Essays in Microeconomic Theory

Scott J. Colby

The first of these three essays is a theoretical model of the household that accounts for the decisions of when and how much to purchase, as well as when and how much to consume, in a unified optimal control theory model with inventory as a state variable. It is shown that under a standard budget constraint, the household's decision reduces to recurrence intervals in which they behave identically ad infinitum. Necessary conditions are derived that can be used for simulation and econometric modeling. The second essay derives the demand functional forms that are permitted when the restrictions of exact aggregability and homogeneity of degree zero in prices are imposed. It is shown that Lau's generalization of Gorman's (1953) theory of exact aggregation implies Gorman's (1981) functional forms for income and multiplicative separability of the demographic variables and income. The third essay presents the necessary and sufficient condition to allow input demands to be specified as functions of input prices, technology, quasi-fixed inputs, and cost in place of planned/expected outputs. These all are observable when inputs are committed to production. Next we derive a flexible, exactly aggregable, economically regular econometric model of input demands. This model is consistent with any dynamic von Neumann-Morgenstern expected utility function. We combine this framework with a model of the life-cycle production, investment and savings, and consumption decisions of owner/operators who face output and output price risk, and who have opportunities to invest in a conditionally risk free asset, other risky financial assets, and farm assets. The econometric framework allows for location specific technological change and production processes, cross-equation, interspatial, and intertemporal correlation among the error terms, and structural simultaneity between inputs and outputs, input and output prices, investment in durable goods used in agriculture, consumption, savings, and wealth. The result is a consistent dynamic structural model of inputs, outputs, savings, investment, and consumption under risk.

Essays in Microeconomic Theory

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