ajaz_eco204_2009_chapter_2.2

ajaz_eco204_2009_chapter_2.2 - 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 2.2: Modeling Consumer Preferences: Utility Functions, Marginal Rate of Substitution, Monotonic Transformations 1 Please help improve the course by sending me an e mail about typos or suggestions for improvements 0. Towards a Model of Consumer Preferences and Behavior Let’s summarize what we did in chapter 2.1. Ultimately, we want to build a model of consumer preferences and behavior. We start by listing the commodities she can consume ‐‐ this list may include 2 : { .. Sushi, Steak, Shampoo, Conditioner, Haircut, Soap, Textbooks, Chocolate, Fries, Jacket, . .} This set of commodities is very large and at this stage it would be difficult to model preferences and choices over all commodities. Thus, for tractability, we could focus on a sub set of these commodities, say, sushi and martinis. The next step is to define the consumption set ‐‐ the set of physically feasible bundles 3 . Next, to model the consumer’s preferences over the selected commodities we’d have to assume she has rational preferences. Depending on her preferences we may also recognize that she may have monotonic preferences (more is better), a plausible assumption if she perceives these commodities as “good” goods 4 . Assuming she has rational preferences, she should be able to rank all bundles (points) in the consumption set by felicity. 1 Thanks: Sunny Hyo, Talha Najam, Manqian (Luna) Zhang 2 Obviously this consumer is not bald ‐‐ although being bald is apparently popular 3 That is, she has complete and transitive preferences. 4 In contrast, if she perceives some commodities as “bad” goods, she won’t have monotonic preferences; in such cases, “less is more”. 1 ECO 204 (Draft) Chapter 2.2
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University of Toronto, Department of Economics, ECO 204 2009 2010 S. Ajaz Hussain As an example, suppose we choose two commodities ݔ and ݕ from the set of all commodities. Suppose these commodities can be consumed in any amounts (continuous numbers). Now suppose we interview four different consumers: we ask each of them to rank all bundles in their consumption set by felicity. Suppose their rankings are given in the felicity plots below. It is very important to note that each consumer is ranking bundles by felicity; they’re not telling us their levels of felicity. As such, the numerical value of the z axis (felicity) has no particular interpretation. Notice how each of these consumers has monotonic preferences (more is better) and moreover, since there are no “holes” in the felicity plots, we can tell these consumers have complete preferences. As we saw in chapter 2.1, all bundles on a given felicity “contour” line in the ݔ,ݕ consumption set have the same felicity ranking. By definition, the consumer is indifferent between all bundles on a felicity contour which is why they’re called “indifference curves”. Notice how the indifference curves above have various shapes: “curved”, “L shaped”, “linear”. As we’ll see
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ajaz_eco204_2009_chapter_2.2 - University of Toronto,...

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