0732fb10778805338d4d690a0168bb0b7a24a17ad9df3e9d5ff467607d24984b_four

Consumer Preferences and Utility 41 b 14, 15. Finding Properties-IV.” Repeat the previous exercise, but assume now that Eric’s preferences are represented with the following utility function for two goods regarded as complements in consumption: u(x, y) = min {3x, 4y}. (a) Find Eric’s marginal utility for books, MUy, and for computers, MUj. (b) Are his preferences monotonic (i.., weakly increasing in both goods)? (c) Fora given utility level %, solve the utility function for y to obtain Eric’s indifference curve. (d) Find Eric’s MRS between x and y. Interpret your results. (e) Are his preferences convex (i.e., bowed in toward the origin)? (f) Consider a given utility level of 10 utils. Plot his indifference curve in this case. Envious Preferences.” Peter’s preferences are represented by the utility function u(x,y) =4x+2(x—y), where x denotes the amount of books he has, while y represents the amount of books his friend has. Intuitively, when x > y, he owns more books than his friend, and his utility increases. When x <y, he owns fewer books than his friend and his utility decreases (he suffers from envy). (a) Find Peter’s marginal utility for the books he owns, MUy, and for his friend’s, MUj,. (b) Are his preferences monotonic (i.e., weakly increasing in both goods)? (c) For a given utility level #, solve the utility function for y to obtain Peter’s indifference curve. (d) Find Peter’s MRS between x and y. Interpret your results. (e) Are his preferences convex (i.e., bowed in toward the origin)? (f) Consider a given utility level of 10 utils. Plot his indifference curve in this case. Guilty Preferences.® Repeat excrcise 14, but assume that Peter’s utility function is now u(x,y)=4x— (x—y); that is, he suffers from guilt when he owns more books than his friend (x > y). Relative to envy aversion in exercise 14, guilt aversion reduces Peter’s utility less dramatically. Stated in words, Peter cares more about feeling envy than about feeling guilt. (a) Find Peter’s marginal utility for the books he owns, MUy, and for his friend’s, MU;,. (b) Are his preferences monotonic (i.e., weakly increasing in both goods)? (c) Fora given utility level %, solve the utility function for y to obtain Peter’s indifference curve. (d) Find Peter’s MRS between x and y. Interpret your results. (e) Are his preferences convex (i.e., bowed in toward the origin)? (f) Consider a given utility level of 10 utils. Plot his indifference curve in this case. . Toddler Rationality.” Eric’s daughter is 4 years old. He has spent a long time trying to figure out her favorite animal. Today he is asking her to pick which animal she prefers among two animals at a time. He learned the following strict preferences: