes. When examining the problem of youth and crime, risk factors and causes include a troubled home life, including absent parents and volatility; truancy and failing at school; mental illness; drug and alcohol abuse; poor housing and homelessness; and peer group pressure. Because the government sees the causes of crime as multi-dimensional and social in nature, the solution it comes up with is similarly expansive and social. The youthful offender is like

Assistive Technology Essay Example | Topics and Well Written Essays - 1250 words

Assistive Technology - Essay Example This paper is meant to assist local school system educators and administrators of Clark County School District in assessing the best type of assistive technology that will meet the needs of the district. Apart from that, this paper will also dwell on how the technology will be sold among other factors of successfully incorporating the technology in learning institutions. As of 2011, the Clark County School District was the 5th leading school county in the U.S. It caters for the whole Clark County and Nevada along with cities such as Las Vegas, North Las Vegas, Mesquite, Henderson and Boulder City. The system also incorporates the census-designated places of Blue Diamond, Laughlin, Bunkerville, Logandale, Goodsprings, Mount Charleston, Indian Springs, Searchlight, Sandy Valley and Moapa. The district is split into seven regions, and it also operates 25 Programs and Alternative Schools (Richmond, 2012). The district has partial association with charter institutions, and, with the exemp tion of offering some transport service, does not have any association with the private schooling institutions in the county. The school district started in 1956 when the Nevada governing body ordered consolidation of each and every state school district into 17 region school districts. This amend confirmed that 14 separate school districts in the county would become elements of the fresh Clark County School District (Richmond, 2012). Owing to the lofty number of households migrating into the Las Vegas region, the school district experienced remarkable growth in learner enrollment from the 90s to the late 2007. Many bond issues were accepted by the supporters to assist the district cope with this growth and development. This led to the creation of new schools. From then, 2007, as many as 16 schooling institutions have been opened. This has led to an expected and also high demand for educators to teach the rising number of students (Richmond, 2012). Due to this, the county had to be innovative in locating educators to hire. They also have to be creative in recruiting educators from other countries or states within the United States. The statewide financial calamity, since 2008, has affected the School District of Clark County. The county has witnessed a decrease in the number of learners and is experiencing budgetary deficits. At the 2010 United States population census, there were 1,951,269 individuals living in Clark County, a raise of 41.8 percent since 2000. The ethnic makeup of the populace was: 10.5% Black, 48.0% Non-Hispanic white (60.9% White), 0.7% Alaska Native and American Indian, 8.7% Asian, 0.7% Native Hawaiian, as well as other Pacific Islander, and 5.1% from other races. The remaining 29.1%, on the other hand, were Hispanics of any race (Richmond, 2012). In 2009, the U.S. Census Bureau projected the population for Las Vegas Metropolitan Area to be at 1,902,834. The region was rated as one of the fastest growing and developing in the United States . 3.1% of the citizens in the county live with disabilities. A majority of these disabled people use wheelchairs to move around (Richmond, 2012). It is, therefore, vital for these individuals to come up with ways of incorporating the people with disabilities into their educational system in order for them also to be competitive in today’s labor market. Therefore, the type of assistive technology that this county needs is wheelchairs for their disabled citizens and

JOHN F KENNEDY Research Paper Example | Topics and Well Written Essays - 1250 words - 1

