Murray Brown

Unsystematic Risk and Coalition Formation in Product Markets

A mounting system for a compressor of a refrigerator includes a floating frame rigidly secured to a compressor housing in which the compressor is resiliently mounted, the floating frame being resiliently secured to the frame of the refrigerator. The floating frame includes a pair of support rails to which the refrigerators condenser is rigidly secured as well as the compressor housing. In one embodiment the floating frame also includes a cross rail to which a first end of each of the support rails in rigidly secured. By increasing the effective mass of the compressor housing to include the condenser and floating frame the amount of vibration transmitted from the compressor to the refrigerator frame is reduced as well as the noise generated thereby.

Uniqueness of equilibrium for smooth multistage concave games

Abstract Smooth, noncooperative, multistage, concave games are formulated so that a new uniqueness condition—based on the Poincare-Hopf theorem—can be applied. The new condition is the weakest to appear in the uniqueness literature. The uniqueness subgame perfect equilibrium is obtained and examples are given.

Complements and Substitutes: Strategies, Endowments, Human Capital, and the Market

This paper disputes the claim that efficiency requires complementarity between innate endowments and human capital investment. This entails that parents invest more in highly endowed children. In an elementary supply-demand model, both substitutes as well as complements can arise. Substitution is consistent with human capital investment in less innately-endowed progeny without invoking Rawlsian rules of allocation. The model is driven by the basic assumption that all parents want their children to achieve the highest status possible. We derive optimal human capital investments in an ideal environment, one that contains no obstruction to the expression of merit. Also, we begin to show how heterogeneous innate endowments affect the marginal cost conditions that yield substitution.

Kindred Distributions: An Application to Wealth and Income Densities

We describe a simple method to obtain kindred stationary densities of random Markov processes with respect to an Ito transformation function. As applied to income and wealth densities, they are akin to one another because they share the income growth and income volatility shape parameters. The procedure first assumes a linear infinitesimal drift and a quadratic infinitesimal variance, which together with the stationary Kolmogorov forward equation gives rise to a power law income distribution. To find a kindred distribution we assume that the rate of change of wealth is a function of savings from income and the returns from accumulated wealth. Applying the Ito transformation, we then obtain an explicit wealth-income density, which turns out to be another power law density with an augmented exponential term. It shares certain shape parameters with the income density. Another objective of the paper is to learn how volatility affects the specific wealth-income prediction in Piketty-Zucman (2014).

A Note on Risk Dominance and Sequential Equilibrium

This note shows that the loss deviations in Seltens (1995) risk dominance measure are the same as the arguments of the probability of a strategy that supports a sequential equilibrium. Risk dominance is used to select among Nash equilibria, while sequential equilibrium, which is stronger than the Nash solution, can be viewed as reducing the set of equilibria. Despite their similarity, examples are given to show they can give materially different predictions. We discuss why the differences arise.