1. Workers are initially unemployed and must decide how much effort to put into job search. Searching intensively enough to find work with probability e generates a utility cost c(e) = 1γe2/2. Workers who find a job receive after tax consumption utility ln(W - t). Workers who do not find a job receive unemployment insurance with associated consumption utility ln b.
(a) Write down an expression for the worker's expected utility.
(b) Find the worker's optimal job search effort e.
(c) If the government could monitor workers' search effort, then the government could require optimal search in order to receive U.I., and thus take optimal search effort as a given when choosing the benefit level b (with corresponding tax policy t = ( 1-e/e)b). If e is a fixed number, what level of b maximizes workers' expected utility?
(d) If government cannot monitor workers' search effort, then policymakers choosing b must recognize that unemployment generosity can influence search effort. The government's balanced budget constraint requires that the revenue raised from taxing the employed (e(b)t) equals the total payout to the unemployed (1 - e(b))b, so: t = ( 1-e(b)/e(b))b. Substitute this expression for t into the expression for workers' expected utility, and solve for the optimal b that maximizes workers' expected utility. [Hint: In general dEU/db =∂EU/∂b +(∂EU/∂t)(dt/db) +(∂EU/∂e)(de(b)/db) . However recall from lecture that you may ignore de(b)/db terms when answering this question, because worker optimization implies that ∂EU/∂e = 0]
(e) Make a conjecture as to whether γ would be higher or lower during are cession, and explain why you think γ might change in this way during are cession. Based on your conjecture, would you recommend more generous or less generous unemployment benefits during recessions?