Consider an economy of identical individuals who earn a wage w while working and nothing when they don't. With probability 0 < p < 1, the individuals become unemployed and earn nothing. When unemployed, individuals get. an employment insurance (El) benefit of b from the government. When working, individuals pay a tax of t * w to finance the El program. Assume that agents have no other source of consumption in either state. Let u(c) = ln(c) denote the individual's utility from consumption c in a given state.

(a) Write the government's budget constraint for an actuarially fair El program.

(b) Write the individual's expected utility as a function of the benefit b.

Now suppose that p is a fund ion of b. Assume that dp/db, > 0 and p(0) = ¼.

(c) Explain the rational for assuming that dp/db > 0 [1-2 sentences|.