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ajaz_eco204_2009_chapter_2.3 - University of Toronto...

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University of Toronto, Department of Economics, ECO 204 2009 2010 S. Ajaz Hussain ECO 204 2009 2010 S. Ajaz Hussain (Draft) Chapter 2.3: Modeling Consumer Choice 1 Please help improve the course by sending me an e mail about typos or suggestions for improvements 0. What’s Ahead In chapters 2.1 and 2.2 we’ve seen how to model a consumer’s preferences. We start by listing the commodities she can consume. Since it’s hard to model preferences over all commodities, we choose to model a sub set of these commodities 2 . 1 Next we’d define the consumption set for the chosen commodities. For simplicity, we’re going to assume the consumption set is a convex set (see graph here). Assuming the consumer has rational preferences she can rank all bundles in the consumption set by felicity. Alternatively, she can tell us how much of (say) good 2 she’s willing to give up to have another unit of good 1 to be equally “happy” (i.e. stay on the same indifference curve) ‐‐ this yields her marginal rate of substitution (MRS). Q 2 Q 1 Q 1 0 1 commodity consumption set 2 commodities consumption set Next, either from her felicity rankings or her MRS we’ll be able to represent her preferences by a utility function. The utility function may tell us whether she perceives two commodities as imperfect substitutes, perfect substitutes, complements; alternatively, her utility function may 1 Thanks: Betty Wang. 2 For example, the sub set could be “Milk”, “Sushi and Martinis”, “Steak, Wine, Potatoes”, “ECO 204 (yuk), RSM 332, Clubbing, Marriage (yuk)” etc. ECO 204 (Draft) Chapter 2.3
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University of Toronto, Department of Economics, ECO 204 2009 2010 S. Ajaz Hussain belong to some recognizable class of utility functions such as the quasi linear or CES utility function. The point is: we know her utility function. In this chapter, we will use models of consumer preferences and budget constraint to model consumer behavior . For example: how much of each commodity will she consume? What are her demand functions for each commodity? How does demand for a commodity respond to changes in prices, income etc.? How will she react to advertising? And so on. To answer these questions, we assume that we know the consumer’s utility function. We will have to make some assumptions about the consumer’s income and commodity prices from which we will construct her budget constraint. We will assume the consumer chooses how much to consume by maximizing her utility given that her expenditure must be less than or equal to her income. As such, the consumer will be solving an inequality constrained optimization problem (if you’re rusty with optimization techniques, you should review chapter 1.1 ). The plan is as follows: we will discuss commodity prices, the consumer’s income and her budget constraint. We will then describe the consumer’s utility maximization problem (UMP) and show that under certain conditions it can be solved using the Lagrangian technique 3 .
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