Microeconomic theory ECON 10A
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This 1 page Class Notes was uploaded by Angelou de Bedout on Saturday October 1, 2016. The Class Notes belongs to ECON 10A at University of California Santa Barbara taught by ROSSIN-SLATER in Fall 2016. Since its upload, it has received 4 views. For similar materials see Microeconomic theory in Economics at University of California Santa Barbara.
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Date Created: 10/01/16
Econ 10A: Problem Set 2 (1) Luke’s utility is U(x ,x ) = 2x + ln x . 1 2 1 2 (a) What is Luke’s marginal rate of substitution (MRS)? (b) Does Luke have a diminishing marginal rate of substitution? (2) Tom, Dick, and Harry, the only three people on a desert island with two consumption goods, apples and bananas, have utility functions U , U , anT D U H respectively, where: UT(xa,xb) = 6x a9x b U Dx ax b = 8x +a2x b 2 UH(x ax b = x ab (a) Relative to Tom, does Dick require more bananas, less bananas, or the same number of bananas to give away an apple? Why? (b) Suppose Harry has 3 apples and 2 bananas. Would he be willing to trade an apple for a banana? Show why or why not. (3) I need a minimum of 7 apples per week to make one apple pie per week. I don’t like to eat apples unless they are in a pie. (They’ll just sit on the shelf and get rotten in a week if I get less than 7.) I do, however, like bananas, even if they are not in a pie. Draw my indiference curves. (4) Utility is U(x,y) = x + y. (a) Derive the formula for the indifference curve that gives me a utility of exactly 8. Draw that indifference curve. (b) Derive the marginal utility functions MU (x,y)xand MU (x,y). y Derive MRS(x,y). (c) Does this utility function satisfy the hypothesis of diminishing MRS? Explain. (d) Name some commodities these might be. (5) My utility function U(x 1x 2 depends on the two commodities x , x . 1f m2 preferences are monotonic and satisfy the Hypothesis of Strictly Diminishing Marginal Rate of Substitution, and if MRS(5,5) = –2, what can you say about how I could rank commodity bundles (4,6) and (6,5)? Draw a graph to illustrate. (Hint: How would each of these bundles compare with the bundle (5,5)?)
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