組別 姓名與學號 Homework #3 Microeconomics (I), Fall 2010 Due day: 7 th Dec., 2010 Part I. Multiple Choices: 60% (5% each) Please fill your answers in below blanks, only one answer for each question. 1 2 3 4 5 6 7 8 9 10 11 12 D A D A B D C A A B B C 1. Mr. Jones was selling his house. The asking price was $220,000, and Jones decided he would take no less than $200,000. After some negotiation, Mr. Smith purchased the house for $205,000. Smith's consumer surplus is: A) $5,000. B) $15,000. C) $20,000. D) not able to be calculated from the information given. 2. You pay $15 for an all-you-can-eat buffet. The food isn't so good, but definitely edible. When you finish eating, what is the marginal value of the last bite of food you consumed? A) zero B) $15 C) negative D) none of above 3. Sarah and David both have linear demand curves for lemonade. Sarah's demand curve for lemonade intersects David's demand curve at a price of 50 cents per glass. Sarah's demand curve is more inelastic than David's. A change in the price of lemonade from 50 cents to 25 cents per glass will: A) decrease Sarah's consumer surplus more than David's. B) decrease David's consumer surplus more than Sarah's. C) increase Sarah's consumer surplus more than David's. D) increase David's consumer surplus more than Sarah's. 1
4. The above figure shows the market demand curve for telecommunication while driving one's car (time spent on the car phone). The current price is 35 per minute. If the price were to increase by ten cents per minute, consumer surplus would: A) fall to $820. B) fall by $84. C) fall by $58. D) fall to $369. 5. A quota will reduce consumer welfare when: A) the quota is greater than the amount purchased without the quota B) the quota is less than the amount purchased without the quota C) the quota is on a good with high income elasticity D) quotas always reduce consumer welfare 6. Efficient production occurs if a firm: A) cannot produce its current level of output with fewer inputs. B) given the quantity of inputs, cannot produce more output. C) maximizes profit. D) All of the above. 7. Which of the following statements best summarizes the law of diminishing marginal returns? A) As more labor is hired, the length of time that defines the short run diminishes. B) In the short run, the amount of labor a firm will hire diminishes as output increases. 2
C) In the short run, as more labor is hired, output increases at a diminishing rate. D) In the short run, as more labor is hired, output diminishes. 8. At Joey's Lawncutting Service, a lawn mower cannot cut grass without a laborer. A laborer cannot cut grass without a lawn mower. Which graph in the above figure best represents the isoquants for Joey's Lawncutting Service when capital per day is on the vertical axis and labor per day is on the horizontal axis? A) Graph A B) Graph B C) Graph C D) Graph D 9. If the average productivity of labor equals the marginal productivity of labor, then: A) the average productivity of labor is at a maximum. B) the marginal productivity of labor is at a maximum. C) Both A and B above. D) Neither A nor B above. 10.Returns to scale refers to the change in output when: A) labor increases holding all other inputs fixed. B) all inputs increase proportionately. C) capital equipment is doubled. D) specialization improves. 11.Let the production function be q=al a K b. The function exhibits increasing returns to scale if: A) a + b = 1 B) a + b > 1 3
C) a + b < 1 D) Cannot be determined with the information given. 12.With capital on the vertical axis and labor on the horizontal axis, vertical isoquants imply that: A) capital and labor are perfect substitutes. B) capital and labor must be used together in a certain proportion. C) capital is not productive. D) labor is not productive. Part II. Problems: 40% 1. During droughts, cities often impose water use restrictions on consumers. Suppose a representative consumer has preferences for Water (W) and other goods (X) given by the utility function: U(W,X) = WX Suppose the price of other goods is $1 and the price of water is initially 50. The consumer has a budget of $50/week. a) How much water will the consumer purchase each week? (8%) b) Suppose the government imposes a quota on water use of 50 units/week. Show that the quota reduces the representative consumer's utility. (10%) Ans: a) The consumer will choose 100 units of water per week. b) Since the consumer can no longer consumer the optimal bundle from before, she will choose a bundle of 50 units of water (costing $25) and spend $75 on other goods. Her utility before was U(100,50)=5000 and now is U(50,75) = 3750. She is indeed worse off from the quota. 2. Ed's building company has the following production function: q= 20L - L 2 where q is the number of houses built and L is the quantity of labor Ed employs. a) Derive the MP and AP. (8%) b) For what values of L is the MP>0? For what values of L is the MP diminishing? (10%) c) Draw the MP and AP on a graph. (4%) 4
Ans: a) MP = dq/dl = 20 2L; AP = 20 L b) MP>0 if and only if 20-2L>0, or L<10. d(mp)/d(l) = 2, so the MP is diminishing for all values of L. c) 5