Suppose a person who lives for T years and decides her demand for consumption goods C and E education maximizing her intertemporal utility (Σ₁ U₁), subject to the intertemporal budget constraint (i.e. the sum of income over their lifetime and initial wealth) and to the time restriction. There is no uncertainty nor discount rate. The per-period utility is U₁ = ln(C). Each unit of C cost p. The time constraint implies that her T years life-span can be devoted either to study E or to work T-E. Each year spent studying has a cost m -h, where m is the cost of education -tuition, travel to the place of study, etc.- This cost is reduced according to her innate ability h. For each year dedicated to work she receives an annual salary w equal to her marginal productivity, with w₁ = a + BE + ½ h; where a is a minimum wage to which we are adding the other two factors that affect productivity: education and ability. ß is the effect of education on the annual salary (called return to education") and assume that = 1. She also has an initial wealth R received from her family. 1 a) Write the intertemporal budget constraint and briefly explain what are the costs of the demand for education. b) Derive the demand for education for this person. c) At what point in her life will she demand that level of education? why? What role is edu- cation playing in this model? Which of the theories of demand for education is described by this model?
Suppose a person who lives for T years and decides her demand for consumption goods C and E education maximizing her intertemporal utility (Σ₁ U₁), subject to the intertemporal budget constraint (i.e. the sum of income over their lifetime and initial wealth) and to the time restriction. There is no uncertainty nor discount rate. The per-period utility is U₁ = ln(C). Each unit of C cost p. The time constraint implies that her T years life-span can be devoted either to study E or to work T-E. Each year spent studying has a cost m -h, where m is the cost of education -tuition, travel to the place of study, etc.- This cost is reduced according to her innate ability h. For each year dedicated to work she receives an annual salary w equal to her marginal productivity, with w₁ = a + BE + ½ h; where a is a minimum wage to which we are adding the other two factors that affect productivity: education and ability. ß is the effect of education on the annual salary (called return to education") and assume that = 1. She also has an initial wealth R received from her family. 1 a) Write the intertemporal budget constraint and briefly explain what are the costs of the demand for education. b) Derive the demand for education for this person. c) At what point in her life will she demand that level of education? why? What role is edu- cation playing in this model? Which of the theories of demand for education is described by this model?
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.12P
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Transcribed Image Text:5. Suppose a person who lives for T years and decides her demand for consumption goods C
and E education maximizing her intertemporal utility (₁U₂), subject to the intertemporal
budget constraint (i.e. the sum of income over their lifetime and initial wealth) and to the time
restriction. There is no uncertainty nor discount rate. The per-period utility is U₁ = ln(C).
Each unit of C cost p. The time constraint implies that her T years life-span can be devoted
either to study E or to work T- E. Each year spent studying has a cost m - h, where m is the
cost of education –tuition, travel to the place of study, etc.- This cost is reduced according to
her innate ability h. For each year dedicated to work she receives an annual salary w equal to
her marginal productivity, with wł = a + ßE + ¹⁄h; where a is a minimum wage to which we
are adding the other two factors that affect productivity: education and ability. ß is the effect
of education on the annual salary (called return to education") and assume that = 1. She
also has an initial wealth R received from her family.
1
a) Write the intertemporal budget constraint and briefly explain what are the costs of the
demand for education.
b) Derive the demand for education for this person.
c) At what point in her life will she demand that level of education? why? What role is edu-
cation playing in this model? Which of the theories of demand for education is described
by this model?
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