Notes Section 5, Econ 100A Spring 06
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Section Notes 5
Covering material from Lecture on January 26th
Class Outline
1. The Optimal Bundle 2. Dissecting Marginal Rate of Substitution 3. Revealed Preference 4. Practice Problems Ch. 3.3-3.6, pg: 83-101
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The Optimal Bundle
To help our intuition, we now look at optimal bundles with dierent types of preferences and a standard budget constraint. Remember our assumptions about consumer preferences and assume diminishing MRS for the top two graphs. Diminishing MRS (internal solution)
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Diminishing MRS (corner solution)
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Section Notes 5, Econ 100A Spring 06
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Dissecting Marginal Rate of Substitution
For the optimal bundles with diminishing MRS you should note the important graphical dierence between those at internal versus corner solutions. Remember, indiference curves and MRS are determined entirely by the specic utility function in question. Lets now look into that relationship more formally. We know that the marginal rate of substitution is determined by the amount of a good we are willing to give up for another good that would keep our utility constant, i.e. on the same indierence cuve. Assuming U (X, Y ) is a utility function with diminishing MRS, how do we determine the MRS mathematically?
Notice, the MRS is literally slope the of the indierence curve at a certain consumption point. Look at the graphs again. Is there something you notice about the optimal bundle? This gives us a clear condition for any internal optimal point. Condition: The above condition is a single equation with two variables. However, we have another equation that has the same two variables: the Budget Line, or PX X + PY Y = I, where PX , PY , and I are known numbers. This gives us a system of equations with two equations and two unknowns we can solve for the optimal bundle for internal solutions! Now, how can we relate the above condition with corner solutions?
Section Notes 5, Econ 100A Spring 06
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Practice Problems
Problem: (P&R Chapter 3, Exercise 15) Jane receives utility from days spent traveling o...