Economics Letters61(1998)391–393Government education spending and human capital formation*Shuanglin LinDepartment of Economics,University of Nebraska at Omaha,Omaha,NE68182,USAReceived29December1997;accepted5June1998AbstractGiven the interest rate,an increase in government education spending increases human capital.But in general equilibrium, more government education spending increases the interest rate,which could reduce the time people spend learning,and therefore could reduce human capital if the initial education spending is relatively high.©1998Elsevier Science S.A.All rights reserved.Keywords:Government education spending;Human capitalJEL classification:H2;J21.IntroductionRecent decades have seen growing emphasis on the importance of human capital in economic development(see,for example,Schultz,1961;Becker,1964;Lucas,1988;Glomm and Ravikumar, 1992).Raising the level of human capital is the desire of every country.But,how?In all countries governments are involved in education and human capital accumulation,such as providing public education,establishing public libraries,funding research projects,cation spending varies greatly among countries.This paper examines how government education spending and time spent learning interact to determine the level of human capital in an overlapping generations model.2.The modelThere are two production sectors,one producing a physical good which can be consumed or invested,and the other producing human capital(units of effective labor).Each individual lives for two periods,working and accumulating human capital in thefirst period,and supplying human and physical capital in the second period.Individuals are identical within and across generations.The population does not grow.Each individual is endowed with one unit of labor in thefirst period,which *Tel.:11-402-554-2815;fax:11-402-554-2853;e-mail:slin@0165-1765/98/$–see front matter©1998Elsevier Science S.A.All rights reserved.PII:S0165-1765(98)00193-1392S .Lin /Economics Letters 61(1998)391–393can be allocated toward either the production of physical goods or the production of human ernment lives forever,collecting taxes to finance its spending.Let H be the output of human capital produced in period t and to be used in period t 11.Human t 11capital production function is as follows:H 5H (h ,g ),where h is the time that each young in t 11t t t period t allocates to human capital production and g is government education spending per capita.t The human capital production is subject to constant returns to scale in the two factors.Individuals supply all human capital inelastically in the second period.Human capital lasts only for one period.The effective labor supplied per young person in period t ,L ,is:L 5(12h )1H (h ,g ).t t t t 21t 21Letting y 5Y /L ,the output–labor ratio,we have:y 5f (k )where k 5K /L is the ratio of t t t t t t t t physical capital to effective labor.Physical capital is also fully depreciated after one period’s production.Factor markets are perfectly competitive,thus the rate of return to each factor is its marginal product,i.e.11r 5f 9(k ),w 5f (k )2f 9(k )k where 11r is the rate of return on physical,t t t t t t t and w is the wage rate.t t t t t The representative agent maximizes u (c ,c )5ln(c )1r ln(c )subject to budget constraint,t t 11t t 11t where c is consumption in period t 1j of an agent born in period t ,j 50,1,r is the pure rate of t 1j time preference and t is the tax.Solving the agent’s maximization problem,with S being savings per t t person,yields:r [(12h )w 2t ]H (h ,g )w t t t t t t 11]]]]]]]]]]]]S 52,(1)t 11r (11r )(11r )t 11w 5[w ≠H (h ,g )/≠h ]/(11r ).(2)t t 11t t t t 11The government budget constraint is g 1z 5t ,where g and z are per capita government t t t t t education spending and other spending,respectively.Letting s 5S /L ,the capital market t t t 11equilibrium condition can be written ash r [(12h )w 2t ]/(11r )j 2h H (h ,g )w /[(11r )(11r )]j t t t t t t 11t 11]]]]]]]]]]]]]]]]]]]]s 55k .(3)t t 11(12h )1H (h ,g )t 11t t 3.The resultIn the steady state all the variables are time-invariant.Differentiating the steady-state versions of 1Eqs.(2)and (3),as well as H 5H (h ,g ),with z being zero,yields the following results.An increase in government education spending increases the real interest rate,tending to reduce the individuals’incentive to invest in human capital which earns income in the future.Meanwhile,an increase in education spending increases the marginal productivity of learning,tending to increase the incentive to invest in human capital.Thus,an increase in education spending will reduce the investment in human capital if the interest effect dominates the productivity effect,while it will increase the investment in human capital if the interest effect is dominated by the productivity effect.If an increase in government education spending increases the time spent on human capital formation it will increase the level of human capital unambiguously;if an increase in government education 1Detailed derivations of these results are available on request.S.Lin/Economics Letters61(1998)391–393393 spending reduces the time spent on human capital formation,it may still increase the level of human capital when the initial education spending is relatively low,but may decrease the level of human capital when the initial education spending is relatively high.ReferencesBecker,G.,1964.Human Capital.Columbia University Press for NBER.Glomm,G.,Ravikumar,B.,1992.Public versus private investment in human capital:endogenous growth and income inequality.Journal of Political Economy100(4),818–834.Lucas,R.E.,1988.On the mechanism of economic development.Journal of Monetary Economics22(1),3–42. Schultz,T.W.,1961.Investment in human capital.American Economic Review51(1),1–17.。