Exact utilities under alternative monetary rules in a simple macro model with optimizing agents

We construct an optimizing-agent model of a closed economy which is simple enough that we can use it to make exact utility calculations. There is a stabilization problem because there are one-period nominal contracts for wages, or prices, or both and shocks that are unknown at the time when contracts are signed. We evaluate alternative monetary policy rules using the utility function of the representative agent. Fully optimal policy can attain the Pareto-optimal equilibrium. Fully optimal policy is contrasted with both 'naive' and 'sophisticated' simple rules that involve, respectively, complete stabilization and optimal stabilization of one variable or a combination of two variables. With wage contracts, outcomes depend crucially on whether there are also price contracts. For example, if labor supply is relatively inelastic, for productivity shocks, nominal income stabilization yields higher welfare when there are no price contracts. However, with price contracts, outcomes are independent of whether there are wage contracts, except, of course, for the nominal wage.