Lecture01-2003 - I. Basic Microeconomic Problem A. The...

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1 I. Basic Microeconomic Problem A. The Microeconomic Problem 1. The typical definition of economics is the study of the allocation of scarce resources to satisfy unlimited and competing human wants and desires. Within this basic definition, we see the elements of a mathematical programming model: a. An objective function, or a measure of human wants and desires which we will attempt to maximize. b. Constraints or limits to simply giving humans all that they could possibly want. c. Implied in the definition is also the concept that we have choice variables or instruments within our control to effect this maxmization. 2. Within the consumer’s problem we define those elements: Max U x s t x p Y ( ) . . ' a. In this problem, the objective function is the consumer’s utility, the constraint is income, and the choice variables are levels of different commodities consumed. b. How do we determine the optimum for this problem? 3. Similarly, the producer’s problem becomes Max y p w x s t y F x ' ' . . ( ) - = a. As in the consumer’s problem, we have an objective function which is profit, constraints which is the production function, and choice variables which are the levels of inputs and outputs. b. Again, how do we determine the optimum in theory and in practice. Moss, Charles B. “Applied Optimization in Agriculture.” In Handbook of Applied Optimization edited by Panos Pardolous and Mauricio G. C. Resende, pp. 957–66. New York: Oxford Press, 2002. II. Agricultural Optimization Problems A. Food and Diet Problems 1. The food and diet research can be characterized by two major focuses: a. Least cost combination of foods to meet dietary needs. Stigler’s “Cost of subsistence”. b. Least cost feed ration studies. 2. The basic application would involve minimizing the cost of a diet subject to some nutritional constraint:
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AEB 6533–Static and Dynamic Optimization Professor Charles B. Moss 2 min .. x cx s t A xb a. c is a vector of prices for each food, b. x is a vector of choice levels for each food, c. A is a matrix of nutrients provided by each food, and d. b is a vector of minimum nutritional requirements. 2. More advanced formulations of the diet problem have been developed in the guise of the household production model.
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This note was uploaded on 11/08/2011 for the course AEB 6533 taught by Professor Moss during the Fall '08 term at University of Florida.

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Lecture01-2003 - I. Basic Microeconomic Problem A. The...

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