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A case study of the supply and demand for morning kindergarten.

I. Background

I became interested in this topic when I prepared to register my older son for kindergarten in the public school. Currently, in Haverford Township, Pennsylvania, kindergarten is half day, with a morning and an afternoon session, Kindergarten registration is a telephone system's nightmare. On the appointed day, the school's phones open at 8:30 am, and the school assigns children to the morning or afternoon time slot according to the order in which it receives calls. Parents whose calls are answered first are the most likely to be assigned their preferred time slot, instead of those with the strongest preferences. Typically, more parents wish to enroll their children in morning kindergarten than there are available slots; therefore, many parents who prefer morning kindergarten lose out. Is there a more efficient way to allocate the scarce supply of morning slots?

II. Public Provision of a Private Good

Much of the allocation problem arises because education can be considered a private good that is publicly provided.(1) Each parent would be more likely to receive the type of education he truly demanded for his children if he purchased it in a private market. Although there are countless private schools in this country, the majority of children are educated in the public schools, which are funded by the taxpayers. The amount of taxes each family pays is not related to the number of children that family has enrolled in the public school system.

In this system, although the marginal cost of providing an education to a child is positive, there is no relation between that marginal cost and the price to the parent of sending a child to school. Essentially, the price paid by a family of sending an additional child to a public school is zero.

Given the nature of the public school system, each child is entitled to attend the public school. All children of kindergarten age will be placed in a class. In this sense, it is impossible to have a scarcity of slots. In the minds of the parents, however, the morning and afternoon classes are not interchangeable; more parents prefer the morning slot. Within the constraints of the public provision of education, is there a way to implement a price system to allocate the morning and afternoon time slots in a way that is superior to the current system?

III. Conventional Price System

Assume that there are 100 kindergarten children in a cohort group. There are 100 kindergarten slots, 50 in the morning, and 50 in the afternoon. Thus, supply of morning kindergarten is fixed at Q = 50. More than 50 parents want their children in the morning session, where "want" is defined to mean willing to pay some positive price. Throughout this analysis, "price" refers to the "surcharge" imposed for morning as opposed to afternoon kindergarten; it is not the price of a kindergarten education. The result is an excess demand for morning kindergarten.

The strength of parental preference is measured by their willingness to pay; those for whom the morning session is more important are willing to pay a higher price than others to obtain it. Figure 1 shows a hypothetical demand for and supply of morning kindergarten. The numbers along the quantity axis should be interpreted for the demand curve in the following manner: Q = 1 means the parent with the strongest preference for morning kindergarten, Q = 2 is the parent with the second strongest preference, etc. The slots themselves are interchangeable; the parents do not care whether they get the first or fiftieth morning slot. Q = 1-25 means the parents with the 25 strongest preferences; Q = 26-50 means the parents with the twenty-sixth through fiftieth strongest preferences, etc. The demand curve indicates that 75 parents demand morning kindergarten; i.e., 75 parents are willing to pay P[is greater than]0. Supply is fixed at Q = 50. There is excess of 25 at the current price of P = 0.

A. Case 1: Q = 1-50 are assigned to Morning Kindergarten

Refer to Figure 1. Assume that the parents with the 50 strongest preferences phone in first and are allocated the 50 morning slots under the current system of P = 0 for morning as opposed to the afternoon slot. Consumer surplus to those parents equals area ACEG.

Now, let parents be charged the equilibrium price of GH. How are parents affected? Once again, the fifty parents with the strongest preference are allocated the 50 morning slots. At P = GH, consumer surplus = area ACH, a net loss in consumer surplus of HCEG. Consumer surplus decreases because quantity remains fixed, and price increases. Thus the implementation of a traditional price system to allocate morning kindergarten results in a net decrease in consumer surplus; parents 1 to 50 are worse off.(2)

B. Case 2: Parents 26-75 are assigned to Morning Kindergarten

In this case, parents 26-75 phone in first and are allocated morning kindergarten slots under the current system. Consumer surplus to those parents equals area BDF.

