Reference no: EM133380668

Case Study: A consumer has preferences represented by the following utility function:
u(c1, c2) = ln c1 + β ln c2, α ∈ (0, 1)
where c1 is period 1 consumption, c2 is period 2 consumption and β ∈ (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. During the first period, he can allocate his time between working ` units at a wage rate ω and studying h units. In the second period, the agent sells all his time on the labor market at a rate of salary ω(α1`+α2h), where h represents the time spent studying during the first period. The salary of the second period therefore depends positively on the experience acquired during the first period, `, and investment in education, h. We assume that as well experience that education positively affects second-period pay. This implies that α1 > 0 and α2 > 0.

Questions:

a) Write down this consumer's problem.
b) How much time will h* spend studying in the first period?
c) How does the wage rate, ω, influence the allocation between work and study in the first period?
d) How does the discount rate, β, influence the allocation between work and study in the first period?
e) How does the return on experience, α1, influence the allocation between work and study in the first period?
f) How does the return on education, α2, influence the allocation between work and study in the first period?
g) Are there values ??of α1, α2 and β such that this consumer will decide to allocate all its time from the first period to study?
h) Are there values ??of α1, α2 and β such that this consumer will decide to allocate all its time from the first period to work?