Problem Set 1

# Problem Set 1 - a. Write Andreas budget constraint assuming...

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Problem Set 1 1. Boy and Girl allocate their consumption between two goods: hats and bats. The price of hats is \$4 each and the price of bats is \$8 each. Boy’s marginal utility of the last hat consumed is 8 and his marginal utility of the last bat is 24. Girl’s marginal utility of the last hat is 6 and the marginal utility of the last bat is 12. a. Which consumer is not maximizing his/her utility? Why? b. How should he/she change their allocation? 2. Suppose that left shoes and right shoes must be purchased separately. Ingrid needs an equal number of each type of shoe (they are perfect complements) and has a budget of \$100 for shoes. Left shoes always cost \$1. a. If right shoes cost \$19 each, how many of each will Ingrid buy? b. If the price of right shoes increases to \$49 each, how will Ingrid react? Explain your answers by drawing the indifference curves and budget lines. 3. Andrea's utility for daily leisure (L) and consumption (C) is U = CL; she can work for \$10 per hour and labor is her only source of income.
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Unformatted text preview: a. Write Andreas budget constraint assuming there are 24 hours in a day. (Hint: labor hours are hours not spent on leisure, so leisure plus labor equal 24). b. Derive Andreas demand for leisure and consumption. c. What is her labor supply N? d. Answer a. and b. if Andreas has non labor income of \$100 per day. 4. For the Constant Elasticity of Substitution (CES) utility function derive the optimal quantity demanded of q 1 and q 2 as a function of their prices and income using the Lagrangian method. Hint: look at problems 32, 37, and 38 in the textbook. 5. Suppose a person's utility for goods x and y is given by u(x,y) = x a y b . a. Compute the demand functions for goods x and y. b. Compute the effect on each demand of a change in the price of the other good. c. Are these two goods complements or substitutes? Explain your answer. d. Compute the effect on each demand of a change in income. e. Are these two goods normal or inferior? Explain your answer....
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## This note was uploaded on 03/10/2012 for the course ECON 1100 taught by Professor Unver during the Fall '06 term at Pittsburgh.

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