Under a conventional price system, equilibrium price = GH. Parents 1 to 50, the ones with the strongest preference, are allocated the 50 morning slots. Area ACH represents the consumer surplus to parents 1 to 50. Area CDE represents the "loss" to parents 51-75, who do not have the morning slots that they would have had when price was zero. Area ICEF represents the loss to parents 26 to 50, who have the same slots as they had before, but they now have to pay price equal to GH for them. Area ABIH is the gain to parents 1 to 25 who now have morning kindergarten, albeit at a positive price of GH. The sum of these losses equals the gain; there is no change. Consumer surplus under the current system is exactly equal to consumer surplus under the price system. In this case, the conventional price system adds nothing.

IV. Voluntary Exchange

A. Case 3: A Modified Market System

How does a change in the allocation system affect the supply and demand analysis? More specifically, are there gains from trade when morning kindergarten is initially allocated under the current system, and then parents are permitted to exchange slots among themselves? Figure 2 shows the resulting, modified, supply of and demand for morning kindergarten slots that are available for trade on the "open market."

Note that the demand and supply curves in Figure 2 measure a slightly different commodity from the curves in Figure 1. Figure 1 depicts a situation where parents demand morning kindergarten from the township, which has a fixed supply. Figure 2 shows the parents' supply of and demand for slots that have already been assigned by the township that are available for trade among parents.

Begin with parents 26-75 phoning in first; they are allocated the 50 morning slots that are available from the township under the current system; then allow voluntary exchange of slots. Parents 1 to 25 demand Q[is greater than]0 at a positive price, because they don't have anything at the zero price. Parents 26 to 75 demand nothing at a positive price because they have already been allocated what they demand at a zero price. This results in a "kinked" demand curve, ABIF, which is a demand for morning kindergarten slots that have already been initially allocated at a zero price.

The derivation of the supply is somewhat less straightforward. For parents 26 to 75, the BCD portion of the original demand curve of Figure 1 defines the maximum they are willing to pay for a morning slot; that price is also their reservation price for selling that slot. Parent 75 is willing to pay zero for a morning slot; P = 0 is his reservation price to sell it. Parent 50 is willing to pay P = CE for a morning slot; P = CE is his reservation slot to sell it. Supply of morning kindergarten slots that have already been allocated at a zero price and are now available for trade is depicted in Figure 2 as the upward sloping curve GIJ until Q = 50, where it becomes vertical.

The more or less conventional supply and demand curves create a market, which provides the opportunity to achieve the gains from trade. Equilibrium price equals to GH, and equilibrium quantity, that is number of previously allocated slots exchanged at that price, equals to 25. Parents 1 to 25 buy the slots from parents 51 to 75. Parents 26 to 50 do not participate in the exchange; the market price is lower than their reservation prices, and they already have been allocated the slot for a zero price, so it makes no sense for them to purchase one for a positive price.

Parents 1 to 25 are willing to pay revenue equal to area ABFG; with equilibrium price of GH, they pay area HIFG and experience a net gain equal to area ABIH, their consumer surplus. Parents 26 to 50 are unaffected. Parents 51 to 75 experience a loss in consumer surplus of area CED, because they no longer have a morning slot, but they gain revenue equal to are HIFG, for a net gain of HGI. Parents 1 to 25 are better off. Parents 51 to 75 lose consumer surplus and gain revenue greater than the loss of that consumer surplus. By voluntarily engaging in trade by selling their morning slots, parents 51-75 reveal that they consider themselves better off under the system of exchange. Parents 1-25 are better off; parents 51-75 are better off; parents 26-50 are no worse off -- the system is Pareto superior to the current system.

B. Case 4: Perfect price discrimination under a modified market system

This case begins exactly as in Case 3. The exchange takes place under different rules. Again, parents 26 to 50 do not participate. Each of parents 1 to 25 pays the highest he is willing to pay, and each of parents 51 to 75 receives his reservation price. There is no consumer surplus for parents 1 to 25; they are not worse off than they were under the initial allocation, when they had nothing. Parents 51 to 75 lose consumer surplus equal to area CED; they no longer have any morning slots, and they gain revenue equal to area ABFG, for a net gain of area ABIG. Parents 1 to 25 are no worse off; parents 51 to 75 are better off than they were under the initial allocation. This system of modified price discrimination has a result similar to that of Case 3 -- parents 1-50 are no worse off, and parents 51-75 are better off -- this system is also Pareto superior to the current system.

V. The Survey

A. Description of the Survey

A two part survey was distributed to 81 parents of kindergarten children enrolled in the 1993-94 kindergarten classes at the Lynnewood Elementary School in Haverford Township, Pennsylvania. Lynnewood has four kindergarten classes, two in the morning and two in the afternoon, with approximately 22 children in each class. 40 parents (50% of those surveyed), responded to Part I, and 26 parents (32% of those surveyed) responded to Part II.

Part I of the survey asked parents whether they had a preference for a morning or afternoon time slot for their child and whether or not their child had been assigned to their preferred slot. Then the survey asked parents if they would approve a system of paying the tonwship, either in dollars or in volunteer time to the school,(3) in order to guarantee a morning time slot. Parents who did approve a payment system were then asked to state the maximum price that they would pay the school, either in cash or in hours of volunteer time.

Part II of the survey asked parents if they would approve of and/or participate in a system of exchange among parents once the time slots had been assigned by the school under the current first come, first served system. Those that approved this exchange system were asked to state the maximum price that they would pay to another parent in order to obtain a morning slot, either in dollars or in kind payment, such as babysitting. They were also asked to state a reservation price that they would accept as payment from another parent to sell their morning slot, also in dollars or in kind payment.

I intended to use data collected from " affected" parents regarding the strength of their preferences to estimate a demand curve for morning kindergarten, which would allow me to determine the equilibrium price in the market and to measure the magnitudes of the changes in consumer surplus under different allocation schemes. The very surprising results foiled my plans. The most striking result of both parts of the survey is the parents' strong negative reaction to using any price system to allocate kindergarten time slots.

B. Results from Part I

In Part I of the survey, which provided for payment directly to the township, only 13 of the parents (approximately 33% of those who responded) were willing to pay a positive price in order to guarantee the morning time slot. Maximum prices ranged from $25 to $250, with a median of $50. Given this demand, the equilibrium price for morning kindergarten, paid to the township, appears to be zero. Fourteen of the parents (approximately 35%) were willing to volunteer time at the school in order to guarantee a morning time slot. Maximum time volunteered ranged from 2 to 10 hours per month, with a median of 4 hours. Only one of the eight parents who preferred morning but was assigned to the afternoon favored a system of payment to the township; that parent was willing to pay $250 to guarantee a morning slot.

Almost half of those who preferred morning and were in fact assigned to a morning class were in favor of a system of payment to the township and were willing to pay a positive price to guarantee that slot. It is significant to note that about 75% of the respondents preferred morning kindergarten, which confirms anecdotal observation that morning is the more popular time slot. Everyone who requests the afternoon slot gets it.

The majority of parents who replied to Part I vehemently opposed the idea of paying the township to guarantee a morning slot. The parents raised two primary objections: (1) it is not right to make additional payment to the township for what was perceived to be a taxpayer's entitlement; and (2) it is not fair, in this context, for those with money to have an advantage. One parent, who reflected the sentiments of many, summed it up this way: " ... (a system of paying is) totally counter to what a public school is supposed to be.... As proposed, I cannot appreciate the fairness of payment for preference." (Emphasis in the original.)

Part II of the survey attempted to address these objections. Under the system proposed in Part II, the township would not receive any payments from parents. Each parent would have the same chance to be assigned to the time slot of his choice, regardless of his income, and the resulting redistribution under trade would be Pareto optimal. The results of Part II were even more surprising than the results of Part I: a significantly larger percent of parents responding to Part II were opposed to using a price system to allocate morning time slots than those responding to Part I.

C. Results of Part 11

Part II of the survey provided that payment would occur only among parents without any township involvement in the exchange or in the payment. Eighteen of the 26 respondents (70%) favored allowing parents to exchange time slots among themselves, and 13 of them (50% of respondents) replied that they would participate in such a program. However, of those 13 parents who said they would participate, only I would sell his morning slot for cash, for a price of $5000. Two would "sell" their morning slot for in kind payment, one for 15 hours of babysitting a week, and the other did not provide an amount. Three would buy someone else's morning slot for cash; prices were $100, $1000, $2000. Only I would buy a morning slot with in kind payment, for 2 hours of babysitting over 2 months.

