We study unemployment insurance for workers who sequentially sample job opportunities. We focus on the optimal timing of benefits and the desirability of allowing borrowing and saving. When workers have constant absolute risk aversion, a simple policy is optimal: a constant benefit during unemployment, a constant tax during employment, and free access to a riskless asset. With constant relative risk aversion, optimal policy involves nearly constant benefits; more elaborate policies offer minuscule welfare gains. We highlight two distinct policy roles: ensuring workers have sufficient liquidity to smooth their consumption; and providing unemployment subsidies to insure against uncertain spell duration.

We study the optimal inflation tax in an economy with heterogeneous agents subject to nonlinear taxation of labor income. We find that the Friedman rule is Pareto efficient when combined with a nondecreasing labor income tax. In addition, the optimum for a utilitarian social welfare function lies on this region of the Pareto frontier. The welfare costs from inflation are bounded below by the area under the demand curve.