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# ps1 - UC BERKELEY Department of Economics Economics 101A-~...

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Unformatted text preview: UC BERKELEY Department of Economics Economics 101A -~ Fall 2008 Problem Set Number 1 Due: Tuesday September 9 in class - 1. Canadian consumers have linear indifference curves between two brands of beer: Molson’s and Dragon’s Breath Lager, as shown: Wt} (£3555 Qwee‘li (vat/{’x/weeéajk at: M0336} ng' [whingJ/fwﬂl/L‘é x. a *3 “f 21. Suppose Molson’s is prices at \$5.00 per 6-pack. At what price for Dragon’s Breath will consumers buy both brands? b. Graph the demand. for Dragon’s Breath for a Canadian who has a \$30 per week beverage budget, assuming the price for Molson’s is \$5.00. Illustrate the effect on the demand curve of a rise in the price of Molson’s to \$6.00. c. Give a utility function that represents preferences. 2. Suppose that preferences for two goods, it}, and x2, are represented by rightwangle indifference curves: 7e; K5,? 2., X; Problem Set 1 Page 2 a. Find the demand functions for the two goods as a function of p}, p2, and I. b. Suppose that good i is taxed with a permunit tax \$1: Iliustrate the effect on the consumer’s optimum, and show the amount of the tax collected in units of good .2. 0. Instead of a tax on good 1, the government proposes a lump sum tax. Illustrate the budget constraint for the consumer assuming the iump sum tax raises the same revenue as the per unit tax. How does the optimum differ depending on which tax is used? Why? d. Find the expenditure function for the consumer, and the compensated demand functions when the consumer is given enough income to reach a level of utiiity U. Take the derivatives of the expenditure function with respect to p,, p2 and verify that these are equal to the compensated demand functions. 3. Suppose a consumer’s preferences over two goods, x and y, are represented by a Cobb- Douglas utility function: 170: U093!) e X“ y a. Find the expenditure function of the consumer, and the compensated demand functions. 1:). Suppose that 06 2 1/2 and that initially a consumer is in equilibrium with px == 1, py : 1, I z 100. What are the demands for x and y. 0. Starting from the position in part b, the price of good y rises to 2. What is the increase in the “consumer price index” for this consumer? d. What is the minimum increase in income necessary for the consumer to be as well off under price px : 1, py = 2, as she/he was at prices pX = 1, py : 1? Explain Why the percentage increase is smaller than the increase in the consumer price index for the consumer that you derived in part c. ...
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