Lecture_03_Choice - Lecture 3: Choice Outline 1....

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Lecture 3: Choice c 2008 Je/rey A. Miron Outline 1. Introduction 2. Optimal Choice: Graphical Analysis 3. Optimal Choice: Math 4. Relation Between Graphs and Math: The MRS and MU 5. Caveats: Some Special Cases 6. Summary 1 Introduction We are in the process of building a model of consumer behavior. So far, we have We have not yet combined those two things to examine what consumers actually choose. That is our next step. There are two approaches: graphs and calculus. Both are useful, as we± ll see. Each has some advantages and disadvantages. 2 Optimal Choice: Graphical Analysis Consider ²rst the graphical treatment of the consumer±s problem. In words, the problem is one of choosing the combination of x 1 , x 2 that is most preferred / leads to the greatest satisfaction / produces the highest amount of utility, given the prices and income the consumer faces. 1
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We take prices and income as given. So, the consumer has a budget constraint: p 1 x 1 + p 2 x 2 = m Put this in the graph. well-behaved preferences. These can be represented by indi/erence curves ± utility functions; for the moment, let²s focus on the ICs. So, we can put in the indi/erence curves. 2
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Graph: Optimal Choice in the Standard Case 4 = x 1 = 2 1 x 1 = 2 2 x 2 = 8 x 1 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 x1 x2 x1* x2* Now, what point should the consumer choose assuming the consumer wants to end up with the most preferred bundle that is a/ordable? inside the budget line. So, we start at the right corner of the budget line and move up. You will cross indi/erence curves. But at some point, we get to one IC that just barely touches where we are on the budget line. This point must be the optimal choice; it is on the highest indi/erence curve the the constraint, this is the best the consumer can do. 3
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This makes perfect sense. You can see how, given this kind of analysis, we might be able to derive results about the e/ects of prices and income on the demand for x 1 and x 2 . For example, a change in one of the prices rotates the budget line, so the optimal choices will change. We can sort of guess in what direction these choices will change, but there turn out to be some subtleties. We are going to hold o/ on these for a moment. In summary, the graphical analysis is useful, but it has two limitations: 1. It is not really a proof.
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Lecture_03_Choice - Lecture 3: Choice Outline 1....

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