JOHN F KENNEDY - Research Paper Example In that context when John F Kennedy took over the presidency of America, through his benign and confident personality, he ushered in a spirit of positivity and reconciliation. He introduced the American masses to the innate strength of their nation and to a large extent inspired them to work for the good of their country. The good thing is that the positivity Kennedy inspired left a legacy of hope that continues to inspire the Americans even today, when Kennedy is no more. John F Kennedy’s father, Joseph Patrick Kennedy was a multi millionaire who accrued his fortunes in banking, stock markets, film industry, and ship building (Kenney 34). John F Kennedy happened to be the second of Joseph Patrick Kennedy’s nine children (Kenney 34). There is no denying the fact that Kennedy was brought up in a family well endowed with fortune and clout. On his mother’s side, Kennedy was related to John F Fitzgerald, his maternal grandfather who at one time also happened to be the mayor of Boston (Kenney 34). In the Kennedy family, competition, hard work and ambition were intensely encouraged amongst children, the traits that were to accompany Kennedy for the rest of his life. In 1941 Kennedy joined the American Navy (Kenney 21). By the time Kennedy got discharged from Navy, his brother Joe was lost to war and the onus to carry on the family ambition and aspirations fell on the shoulders of John F Kennedy (Kenney 21). Kennedy geared up to accept t his responsibility and in 1946, at the age of 29, became a congressman, the outcome of a determinedly and sincerely run campaign (Kenney 28). However, this achievement was still small to wet the ambition of Kennedy and so he decided to fight for the Senate in 1952 (Kenney 28). In 1953 John F Kennedy expanded his social and political clout by marrying Jacqueline Lee Bouvier, associated with a privileged and famous family (Kenney 29). The couple indeed

Where You Go To Achieve Your Fitness Desires Essay Example for Free

Where You Go To Achieve Your Fitness Desires Essay Situated, and being the sole tenant at the top-most floor of a 40-story building, Feat to Fit enjoys the freedom of its location. It is around a thousand square meter facility with various fitness machines in various corners of the facility. The wall is made of glass panels where men and women doing their fitness activities, unassisted or not, have the freedom to look at the clear view of the city laid out before them at the foot of the building or somewhere far so long their eye sight can reach the view. The center itself is situated in the middle of the building as there is a terrace portion on all four corners of the building. Anyone can enjoy the fee sunlight after their shower or pass a few minutes drinking iced-tea or some refreshments right after they have burned out some calories. There are adjustable gazebos (it can be closed or opened as umbrellas). There is a little bar inside offering drinks to the always thirsty Feat to Fit clients. There are 12 shower rooms, 3 each in every corner of the facility. At the entrance, there is the lobby, where drinking and reading and watching the fitness center’s wide LCD screen (approximately 60 inches wide) that’s always tuned in a sports channel. That’s where the reception lady and/or guy always busy herself or himself with the customers or some administrative tasks. From the ground floor, the Feat to Fit center can be accessed through 2 possible options of taking elevator, one arriving at the side (minor) entrance of the center and another stopping right in front of the main entrance where the reception is. At the south of the entrance (across it), there is the stairway, another option to use in order to reach or leave the center. There is a fire exit near this stair. Below, the property is mixed residential-commercial. I wonder why this was possible but it was already this mix when Feat to Fit opened in this location. It was blessing in disguise though as there are a lot of both residential tenants and office employees using the center now.

Metronidazole Retention Enema Experiment and Study

Metronidazole Retention Enema Experiment and Study 1. Introduction 1.1. Rectal dosage forms   The most common and usually most convenient route for administering conventional pharmaceutical dosage forms is orally, where the drug dissolves in the gastric and/or intestinal fluids and is absorbed to reach the site of action. Dissolution and absorption of the drug from the gastro-intestinal environment depends upon many factors e.g. the physico-chemical properties of the drug, enzymes, metabolism, pH of the fluids etc. and these are considered as major drawback when localized drug delivery in the colon is required. Colonic drug delivery system offers advantages over oral dosage forms in improving the efficacy and achieving high concentrations with minimal side-effects1. 