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We show that for generic economies, every equilibrium admits Pareto improving monetary policy, even with multiple commodities per state. The main assumption is that asset incompleteness be intermediate, in that household heterogeneity does not exceed the number of assets present and absent. We argue this as a special case of the general framework in Turner (2003b) for proving the generic existence of Pareto improving taxes.

"An entrepreneur faces substantial non-diversifiable business risk and liquidity constraints, both of which we refer to as frictions. We show that these frictions have significant economic effects on business start-up, capital accumulation/asset sales, portfolio allocation, consumption/saving, and business exit decisions. Compared with the complete-markets benchmark, these frictions make entrepreneurs invest substantially less in the business, consume less, and allocate less to the market portfolio. The endogenous exit option provides flexibility for the entrepreneur to manage downside risk. The entrepreneur's optimal entry decision critically depends on the outside option, the start-up cost, risk aversion, and wealth. We show that the flexibility to build up financial wealth before entering into entrepreneurship is quite valuable. Finally, we provide an operational framework to calculate the private equity idiosyncratic risk premium for an entrepreneurial firm and show that this premium depends on entrepreneurial wealth, non-diversifiable risk exposure, and risk aversion"--National Bureau of Economic Research web site

This paper solves a real business cycle model with heterogeneous agents and uninsurable income risk using perturbation methods. A second order accurate characterization of agent's optimal decision rules is given, which renders the implications of aggregation for macroeconomic dynamics transparent. The role of cross-sectional holdings of capital in determining equilibrium dynamics can be directly assessed. Analysis discloses that an individual's optimal saving decisions are almost linear in their own capital stock giving rise to permanent income consumption behavior. This provides an explanation for the approximate aggregation properties of this model documented by Krusell and Smith (1998): the distribution of capital does not affect aggregate dynamics. While the variance-covariance properties of endogenous variables are almost entirely determined by first order dynamics, the second order dynamics, which capture properties of the wealth distribution, are nonetheless important for an individual's mean consumption and saving decisions and therefore the mean equilibrium capital stock. Policy evaluation exercises therefore need to take account of these higher order terms.