Intermediate Microeconomics Ch5 notes

Intermediate Microeconomics Ch5 notes - Ch 5 Choice This...

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1 Ch 5 Choice This chapter will analyze the optimization problem of consumers. As stated previously, people choose the best thing they can afford; in more professional terms, this is equivalent to saying that a consumer selects the most preferred bundle from her budget set. 5.1 Optimal Choice A consumer maximizes her utility by choosing the best bundle subject to her budget set. To study how she does this, we put together her budget set and preferences, which can be expressed as () m x p x p t s x x u u x x + = 2 2 1 1 2 1 , ....... : . . , ........ max 2 1 ……. . (Ex 1) We focus only on the graphical interpretation of her best choice to avoid the algebraic treatment of her optimization problem. We want to find the bundle in the budget set that is on the highest IC. See figure 5.1 in the case of smooth and well-behaved preferences. In Panel A of this diagram, X’ is affordable but not optimal, X” is more preferable but unattainable, and X* = (x 1 *, x 2 *) is her best choice because only this bundle is utility-maximal as well as affordable. Notice that the highest possible IC subject to affordability just touches the BL at the best bundle X* . In mathematical terms, optimum arises at X* where the IC is tangent to the BL. IC” does not cross the BL and IC’ cuts the BL rather than being tangent to it. Q1: Describe the optimal choices under convex preferences as in Panel A of figure 5.1. You may need to add labeling to the Panel before writing out the optimal bundles. X’ X’’ X * IC’’ IC IC’ Panel A
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2 Affordability within the budget set becomes irrelevant in the case as shown in figure 5.1. So we actually need to work with the BL. The above best point X* is referred to as an interior optimum since it lies within the BL. It is attained under well-behaved preferences. However, in the case of such preferences, a boundary optimum (or corner solution) can possibly arise. See figure 5.2 for this possibility. In this diagram, the corner optimum X* = (x 1 *, 0) indicates that the consumer will optimally specialize in consuming only good 1 at the level of x 1 *= m / p even if she has smooth and well-behaved preferences. This thing happens because she cares so much about good 1 that the tangency condition may hold at the corner or may be violated, as shown in both panels of figure 5.2. This suggests that tangency is a necessary condition for the optimal choice to involve consuming some of both goods in the case of
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This note was uploaded on 02/19/2009 for the course ECIF ECIF201 taught by Professor Gu during the Spring '09 term at University of Manchester.

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Intermediate Microeconomics Ch5 notes - Ch 5 Choice This...

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