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 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 Powered by TCPDF www tcpdf org