# MIDTERM EXAM August 16th, Monday, 2010 (80 POINTS)

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1 MIDTERM EXAM August 16th, Monday, 2010 (80 POINTS) UID: NAME: TYPE: DEMAND READ CAREFULLY. 1. You have 1 hour and 30 minutes. Allocate your time wisely. 2. Solve ALL questions. 3. Show your work for essay questions. A correct answer without necessary steps may earn less points than a wrong answer with correct steps. TO DO and NOT TO DO: 1. Do NOT open the cover sheet until you are told to do so. 2. As soon as the exam starts, check and make sure that you have 8 questions and 12 pages. 3. You are NOT allowed to use calculators, notes, and books. 4. You are NOT allowed to leave the classroom for any reason until 30 minutes after the exam starts. Then only one student can go to the restroom at a time. 5. Make sure that your name is written on the cover sheet, and on separated sheets if any. 1

2 1. Demand Curve (4 pts) ( ) Which one of the following is true? (Caution: the answer not written in the above parantheses will be ignored. Write clearly only one.) (a) A demand curve is negatively sloped if the good is a Giffen good. (b) The unit elastic point is exactly the midpoint of the linear demand curve. (c) At an elastic point of the demand curve, an increase in the price raises the expenditure. (d) The expenditure is minimized at the unit elastic point if the demand curve is linear. 2. Elasticities (4 pts) ( ) Suppose there are two commodities. Which one of the following is false? (Caution: the answer not written in the above parantheses will be ignored. Write clearly only one.) (a) It is impossible that both are inferior goods. (b) If one is a luxury good, the other must be a necessity good. (c) If one is a normal good, the other must be an inferior good. (d) It is possible that both are gross substitutes of the other. (e) It is possible that one is a gross substitute of the other but the latter is a gross complement of the former. Yong Yang 2

3 3. Economic Incidence of a Policy ((4 pts) ) Which one of the following is false? (Caution: the answer not written in the above parantheses will be ignored. Write clearly only one.) (a) If the sales tax is imposed, the consumer surplus may decrease. (b) If the excise tax is imposed, the consumer surplus may increase. (c) If the government abolishes the sales tax but imposes exactly the same amount of excise tax, neither of buyers and sellers are better off. (d) Suppose a restaurant adds a service to the meal which costs \$5. If this benefits consumers by \$8 in addition to the utility from the meal, both buyers and sellers are better off. (e) If price ceiling is strictly implemented and therefore consumers buy less amount of goods at a lower price than at the equilibrium, the consumer surplus may increase. 4. Marginal Rate of Substitution (4 ( pts) ) Which one of the following is true? (Caution: the answer not written in the above parantheses will be ignored. Write clearly only one.) (a) The marginal rate of substitution is defined as the ratio of consumption of X and that of Y. (b) Marginal utilities must decrease in order that the marginal rate of substitution is diminishing. (c) The condition for optimal consumption is that the marginal rate of substitution is equal to the price of at least one good. (d) If P X = 4, P Y = 2, and the marginal rate of substitution is 3, consuming more X on the budget line increases utility. Yong Yang 3

4 5. Marginal Utilities and MRS (4 pts) Obtain the expression for the marginal rate of substitution in each of the following cases. (4 pts) (a) U = X + 2 Y (b) U = 1 X + Y Yong Yang 4

5 6. Optimal Consumption (20 pts) Suppose Yuna Kim is willing to use up her income 60 golds on a pair of figure skating shoes and a lesson from her coach. X denotes the quality level of the shoes, and Y denotes months of lesson. It costs 2 golds to raise the quality by 1, and a month of lesson costs 8 golds. Suppose the quality of her shoes was 0 and she took 0 week of lesson initially. Her perfomance is given by U = XY 2. She wants to maximize the performance. Answer the following. (a) Find the optimal quality of the shoes (X) and the optimal amount of lesson (Y ). (10 pts) Yong Yang 5

6 (b) Kobe wants to help her by making an agreement with her coach that he would pay the coach 3 golds per a month of lesson, so she only needs to pay 5 golds per a month of lesson. Her budget is still 60 golds. Find her new choice under the agreement. (4 pts) Yong Yang 6

7 (c) Kobe comes up with a new idea that he would give Yuna Kim the amount of money he might have spent if he made an agreement with the coach as in (b). So she still pays 8 golds per a month of lesson, but her budget increases by the amount of subsidy from Kobe. (A) Find Kobe s expenditure on her lesson in (b). How much is her budget after she gets such a subsidy from Kobe? (1 pt) (B) Find her new choice with the increased budget. (4 pts) (C) Do you think her performance is higher in (c) than in (b), or less? A guess without correct reasoning earns no point. (1 pt) Hint: A way to answer this is to compare the performance in (c) with that in (b). (Note the performance would be 686 in (c) if you solve correctly.) A brief comment on per-unit subsidy and lumpsum subsidy is fine as well. Yong Yang 7

8 7. Sales Tax (20 pts) The demand function is given by Q D = 26 2P D, and the supply function by Q S = 9 + 3P S. (a) Find the equilibrium and show it in a figure. (5 pts) (b) Calculate the consumer surplus, the producer surplus, and the social total surplus. (5 pts) Yong Yang 8

9 (c) Suppose that the government imposes \$5 of sales tax each unit to consumers. To find the deadweight loss, follow the steps: (1) Let P be the price on the tag. (Note consumers pay extra \$5 for tax in addition to P.) Find the relationship between P and P D, and that between P and P S. (2) Obtain the demand and the supply functions in terms of P. (3) Find the new equilibrium as well as P D and P S at the equilibrium. (4) Calculate the consumer surplus, the producer surplus, the government revenue, and the social total surplus. (5) Compare the social total surplus with that in (b), and compute the deadweight loss. (10 pts) Yong Yang 9

10 8. Uncompensated/Compensated Demand Curve (20 pts) Consider two commodities X and Y. Let P Y and I fixed. The price of X is originally P X, and goes UP to P X. (A) Suppose X is a normal good. (1) Draw the change in the optimal consumption of X in the X-Y space, (2) show the substitution effect and the income effect on the graph, and (3) draw the uncompensated demand curve and the compensated demand curve for X in the X-P X space. (B) Repeat (1), (2), and (3) assuming X is a Giffen good. Yong Yang 10

11 EXTRA PAGE Yong Yang 11

12 EXTRA PAGE Yong Yang 12