Question

Consider a consumer who lives for two periods. The consumer gets utility from consumption in each period. The consumer also gets an endowment of time in each period, L hours, which the consumer can use to work or consume as leisure . The consumer gets NO utility from leisure, however. There is no borrowing or lending.

(a)(10%) Let w1 and w2 be the wage rates per hour in periods 1 and periods 2 respect- ively. In period 1, the consumer can spend some of the time endowment of obtaining education. Call this amount of time h. This time provides neither utility nor disutility, but it reduces the time available for working. The benefit of spending time on education is that this raises the wage the consumer can earn in period 2. In particular, assume w2=h．w1 Under these assumptions, draw the intertemporal budget set of the consumer.

(b)(10%) The consumer's utility function is u(c1,c2)=lnc1+βlnc2 where c1 is the consumption of period 1, c2 that of period 2 and β>0 a constant. Write down the optimization problem this consumer faces and solve for the optimal h of this consumer.

(c)(10%) What effect does an increase in β have on the decision to invest in eduction? Interpret.

Answer 1

c)

The increase in β changes h* as

$\frac{\partial h*}{\partial \beta}=\frac{\bar L}{(1+\beta)^2}>0$

Therefore, increase in β increases the investment in education at equilibrium.