This paper develops a model of a monetary economy in which individual firms are subject to idiosyncratic productivity shocks as well as general inflation. Sellers can change price only by incurring a real "menu cost." We calibrate this cost and the variance and autocorrelation of the idiosyncratic shock using a new U.S. data set of individual prices due to Klenow and Kryvtsov. The prediction of the calibrated model for the effects of high inflation on the frequency of price changes accords well with international evidence from various studies. The model is also used to conduct numerical experiments on the economy's response to various shocks. In none of the simulations we conducted did monetary shocks induce large or persistent real responses.

We analyze a dynamic stochastic general-equilibrium (DSGE) model with an externality through climate change from using fossil energy. A central result of our paper is an analytical derivation of a simple formula for the marginal externality damage of emissions. This formula, which holds under quite plausible assumptions, reveals that the damage is proportional to current GDP, with the proportion depending only on three factors: (i) discounting, (ii) the expected damage elasticity (how many percent of the output flow is lost from an extra unit of carbon in the atmosphere), and (iii) the structure of carbon depreciation in the atmosphere. Very importantly, future values of output, consumption, and the atmospheric CO2 concentration, as well as the paths of technology and population, and so on, all disappear from the formula. The optimal tax, using a standard Pigou argument, is then equal to this marginal externality. The simplicity of the formula allows the optimal tax to be easily parameterized and computed. Based on parameter estimates that rely on updated natural-science studies, we find that the optimal tax should be a bit higher than the median, or most well-known, estimates in the literature. We also show how the optimal taxes depend on the expectations and the possible resolution of the uncertainty regarding future damages. Finally, we compute the optimal and market paths for the use of energy and the corresponding climate change.

We consider an environment in which agents' skills are private information and follow arbitrary stochastic processes. We prove that it is typically Pareto optimal for an individual's marginal benefit of investing in capital to exceed his marginal cost of doing so. This wedge is consistent with a positive tax on capital income. We also prove that it is Pareto optimal for the marginal rate of substitution between any two consumption goods to equal the marginal rate of transformation. This lack of a wedge is consistent with uniform taxation of consumption goods within a period.

This paper presents a simple dynamic Mirrleesian model. There are two main goals for this paper: (i) to review some recent results and contrast the Mirrlees approach with the Ramsey framework in a dynamic setting; and (ii) to present new numerical results for a flexible two-period economy featuring aggregate shocks.