The startling result of Part II is that while only a few parents would participate in an exchange for cash or in kind payment, 15 parents (over 50% of those who replied) were willing to swap their morning slots without receiving any payment in return, and 21 (80% of those who replied) were willing to swap their afternoon slots without receiving any payment in return. Thus the majority of parents who responded were in favor of allowing an even exchange -- your time slot for mine -- but they were strongly opposed to allowing payment, either in cash or in kind, in the exchange.

Judging from the written comments, these negative sentiments about payment were stronger in Part II of the survey. In Part I, parents expressed an aversion to paying the township for something to which they felt they were already entitled (and perhaps already paying for in taxes) and to giving an advantage to those with more income. In Part II of the survey, parents expressed a sense of moral outrage that one parent could "take advantage" of another by paying him just because one parent had a greater income. Many parents stated that they could not understand how this was an economic problem.

The following comments are representative of many parents' sentiments. "I wouldn't want a good slot going to the `highest bidder'." "Charging (for a time slot) then would go against my own value system." "If parents wish to trade time slots, it should be done out of kindness only. I would never accept a `deal or bribe' nor would I offer one." "I feel that it is a sad commentary that a parent would want to be paid to help out another parent." Thus, there does not appear to be a market among parents for morning kindergarten.

These reactions are particularly surprising, because under the proposed allocation, everyone starts out with the same opportunity, and no one is made worse off through the exchange.

VI. Conclusion

Standard microeconomic theory teaches that price is the most efficient way to allocate a scarce resource. In this paper, I have shown that in the case of a fixed resource, morning kindergarten, the standard price system is not in any way superior to the first come, first served system that is currently in use in Haverford Township, Pennsylvania. I demonstrate that if those with the strongest preferences are not initially allocated morning kindergarten, then a modified price system, one that allows transfer of "ownership," first with a single price, and then with perfect price discrimination, is Pareto superior to the current system.

Despite the unqualified superior result of a system that allows transfer of ownership for a price, parents responding to a survey of preferences about kindergarten scheduling were overwhelmingly opposed to such a system. They objected strongly to "reducing everything to a price" and letting things go to "the highest bidder," despite the fact that no one is worse off under such a system. The comments of one parent who requested morning kindergarten and was assigned to the afternoon session, even after successfully pleading her case to township officials because of the unique work schedule dictated by a family business sum up the intensity of the prevailing attitude: she wrote, "pay for a time slot? what kind of society is this?"

One could speculate that these same people do not object to those with greater income owning larger houses or driving more expensive cars. The question of why people have a strong visceral objection to paying money for some commodities but not for others, what the qualitative differences might be between these types of commodities, and the implications for formulating public policy based on assumptions of a "rational" economic person is beyond the scope of this paper, but it is a fascinating topic for future research.

Nancy Ruth Fox(*) (*) Saint Joseph's University, Department of Economics, 5600 City Avenue, Philadelphia, PA 19131, (610) 660-1596, Internet:, Fax: (215) 473-0001. I would like to acknowledge the helpful contributions of several colleagues. Pete Zaleski, George Prendergast, Zora Pryor, and Claire Renzetti contributed significantly to the formulation of the survey. The office of the Dean of the College of Arts and Sciences at Saint Joseph's University generously funded the survey. Dori Pappas typed the survey and stuffed numerous envelopes in the most efficient manner. Comments from an anonymous referee enabled me to clarify several points in the paper. Finally, I would like to thank my brother, Kenny Fox, and my husband, Ron Krauss, each, for serving as a sounding board for many of my ideas and for contributing several of their own.


(1.) I am indebted to an anonymous referee for suggesting this approach.

(2.) I am intentionally ignoring the effect of the revenue that the township would earn if the price were positive. That is merely a distributive effect between parents and government and is not the focus of this paper.

(3). Zora Pryor suggested this alternative to me as a way of addressing the possible objection that the system favored those with more income, or, more specifically, two income families. This option allows stay at home parents to pay with their time, in the same way that working parents could pay with money.

Katz, Michael, L. and Rosen, Harvey S.
Microeconomics. Homewood, Illinois: Irwin, 1991.

Pindyck, Robert S. and Rubinfeld, Daniel L.
Microeconomics. New York: Macmillan Publishing
Company, 1989.
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Author:Fox, Nancy Ruth
Publication:American Economist
Date:Mar 22, 1996
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