Economics 300, Section 010Intermediate Microeconomic TheoryDepartment of EconomicsUniversity of DelawareSpring 2018Elizabeth B. BayleyProblem Set IIDue Tuesday, March 6, 2018 by 9 am in my office, 421 Purnell.Total Points = 50 PointsGive clear, well-written answers to the questions below. Please make your graphs large and legible, and labelall parts of the graph (e.g., axes, lines, etc.). Assume that goods may be consumed in partial quantities (e.g.,3.54 espressos). Please round your answers to two decimal places.1.(10 points) Suppose that Penny is currently consuming at a level in which her marginal utility of consumingan extra coffee (X) is 10 and her marginal utility of consuming an extra donut (Y) is12. Assume that herpreferences are convex.a.(2 pts) What is Penny’s MRS of coffee for donuts? That is, what is the number of donuts that she iswilling to give up to get one more coffee?b.(8 pts) Suppose that the price of a coffee is $2, and the price of adonut is $3. Is Penny maximizing herutility at her current consumption? If not, how should she change her bundle to reach her optimum? Explain your answer using the marginal utility condition at the optimal choice.2.(10 points) Assume that Sheldon has an entertainment budget of $5,000, and he spends his income on comic books (X) and all other goods (AOG) (Y). The price of a comic book is $5,and the price of AOG is$1/unit. His preferences can be represented by convex indifference curves: U(X,Y) = (X*Y)1/2, and the equation for his MRS of X for Y = f(X,Y) = Y/X. What is Sheldon’s optimal choice of comic books and AOG? Illustrate his optimal choice on a graph, using indifference curve-budget line analysis.Include the value of his utility at his optimal choice in your answer.3.(10 points) Howard likes to have 5 dumplings (X) with 2 packets of soy sauce (Y). His preferences are represented by the following utility function: U(X,Y) = min(2X, 5Y). His dinner budget is $25, and the price of a dumpling is $2.50 and 1packet of soy sauce is $0.50. What is Howard’s optimal choice for dumplings and soy sauce given his budget? Illustrate his optimal choice on a graph, using indifference curve-budget line analysis. Include the value of his utility at his optimal choice in your answer.ECON300 Spring 2018 Page 2 of 24.(10 points)
Mary is indifferent between 3 hours of basketball (Y) and 1 hour of swimming (X). Her preferences are represented by the following utility function: U(X,Y) = 3X + Y. She has a budget of $100. Swimming costs $10 per hour, and playing basketball costs $20 per hour. a.(2 pts) Graph Mary’s budget line. What is the relative price of swimming in terms of basketball?b.(2 pts) What is Mary’s MRS of swimming in terms of basketball? That is, how many hours of basketball is she willing to giveup to get one additional hour of swimming? Do her indifference curvesexhibit diminishing MRS or constant MRS?c.(2 pts) What is the relationship between the relative price of swimming in terms of basketball and theMRS of swimming for basketball? (Hint: less than, greater then, orequal.) Are Mary’s indifferencecurves steeper or flatter than her budget line?d.(3 pts) Identify Mary’s utility-maximizing consumption bundle on your graph, including herindifference curve that is associated with her optimal bundle. e.(1 pts) What is the value ofher utility atthis bundle?
5.(10 points) Suppose David buys cheese (X) and fruit (Y) with his income of $48 per week. Suppose theprice of cheese has recently risen from $4 to $6 perpounds, while the price of fruit has fallen from $8 to $6per pound. Before the price changes,David had been buying 4 lb. of cheese and 4 lb. of fruit each week. Since the price changes, he has been buying 2 lb. of cheese and 6 lb. of fruit weekly. Assuming David’spreferences have not changed, is itpossible to say whether the price changes have made him better off orworse off? Use an indifference curve-budget line analysis toexplain your answer.
