We consider an efficiency-wage model with the Calvo-type sticky prices and analyze the optimal monetary policy when the unemployment insurance is not perfect. With imperfect risk sharing, the strict zero-inflation policy is no longer optimal even when the steady-state equilibrium is made (conditionally) efficient. Quantitative results depend on how the idiosyncratic earnings loss due to unemployment varies over business cycles. If the idiosyncratic income loss is acyclical, the optimal policy differs very little from the zero-inflation policy. However, if it varies countercyclically, as evidence suggests, the deviation of the optimal policy from the complete price-level stabilization becomes quantitatively signifficant. Furthermore, the optimal policy in such a case involves stabilization of output to a much larger extent.