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# ARE100A+PS+3+answer+2009 - vertical of horizontal depending...

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ARE100A INTERMEDIATE MICROECONOMICS: THEORY OF PRODUCTION AND CONSUMPTION FALL QUARTER 2009 Problem Set 3 Answer guide 1. Three indifference curves for left gloves and right gloves. For almost everyone these are right angles with the angle at 1:1, 2:2, 3:3 … 2. Indifference curves for eggs from Modesto or Merced. Most of us do not care which town the eggs come from so the indifference curve is a straight line with slope -1. 3. Income of \$2,000, P course = \$200; P ao = \$1. \$2,000 = \$200(C) + \$1(AO). Straight downward sloping line with Course intercept at 10 and AO intercept at \$2,000. 4. Income \$2,000. P course = \$200; P ao = \$1; no more than 5 courses allowed. The straight-line slope is -200, but the line kinks and goes straight to the “courses” axis at 5 (either
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Unformatted text preview: vertical of horizontal, depending which axis is used for courses). 5. U(X,Z) = AX 1/2 Z 1/2 . Role of A? No role at all. That is what ordinal means. 6. U(X,Z) = AX 1/2 Z 1/2 . P x =P z . A plays no role. Shares are 50%. Indifference curves are symmetric about 45-degree line. Budget has slope -1. X and Z are just interchangeable. 7. U(X,Z) = X 1/2 Z 1/2 ; P x = 2 and P z = 4; Y = 100. Budget constraint? 100 = 2X + 4Z. Maximum X? Y/P x = 50. 8. U(X,Z) = X 1/2 Z 1/2 ; P x = 2 and P z = 4; Y = 100. Consumption of X and Z? Z = 25 – 0.5X. [(∂U/∂X)/(∂U/∂Z)] = 2/4 = 0.5. [(0.5)X-1/2 Z 1/2 ]/[(0.5)X 1/2 Z-1/2 ] = Z/X = 0.5 Z = 0.5X 100 = 2X + 4(0.5)X => X =25. Expenditure shares must be equal to 0.5. Therefore, 2X=4Z=100, X = 25 and Z = 12.5....
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