10fB_ps06 - Microeconomics ECON 100A Problem Set 6 Due...

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Microeconomics ECON 100A Problem Set 6 Due November 2, 2010 (Solutions Posted November 5, 2010) 1. Let’s 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 β α z Ax U = a. What are the first order conditions for this constrained optimization problem ? b. Solve for the optimal consumption bundle, X h and Z h , as a function of x p , Z p , and U . 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. 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
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10fB_ps06 - Microeconomics ECON 100A Problem Set 6 Due...

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