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Unformatted text preview: Microeconomics ECON 100A Problem Set 6 Solutions Due November 2, 2010 (Solutions Posted November 5, 2010) 1. Lets get the Hicksian (compensated) demand functions for any Cobb-Douglas Utility function. Recall that the expenditure minimization problem is: z p x p z x z x + , min Subject to 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 b. Solve for the optimal consumption bundle, X h and Z h , as a function of x p , Z p , and U . + + = ) ( ) ( ) , , ( 1 x z z x h p p A U U p p X + + = ) ( ) ( ) , , ( 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 consumers 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 consumers 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 consumers 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 qs in both the top and bottom diagram lined up vertically, for better readability. Draw many budget lines with the same y-axis 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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