Assuming a consumer has preferences represented by the following utility function: u(c1, c2) = ln c1 + ln c2, (0, 1) where c1 is consumption in period 1, c2 is consumption in period 2 and (0, 1) represents a discount rate related to this consumer's preferences for time.1 The consumer has 1 unit of time in each period. In the first period, he can allocate his time can allocate his time between working L units at a wage rate and studying H units. In the second period, the agent sells all his time in the labour market at a wage rate wage rate (1L+2H), where H represents the time spent studying in the first period. The wage in the second period thus depends positively on the experience gained during the first period, L, and the investment in education, H . It is assumed that both experience and education positively affect the wage in the second period. This implies that 1 > 0 and 2 > 0

Mathematically,

1) Write this consumer's problem

2) What time H, will he invest in study in the first period

3)How does the wage rate W, influence the allocation between work and study in the first period

4) How does the discount rate , influence the allocation between work and study in the first period

5 ) How does the return on experience, 1, influence the allocation between work and study in the first period? and study in the first period?

6) How does the return to education, 2, influence the allocation between work and study in the first period?

7) Are there values of 1, 2 and such that this consumer will decide to allocate all his time in the first period to study?

8) Are there values of 1, 2 and such that this consumer will decide to allocate all his time in the first period to work?