1.1.1. Advantages and limitations of rectal dosage forms Advantages: Safe and painless form of administration. Drugs liable to degradation in the gastrointestinal tract can be administration. First pass elimination (drugs liable to degrade before reaching the site of action) of high clearance drugs is partially owing to bypassing the liver. Even larger doses can be administered. Drugs can be administered rectally in the long term care of geriatric and terminally ill patients. Administration of rectal suppositories or capsules is a simple procedure that can be under taken even by unskilled healthcare personnel and patients. Limitations: Patients acceptability and compliance is poor, especially for long term therapy. Suppositories can leak. Drug absorption from suppositories is slow in comparison to oral or intravenous administration. 1.2. Different rectal drug formulations Many formulations are developed for rectal use and these include suppositories (in the form of solid dose suspensions and emulsions), irrigations, gelatine capsules (used for non-steroidal anti-inflammatory drugs, encapsulated in a soft gelatine capsules as a reverse micellar solution for rectal application) 2, and enemas. Enemas are aqueous solutions are suspensions intended for instillation into the rectal region for evacuation of bowel and to treat microbial infections. Enemas are of two types macro enemas (100ml or more) and micro enemas ( 1.3. Anatomy of Rectum and lower colon The terminal 15- 19cm portion of the large intestine is rectum; it has a circumference of 15-35cm. The rectal pH is around 7-8. The absorptive area of rectum is less when compared to that of small bowel because the rectal surface area is 200-400cm2 compared to that 200m2 of small bowel, due to very much shorter surface area per unit length 4. Generally medications for rectal delivery are better absorbed as weakly alkaline solutions. For rapid absorption of the medication aqueous solutions are preferable rather than suppositories or suspensions. Rectal absorption takes place by active absorption and for maximum retention without any rectal urgency to vacate bowels small volume of the fluid is recommended5.The diagram with a section of colon is shown below in fig-1. 1.3.1. Physiological considerations of colon 1.3.1a. Intestinal colonic micro flora The human colonic atmosphere supports over 400 distinct species of bacterium with a population of 1011 to 1012 CFU/ml with mostly Eubacterium, Bacteriodes etc6. The enzymes produced by these bacterium has wide spectrum of action, that being hydrolytic and reductive in nature, these enzymes are actively involved in many processes, such as steroidal transformation, protein and carbohydrate fermentation, and destruction of mutagenic metabolism. Nitroreductase, azoreductases, and N-oxide and sulfoxide reductases are the most extensive reductive enzymes produced by the intestinal flora7. 1.3.1b. Colonic motility Under the normal physiological conditions the colonic motility is described as irregular alternation of inactive, non-propagative, segmental contractions and infrequent propagative contractions that can be further classified into high amplitude contractions (> 100 mmHg) and low amplitude contractions ( 1.3.1c. Ascending colonic volume The ascending colonic volume was found to be 170 ±40 ml as per the studies conducted on healthy subjects using single photon emission computed tomography11. Metronidazole Metronidazole is a nitro-imidazole bactericidal agent primarily used against obligate anaerobic bacteria including Bacteroides, Clostridium spp., and certain protozoal parasites like Trichomonas vaginalis, Entamoeba histolytica, Giardia lamblia, Blastocysistis hominis, Balantidium coli and also some of the facultative anaerobes Gardnerella vaginalis and Helicobacter pylori16. Gram negative anaerobes like bacteroides and fusobacterium species and the gram positive anaerobes like Peptosteptococci and clostridium species typically test sensitive to metronidazole. It is particularly used against Helicobacter pylori associated to duodenal ulcers and gastritis. Metronidazole is also used against anaerobic bowel flora for the prophylaxis and for the treatment of Crohns disease where patients might develop complications of infections in bowel12. Metronidazole supports the overgrowth of aerobic microbial flora of the large intestine by reducing the number of anaerobic micro-organisms with acceptable profile of adverse effects13. 1.4.1. Anti microbial action of Metronidazole Metronidazole as anti microbial agent was first introduced in 1959 for the treatment of Trichomonas vaginalis infections, and used subsequently for invasive giardiasis and amebiasis. Metronidazole is highly effective and show rapid onset of action against anaerobic infections. Antimicrobial action of Metronidazole is mainly due to the toxic intermediates which are produced during the reduction of the compound14. Interaction of these intermediates with deoxyribonucleic acid in protozoan inhibits nucleic acid synthesis and there by exerts antimicrobial effects15. Mechanism of action of Metronidazole is shown in the fig-2. 