Please figure out this question. Thanks.

1. Assume a country consists of identical workers. Each worker earns a wage W when working and faces a probability a 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? [Hintz you cannot get a numerical solution; instead write the mathematical expression for the expected utility as a function of W, o: and non-labour income] [1 mark] Assume the government implements an employment insurance program. Under this programs, individuals pay a lump-sum tax T when they are employed, and get benets B while they are unemployed. The system must break even at a point in time, i.e. benets 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. [Hint: again, you cannot get a numerical solution; instead express the optimal 'r and B as functions of W and 05.] [2 marks] (c) Explain the intution behind your result in (b) (1-2 sentences). [1 mark] 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