Microeconomics of Education
(Subsidies or Vouchers?)[1]
František Turnovec[2]
(Draft May 12, 2001)
Education is one of commodities provided and consumed through the market. While it has some features of a public good (as a form of development of human capital), it can be on the other hand treated also as a private good (investment increasing personal life-time income) and dichotomy: education (especially higher education) as a private good versus education as a public good is an important part of recent ideological discussions and practical policies in post-communist countries.
Economic theory has efficient instruments to analyze both private goods and public goods provision of education in a market economy. To analyze the problem of education as the private good problem, the behaviour of agents, education providers and education consumers, one can use standard microeconomic theory, either on the level of individual behaviour (the theory of consumers, the theory of producers), or on the level of market equilibrium (partial and general equilibrium theory).[3] Considering public good feature of education one can use the public choice and welfare theory with concepts of financing of public goods and economic theory of redistribution and fairness.[4] Such a discussion provides much more soundable arguments for political decisions than ideological disputes.
To illustrate the possibilities of theoretical analysis of the problem I will present a rather partial exercise, analysis of subsidy principle and voucher principle in state financing (or co-financing) the education.
Suppose that the government wants people to consume more of a particular good, education, let us say. One possibility might be a general subsidy to producers and consumers (free public education is of course an extreme type of subsidy). Voucher schemes represent a somewhat different technique, when the voucher is a contribution to income spendable only on the specified commodity, in our case education.
We shall illustrate our conclusions on a simple model of consumer behaviour, considering an individual utility function u(e, x), where e is the level of education consumed and x is an aggregation of all other consumer goods. Let pe be the "price of unit of education" (say, the fee and related cost) paid by the consumer, px be the price of "other goods" and s be a subsidy (a part of the price of education covered by public funds or government), M be the consumer income.
The consumer behaviour in the case of fully private education (without state subsidy) can be described by utility maximization subject to budget constraint:
maximize
1(1.1)
subject to
2(1.2)
The consumer behaviour in the case of subsidies can be described by the problem
maximize
3(2.1)
subject to
4(2.2)
The consumer behaviour in the case of vouchers (we assume value v for one voucher submitted to each individual):
maximize
5(3.1)
subject to
6(3.2)
For clarity (not to keep discussion on a too abstract level) we shall assume a particular family of utility functions
7(4)
where a, b 0.
Let us start with the problem (1.1) - (1.2) with utility (4). The first order conditions for utility maximization are
8(5.1)
9(5.2)
10(5.3)
Solving the system (5.1) - (5.3) with respect to e and x and taking prices and income as parameters, we obtain demand functions for education e and "other" consumption x as functions of prices and incomes:
11(5.4)
In the case of subsidy system we have to solve the utility maximization problem (2.1) - (2.2) with utility function (4), The first order conditions:
12(6.1)
13(6.2)
14(6.3)
Solving the system (6.1) - (6.3) with respect to e and x and taking prices, subsidy and income as parameters, we obtain demand functions for education e and "other" consumption x as functions of prices, subsidy and incomes:
15(6.4)
Finally, let us consider the voucher system and utility maximization problem (3.1) - (3.2). Using Kuhn-Tucker conditions for constrained maximization we obtain the following demand functions for education and "other" consumption as functions of prices, value of vouchers and income:
1(7.1)
and
2(7.2)
Comparing different demand functions for different regimes of financing of education gives us a possibility to evaluate these regimes. Let us illustrate such a comparison by a particular example.
Let us consider utility function with a = 1, and b = 4, i.e.
18
and prices and income
19
a) Completely private financing (no subsidies, no vouchers) of education will lead to demand (substituting to (5.4))
20
b) Subsidy s = 5 will increase demand both for education and for other goods (substituting to (6.4))
21
The total value of subsidies used by given individual will be in this case
22
c) Let us assume that the system is subsidies is substituted by voucher financing and the same value of voucher is used as was the subsidy in case b), i.e. v = 40, then the individual demand will be
23
Our numerical example indicates, that while the subsidy system in reality subsidizes not only education, but also the consumption of other goods (substitution effect), the voucher system leads (using the same funds) to higher level of consumption of education in optimal consumer behaviour.
Concluding remarks
In the paper I tried to demonstrate (by standard microeconomic reasoning) that the voucher system has some objectively justifiable advantages compared to direct subsidies. One can reasonably expect that, using the same level of government funding, the voucher system increases consumption of education compared to the direct subsidies.
This result, of course, represents only a very partial illustration of usefulness of economic analysis of the problems of economics of education. The model should be developed in a more general framework to express different type of education, equilibrium on the education market, different prices charged by different educational institutions reflecting different prestige and quality of this institutions etc. Surprisingly there is not much work done by economic theory in this area.
An economics of education as a comprehensive theory of the proper mix of private good and public good attributes of a specific commodity - education (and, also very close problems of economics of health care), is a challenge for economic theory and the message of the paper is to initiate a more intensive economic research in this field.[5]
[1] Prepared for the Wroclaw Colleage of Management and Finance Conference "Nauczanie zawodowe w szkolach wyzszych w dobie integracii europejskiej", Wroclaw, May 15-16, 2001.
[2]CharlesUniversity in Prague, Faculty of Social Sciences, Institute of Economic Studies, Department of Economics of European Integration and Economic Policy, and the WroclawCollege of Management and Finance. Contact address: Opletalova 26, 110 00 Praha 1, CzechRepublic. Tel.: (+420 2) 22 112 307, fax: (+420 2) 22 112 304, e-mail: .
[3] See e.g. Hirschleifer, J., Price Theory and Applications, Prentice Hall International, Englewood Cliffs, New Jersey, 1984.
[4] See e.g. A. M. Feldman, Welfare Economics and Social Choice Theory, Kluwer Academic Publishers, Dordrecht, 1989, J. G. Gwartney and R. Stroup, Microeconomics, Private and Public Choice, Academic Press, New York, 1982.
[5] An inspiration in this field can be found in the innovative approaches of Nobel Price Laureate Garry Becker His work (see G. Becker, Human Capital, Columbia University Press, 1964) developed a theoretical foundations for human investments decisions in education, on the job training, migration and health. Becker looks at the individual as "firm" that will invest in human resources if it is "profitable" to do so. Considering both monetary and-monetary factors, the human capital decisions of these profit-maximizing (or utility-maximizing) individuals will be based on the attractiveness (rate of return) of alternative investment opportunities.