Problem Set 3 – ECN 312 – Intermediate Microeconomic Theory Spring 2017 Please make sure that your problem set is legible and stapled. Please write your name and SECTION number on your problem set. On your graphs, please label axes, curves, intercepts, and all points relevant to the question. Explain your work thoroughly in order to receive full credit. Possible points are given in parentheses. 1. (15) Cheri is given $600 on the first day of this month and $600 on the first day of next month. Cheri has a credit card that charges 20% interest per month. She can use the credit card this month, but must pay the balance in full (plus interest) next month. She cannot use the credit card next month. In addition, Cheri is able to put money under her mattress this month for next month. (a) (2) Plot and label Cheri’s endowment (the bundle she starts off with) in the space of consumption this month (C1 ) and consumption next month (C2 ). Put C1 on the horizontal axis. (b) (3) Plot and label the point indicating the maximum amount of consumption that Cheri can get this month. Plot and label the maximum amount of consumption that Cheri can get next month. Use these points, along with the endowment from (a), to draw Cheri’s budget line and label its slope. (c) (3) Suppose that Cheri’s preferences are given by the following utility function: U (C1 , C2 ) = 2C1 + C2 Draw and label three indifference curves associated with these preferences. (d) (2) What is Cheri’s optimal consumption bundle given the preferences in (c)? Does she use her credit card? If so, how much does she charge? (e) (3) Suppose that Cheri’s preferences are instead given by the following utility function: U (C1 , C2 ) = min{2C1 , C2 } Draw and label three indifference curves associated with these preferences. (f) (2) With the preferences in (e), does she use her credit card to consume at her optimal bundle? Describe in two sentences or less. 2. (20) Suppose that David (an automobile enthusiast) has Cobb-Douglas preferences over vans (V) and sports cars (S): 3 1 U (V, S) = 4V 4 S 4 When David goes to the car dealership, he finds that the price of vans is $25, 000 and the price of sports cars is $100, 000. David has $850, 000 to spend on new automobiles. (a) (5) What is the marginal utility of V? What is the marginal utility of S? What is the marginal rate of substitution of vans for sports cars (M RSV,S )? (b) (5) In what ratio will David purchase V and S at the optimum (solve for tangency condition and express S as a function of V)? (c) (5) How many vans will David buy? How many sports cars will David buy? (d) (5) Show this solution graphically (label V ? and S ? , the IC at the optimum (does not need to be exact – make sure that you get the correct shape and the correct tangency), the budget line, and all axes and other relevant points). Put vans on the horizontal axis. 3. (15) In answering this question, please refer to the attached graph. For part (e) of this question, add to the existing graph by using a ruler to draw budget constraints. Attach the graph to your write-up when you turn in your work. Suppose that a typical poor family chooses to allocate its income between food (F) and other consumption (C) in such a way that it picks point A on budget line 1 in the graph on the following page. At this point, the family spends $1, 000 of its $5, 000 income on food. The price of other consumption is $1 per unit. In an effort to win votes from this segment of Americans, the government decides to lift the typical poor family’s level of utility from that implied by indifference curve I to that implied by indifference curve II. (Please note that when I solve this question, I get relatively easy numbers to work with….) (a) (3) Suppose the government does this by subsidizing the family’s consumption of food (i.e, by paying part of the price of food). What is the initial price of food? To what does the government need to lower the price of food to get the family to indifference curve II? (b) (3) What is the cost to the government (per poor family) of this price subsidy? (c) (3) How could the government achieve the same result by way of a simple income subsidy? What would be the cost to the government per poor family? (d) (3) Suppose that the government’s objective is to both increase the utility of poor families to indifference curve II and to raise their quantity of food as much as possible. Cost is not a concern. Which policy (price subsidy or income subsidy) would the government choose? (e) (3) Describe the two policies graphically. 2 3
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