Consumer Inputs I - UNC-Wilmington Cameron School of...

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UNC-Wilmington ECN 321 Cameron School of Business Dr. Chris Dumas Dept. of Economics and Finance Consumer Choice I -- Optimization & Linear Programming We begin our study of microeconomics by building models of the economic behavior of individual consumers. This is known as the study of Consumer Choice . We build models of consumer behavior in order to forecast and predict consumer decisions such as: how much of a product to buy when price, income, quality or other parameters change; how much of one product to buy vs. another product; how much time to spend working vs. vacationing; how much income to save; how much of a retirement portfolio to allocate to stocks vs. bonds; etc. The models of Consumer Choice can be used as well to measure how much a consumer values a particular good or service (the value a consumer places on a good or service may be different from its market price). In our study of Consumer Choice, we will encounter many concepts that should be familiar to you from your Microeconomic Principles course, concepts such as Utility, Indifference Curves, Budget Constraints, Demand Curves, Consumer Surplus, etc. However, we will also discover many new concepts, and we will become acquainted with some new and very powerful analytical techniques. Wow, sounds like fun! Let's go! . . . Optimization Recall the definition of economics: "The study of the rational allocation of resources under constraints to meet objectives." We would like to build models of consumer economic behavior, so we desire to study "how consumers rationally allocate resources under constraints to meet objectives." A branch of mathematics called Optimization is well suited for formulating and solving such problems. Optimization is a collection of mathematical methods used to find the maximum (or minimum) value of an equation while ensuring that other, "side equations" still hold. If we are trying to find a maximum value, then the problem is called a Maximization Problem . Similarly, if we are trying to find a minimum value, then the problem is called a Minimization Problem . If we conceive of a consumer as someone trying to use her resources to maximize her objective while not violating any constraints that she might be operating under, then the "consumer's choice problem" translates directly into an optimization problem: the consumer's objective is the equation being maximized, and the consumer's constraints are the "side equations" that must hold (must not be violated). A key insight is that almost all economic behavior (including that of consumers) can be modeled as some type of optimization problem. Optimization Problem Format (how to write down an optimization problem) Every optimization problem is a model of something. Because an optimization problem is a model, it is composed of the three basic model elements: variables, parameters and
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operators. Optimization problems feature two operators with which you may not be familiar. The "max" operator is an operator that means: "find the maximum value of
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Consumer Inputs I - UNC-Wilmington Cameron School of...

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