A country consists of identical workers, where each worker earns a wage W when working and faces a probability of losing the job. If the worker loses the job, earnings drop to W = 0. Although, the worker always has some non-labor 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? [Hint: write the mathematical expression for the expected utility as a function of W, and non-labor income.]

Assume the government implements an employment insurance program. Under this programs, individuals pay a lump-sum tax when they are employed, and get benefits B while they are unemployed. The system must break even at a point in time, (ex. 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 benefit level for this program. Explain the intuition behind this result. [Hint: Express the optimal and B as functions of W and .]

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 ).

(c) What is the expected utility if there is no employment insurance program? [Hint: write the mathematical expression for the expected utility as a function of W, , k and non-labor income.]

(d) Reintroduce government unemployment insurance, which must break even. What is the optimal unemployment insurance system now (both optimal tax rate and benefit level)? How does this compare to b?