With probability p (0, 1), an unemployed agent draws a wage offer w from the set W = {wL, wH} , where wH > wL > 0. The wage offer can be wH or wL with equal probability. The agent becomes employed if the wage offer is accepted. With probability 1 p, the agent does not get an offer and remains unemployed. The agent's utility is u(c), where c denotes the consumption level. Assume that u is continuously differentiable, strictly increasing, and strictly concave. Furthermore, suppose that there is a disutility from working v > 0, which is constant across all jobs. In essence, employed agent's utility is u(c) v. The government designs an unemployment policy that maximizes the agent's expected utility. If the agent accepts a job, then the wage is taxed by (w), so an employed agent consumes w (w). Notice that the tax can vary with wage. If the agent remains unemployed (either because the offer was rejected or the agent did not receive an offer), then the agent consumes unemployment benefit b 0. The policy has to satisfy the following budget constraint: p (wL) 2 + (wH) 2