Assume a country consists of identical workers. Each worker earns a wage W when working and faces a probability of losing the job. If

Assume a country consists of identical workers. Each worker earns a wage W when working and faces a probability α of losing the job. If the worker loses the job, earnings drop to zero (W = 0). However, the worker always has some non-labour income of 10 (even when working). The worker's utility is U = log(C), where C is consumption. Consumption is equal to a worker's total income.

(a) What is the expected utility of each worker?

Assume the government implements an employment insurance program. Under this programs, individuals pay a lump-sum tax τ when they are employed, and get benefits B while they are unemployed. The system must break even at a point in time, i.e. benefits paid to unemployed workers must equal taxes collected from employed workers.

(b) What is the optimal employment insurance program, i.e. the program that, subject to the balanced-budget constraint, maximizes worker utility? Present both the tax rate and the benet level for this program.

(c) Explain the intution behind your result in (b) (1-2 sentences).

Now assume that each worker who loses the job gets an amount kW from a friend to help out, where k is some constant such that 0 < k < (1 − α).

(d) What is the expected utility now if there is no employment insurance program?

(c) Now, reintroduce government unemployment insurance, which once again must break even. What is the optimal unemployment insurance system now (both optimal tax rate and benefit level)?

(a) How does this compare to your answer to (b)? Explain the intuition (1-2 sentences).