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Unformatted text preview: Microeconomics ECON 100A Problem Set 6 Solutions Due November 2, 2010 (Solutions Posted November 5, 2010) 1. Let’s get the Hicksian (compensated) demand functions for any CobbDouglas Utility function. Recall that the expenditure minimization problem is: z p x p z x z x + , min Subject to β α z Ax U = a. What are the first order conditions for this constrained optimization problem ? ) 3 ( ) 2 ( ) 1 ( . . . ) ( 1 1 = = ∂ ∂ = = ∂ ∂ = = ∂ ∂ + = U z Ax L z x A p z L z x A p x L C O F U z Ax z p x p L z x z x β α β α β α β α λ β λ α λ λ b. Solve for the optimal consumption bundle, X h and Z h , as a function of x p , Z p , and U . β α β β α β α + + = ) ( ) ( ) , , ( 1 x z z x h p p A U U p p X β α α β α α β + + = ) ( ) ( ) , , ( 1 z x z x h p p A U U p p Z 2. A consumer gets utility from two goods, X and Z. Suppose the consumer’s income increases and that, in this income range, X is a normal good and Z is an inferior good. Using budget lines and indifference curves, illustrate this consumer’s response to the change in income. Z X Notice that as income increases (budget line shifts right), X increases but Z decreases. 3. A consumer gets utility from two goods, X and Z. Using budget lines and indifference curves, draw the optimal choice for the consumer under a variety of different prices p X . Label these prices p X A , p X B , p X C , etc, and the corresponding quantities q X A , q X B , q X C , etc. Then directly underneath this diagram, draw the consumer’s ordinary demand curve for good X with X on the horizontal axis and p X on the vertical, again labeling the points p X A , p X B , p X C , q X A , q X B , q X C , etc. It would be helpful if your labeled q’s in both the top and bottom diagram lined up vertically, for better readability. Draw many budget lines with the same yaxis intercept, and find the optimal point on each. Each budget line corresponds to a different price of good X. Each generates a different quantity of X. Plot the corresponding prices and corresponds to a different price of good X....
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This note was uploaded on 11/30/2011 for the course ECON 311 taught by Professor Zambrano during the Fall '08 term at Cal Poly.
 Fall '08
 ZAMBRANO
 Microeconomics, Utility

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