1.4.2. Physico-chemical properties Chemically metronidazole is 2-methyl-5-nitroimidazole-1-ethanol or 1-(2-hydroxyethyl)-2-methyl-5-nitroimidazole. Its formula is C4H9N3O and its chemical formula is in the fig-3. Metronidazole is white to pale yellow coloured, odourless, crystalline powder. It is sparingly soluble in water, alcohol and slightly soluble in ether16.It is generally stable in aqueous solutions of pH 2.0-7.017. 1.4.3. Metabolism of Metronidazole Metronidazole is metabolised in the liver into two metabolites. These metabolites include 2-hydroxy-methyl-5-nitroimdazole-1-acetic acid (HM) and 2-methyl-1-2-nitroimidazole-1-acetic acid (MAA). Hydroxy metronidazole is pharmacologically active with antimicrobial action and its potency is 30% to that of metronidazole and the acetic acid metabolite of metronidazole is pharmacologically inactive but its activity is noticed in patients with renal dysfunction, small amount of metronidazole is oxidised to acetamide18. The metabolization pathway and chemical formulas can be seen in the figure 419. Study objective Metronidazole is commercially available in the form Tablets, Suppositories, Gels, and suspensions20. But metronidazole in the form of enema is not available commercially. Olumide F et al. 1976, described metronidazole in the form of enema (2gm. of metronidazole in 200ml of normal saline) for management of severe intestinal amoebiasis21. No extensive pharmaceutical data about the formulation and stability of the metronidazole enema is available at this moment. Hence, the development of a metronidazole enema was undertaken. The present objective of the study is to formulate Metronidazole retention enema in a suitable aqueous media using carbopol and tragacanth as suspending and viscosifying agents. Chemical stability of the formulated enema is analysed with an analytical method: high performance liquid chromatography (HPLC) and viscosity of the formulation is checked by Brook field viscometer. Aim To formulate a metronidazole retention enema and analyze physico-chemically. 2.0. Materials and Method 2.1. Chemicals Metronidazole (98.9% pure) used is a gift sample from Thrope Laboratories (India) Ltd, Mumbai. 2-methyl-5-nitro-imidazole is used as a standard impurity. Cardopol (35% w/v), tragacanth, methyl paraben, propyl paraben, tris buffer were purchased from Aldrich. The methanol and acetonitrile used were of high performance liquid chromatography (HPLC) grade along with distilled water; other materials namely potassium hydrogen phthalate (KHP), sodium hydroxide (NaOH), sodium chloride (NaCl), potassium di-hydrogen phosphate (KH2PO4), acetic acid (CH3C OOH), sodium acetate (CH3COONa), sodium citrate (Na3C6H5O7) and 0.1M hydrochloric acid (HCl) were of analytical quality. 2.2. Instrumentation High Performance Liquid Chromatography apparatus and conditions The liquid chromatography used was a Varian Prostar HPLC system (Model 410), equipped with an auto sampler serial mode system with a 20 µl loop. Detection is accomplished with a UV-Visible detector. Integration and the system parameters were controlled by Galaxy software running on a PC. Viscometer The viscometer used was Brook field viscometer (Model LVDV II + PRO); displays temperature (C or F), viscosity, % scales, shear rate, shear stress, speed, % torque, and spindle. Technical specifications include 0.01 to 200/rpm, viscosity range of 1 6Million cP, with 4 supplied spindles. 2.3. Preparation of buffer solutions22, 23 2.3.1. Preparation of Phthalate buffer Phthalate buffer was prepared by dissolving 20.42g of potassium hydrogen phthalate in 1000ml of water (0.1M). The pH was adjusted with 0.1M hydrochloric acid, 0.1M sodium hydroxide. Preparation of different pH ranges of phthalate buffer is shown in the table-1: 2.3.4. Preparation of tris buffer Tris buffer was prepared by dissolving 12.11g of tris (hydroxymethyl aminomethane) in 1000ml of water (0.1M). The pH of the buffer was adjusted with 0.1M hydrochloric acid. Preparation of different ph ranges of tris buffer is shown in the table-4. 2.4. Pre-formulation studies 2.4.1. Pre-formulation solubility studies The main problem associated with developing any of the solution formulation of a compound is its aqueous solubility. Metronidazole is poorly aqueous soluble drug24. For enhancing the poorly aqueous solubility of drug there are several alternatives and these include pH manipulation, co-solvency, surfactants, chelating agents and emulsion formation25. In the present experiment the solubility of metronidazole, 2-methyl-5-nitro-imidazole in water, buffered solutions of phosphate, acetate and tris in various pH ranges were determined by adding a weighed amount of drug to the solvent by stirring with a glass rod at 20 ±2oC. Excess amount of solvent was added until the drug completely dissolved in that solvent. 