Question 1 Andy purchases only two goods, apples (a) and kumquats (k). He has an income of $40 and can buy apples at $2 per pound and kumquats at $4 per pound. His utility function is U(a, k) = 3a + 5k. That is, his constant marginal utility for apples is 3 and his constant marginal utility for kumquats is 5. What bundle of apples and kumquats should Andy purchase to maximize his utility? Why? [Solution] Andy’s marginal utility of apples divided by its price is 3/2=1.5. The marginal utility for kumquats is 5/4=1.25. That is, a dollar spent on apples gives him more extra utilities than a dollar spent on kumquats. Thus, he maximizes his utility by spending all his money on apples and buying 40/2=20 apples. Question 2 Yuka consumes mangos and oranges. She is given four mangos and three oranges. She can buy or sell mangos for $2 each. Similarly, she can buy or sell an orange for $1. If Yuka has no other source of income, draw her budget line and write the equation. [Solution] It is given: C(mango) = 4, O(orange) = 3, PC = $2, PO = $1. The most he can spend on these goods, Y = 4 × 2+3 × 1 = 8+3 = $11. The budget constraint: 2C +1O = 11 → 2C +O = 11. Question 3 Nadia likes spare ribs(R) and fried chicken(C). Her utility function is U = 10R2C. Her weekly income is $90, which she spends on only ribs and chicken. a. If she pays $10 for a slab of ribs and $5 for a chicken, what is her optimal consumption bundle? Show her budget line, indifference curve, and optimal bundle, e1, in a diagram. b. Suppose the price of chicken doubles to $10. How does her optimal consumption of chicken and ribs change? Show her new budget line and optimal bundle, e2, in your diagram. [Solution] a. Setting MUR/pR = MUC/pC yields 20RC/10 = 10R2/5 or 2C = 2R. Therefore R = C. We then substitute R = C into the budget equation to obtain: 10C + 5C = 90 or C = 6 (and R = 6). The diagram looks like Figure 4.8 with only the middle indifference curve shown and with R and C on the axes. b. Using the same method as in part a), the new solution is R = 6, C = 3. In this case the budget line from part a) has the same intercept on the R axis, but the intercept on the This study source was downloaded by 100000804585776 from CourseHero.com on 07-08-2023 17:23:38 GMT -05:00 https://www.coursehero.com/file/65290196/Tutorial-3pdf/ C axis falls by half, so the budget line pivots inward. Question 4: Julie consumes two goods, X and Y. Julie has a utility function given by the expression: U=4X0.5Y0.5 The current prices of X and Y are 25 and 50, respectively. Julie has an income of 750 per time period. a. Write an expression for Julie’s budget constraint. b. Calculate the optimal quantities of X and Y that Julie should choose, given her budget constraint. Graph your answer. c. Suppose that the government rations purchases of good X such that Julie is limited to 10 units of X per time period. Assuming that Julie wants to spend her entire income. How much Y would Julie consume. Calculate the impact of the ration restriction on Julie’s utility. [Solution] This study source was downloaded by 100000804585776 from CourseHero.com on 07-08-2023 17:23:38 GMT -05:00 https://www.coursehero.com/file/65290196/Tutorial-3pdf/ This study source was downloaded by 100000804585776 from CourseHero.com on 07-08-2023 17:23:38 GMT -05:00 https://www.coursehero.com/file/65290196/Tutorial-3pdf/ Powered by TCPDF (www.tcpdf.org)