2.5. Stability Indicating HPLC studies The stability studies are particularly demonstrated to analyse the quality, concentration and purity of the pharmaceutical dosage form. For demonstrating stability of pharmaceutical dosage forms HPLC is prominently used. Szepesi et al.26 described some special stability-indicating requirements for HPLC and these include: 2.5.1. Stability- indicating assay The peaks of the drug substance and its decomposition product should not elute at same time; any decrease in the active drug concentration should be detected by the method. Stability-indicating purity: The resolutions between the active component peak and the adjacent peak should be higher to identify any decomposition of the active component similar in its structure formed during different storage conditions. 2.5.3. The main impurity peak(s) should be separated from degraded product peak(s) of different chemical structure, so that evaluation of purity and assay are carried out together. 2.5.4. The peaks of the degraded products or secondary degraded products formed by the decomposition of by-product can also be separated from other peaks. 2.6. Stability-indicating purity: Pre-formulation stability studies were conducted to determine the stability of metronidazole in water and various buffered pH ranges using reverse phase high performance liquid chromatography (HPLC). All the solutions were stored at room temperature 20 ±2oC for approximately 20 days in glass beakers and then analysed for stability. Results and Discussion Solubility study of Metronidazole The aqueous solubility and pH solubility profiles for Metronidazole and 2-methyl-5-nitro-imidazole are shown in Table-7, 8, 9. Overall solubility of Metronidazole and 2-methyl-5-nitro-imidazole is determined at all pH values. Both Metronidazole and 2-methyl-5-nitro-imidazole exhibited high solubility at a pH range à ¢Ã¢â‚¬ °Ã‚ ¥4. For example, at room temperature the aqueous solubility of Metronidazole was 100mg/50ml, respectively. Metronidazole, being a weak base, appears to dissolve maximally at a pH à ¢Ã¢â‚¬ °Ã‚ ¥ 4.0. High performance liquid chromatography method development The new method developed in this present study was very closely related to that of British Pharmacopoeia. British pharmacopoeia specifies reverse phase chromatography carried out using stainless steel column (20cmÃÆ'-4.6 mm) packed with octadecylsilyl silica gel of particle size 10 µm (spherisorb ODS), using a mixture of 30 volumes of methanol and 70 volumes of 0.01M potassium di-hydrogen orthophosphate as the mobile phase with a flow rate of 1ml per minute and a detection wavelength of 315nm. To establish a new stability indicating chromatographic nature of the HPLC method, we have changed the column to 5 µm C18 (150 ÃÆ'- 4.60 mm i.d., Phenomenex) stainless steel column, packed with Sphereclone octadecylsilane (ODS) and an (eluent) mobile phase to carry out the stability analysis in the solution at ambient room temperature with a flow rate of 1.0ml/min and at a detection wave length of 325nm. Each chromatographic run required about 10 minutes and the elution time obtained for metronidazole and the standard impurity were different for different mobile phases. For methanol: KH2PO4 in the volume of 30:70v/v retention times of drug and the impurity was1.89min and 2.00min, for methanol: KH2PO4 in the volume of 80:20v/v retention times were very narrow, like wise all the mobile phase in different proportion showed a little retention time gap between drug and impurity. When acetonitrile and sodium citrate was used in the volumes of 10:90 v/v retention time gap of 2min was achieved. Elution of Metronidazole and 2-methyl-5-nitro-imidazole was achieved with a retention time of 3.19Min and 4.99Min respectively. Stability indicating solubility studies Metronidazole was observed to be relatively stable in water and buffer pH conditions. The results obtained in our stability indicating solubility study showed an agreement with solubility and studies conducted by Yunqi et al., 200527. Test for clarity and sedimentation Sedimentation was observed when the water (400C) solubilized metronidazole is stored for 20 days, this might be due to the super saturation of the solution during solubilization of the drug at high temperature. Rest of the solutions were free from particles and sedimentation when observed against a black and white back ground. Solubility studies of metronidazole and its standard impurity (2-methyl-5-nitro-imidazole), indicates solubility of metronidazole was more in aqueous solvents including various buffered pH systems. These solubility profiles help to understand the chemical nature (polarity) of drug and the impurity. Solubility of metronidazole was observed to be high in acetate buffer (100mg/30ml) than any other buffer solutions. Taking the solubility profiles and colonic pH (5.5-7) into consideration, acetate buffer of pH 6 was used to formulate enema 4. Formulation of enema Our aim to formulate retention enemas is based on the studies conducted by Nyman-Pantelidis et al., 1994. There study proved low viscous enemas superiority over high viscous enemas in retention and colonic spread28. 4.1. Preparation of metronidazole- tragacanth enema Metronidazole-tragacanth enema was prepared by simple titration technique using motor and pestle. Metronidazole retention enema prepared was an aqueous formulation with a viscosity of 6.00 cPas, containing metronidazole in a buffered pH. The formulation includes tragacanth as suspending and viscocifying agent. Methyl paraben as a preservative and NaOH (0.1M) was used to maintain the pH of the formulation. Metrinidazole was dissolved in buffered solution and then added to tragacanth gum, while triturating methyl paraben was added and pH of the final formulation is maintained at pH-6 using NaOH. The composition of the enema prepared in the study contains 1g of Metronidazole as shown in table 9. Preparation of metronidazole- carbopol enema For the treatment of anaerobic infection of colon we have formulated Metronidazole as enema using carbopol, a high molecular weight polymer of acrylic acid cross linked to allyl sucrose. Carbopol increases the viscosity of the enema and so help in retaining in the colon for maximum efficacy of metronidazole29. Metronidazole was dissolved in buffered solution 1.0g/300ml. This solution was added under constant stirring to carbopol. Methyl paraben was dissolved in water and under  constant stirring this mixture was added to the suspension. The pH of the final formulation is maintained at 6 by the addition of NaOH. The composition of the enema formulated is shown below in the table-10. Storage of enemas for stability and viscosity studies The formulated enemas were filled in 100 ml glass beakers and stored for 2 days at refrigerated conditions 40C, room temperature 200C and at accelerated conditions 400C and analysed for stability and viscosity. Stability studies of the formulated enemas Both the enemas were found to be stable for 3 days at various temperatures (2-100C, 25 ±20C, 40 ±20C). The chromatograms show no peak of degraded metronidazole. Chromatograms of both the enemas is shown in the fig-9, fig-10. Viscosities of the formulated enemas The viscosity measurements for both rectal enemas were performed by Brooks field viscometer, using spindle 62 revolving at 22 rpm. Both the rectal enemas were prepared with a viscosity of 6.0 cP using tragacanth and carbopol. The viscosities of both rectal enemas were then analysed after storage for 2 days at 2-100C, 20 ±20C, and 40 ±20C respectively and there results are shown in table-10. There was a little variation of viscosities in the formulated enemas after their storage at various temperatures, and this variation is seen especially in enemas stored at accelerated temperature (40 ±20C) for 3 day. Because viscosity is inversely related to temperature, as temperature increases viscosity decreases. Test for clarity and sedimentation Both the formulated enemas were clear without any particles when observed against a black and white background. When the enemas are further analysed, phase separation was observed in the enema formulated using tragacanth and stored at 2-100C, 20 ±20C, and 40 ±20C. Conclusion The solubility studies results indicate that metronidazole showed a good solubility at various pH levels (à ¢Ã¢â‚¬ °Ã‚ ¥4.0). Maximum solubility of metronidazole was shown in acetate buffer of pH 6 (100mg/30ml). The stability studies indicate that metronidazole was stable at all the pH ranges without any degradation. The Metronidazole enema formulated using tragacanth and carbopol was chemically stable with no degradation when stored for a period of 3 days at 2 ±100C, 20 ±20C, 40 ±20C respectively. And there is no remarkable effect on the viscosities and pH of the enemas when stored at these temperatures. Future work In the present study stability studies were conducted for only 3 days, the results would be more appropriate if the stability studies of the formulated enema were carried for some more days. The new methodology developed for demonstrating High Performance Liquid Chromatography indicating stability studies using acetinitrile and sodium citrate in the volumes of 10:90v/v should be validated.