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exam05

# exam05 - THE UNIVERSITY OF HONG KONG School of...

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Unformatted text preview: THE UNIVERSITY OF HONG KONG School of Economics & Finance 2005-2006 1st Semester Examination Economics: ECON2101 Microeconomic Theory Dr W Chan December 23, 2005 ' 2:30-4:30p.m. Candidates may use any self-contained, silent, battery-operated and pocket—sized calculator. The calculator should have numeral—display facilities only and should be used ' only for the purposes of calculation. It is the candidate’s responsibility to ensure that his calculator operates satisfactorily. Candidates must record the name and type of their calculators on the front page of their examination scripts. ‘ A. Multiple Choice Questions (5 points each. Please note that 1 point will be deducted for each wrong answer.) v - . . . 1. A consumer’s utility function is U(x,y) = xy. His income is \$100; the price of y is \$10, while the price of x is as follows: the ﬁrst 6 units cost \$10 per unit and any additional units cost \$5 per unit. What consumption bundle will the consumer choose? a. (5,5). 'b. (7, 3.5). c. (9,3). (1. (6,4). 6. None of the above. 2. Which of the following relationship between a ﬁrm’s short—run and long-run cost curves is incorrect: - v a The long—run total cost curve is the lower envelope of the short-run total cost curves. b. The long-run average cost curve is the lower envelope of the short-run average cost curves. ' c. The long-run marginal cost curve is the lower envelope of the short-run marginal cost. curves. ' . d. The long-run marginal cost curve intersects a short-run average cost curve at its minimum only at the entry price. e. All of the above are correct. 3. A Stackelberg leader a. will necessarily make at least as much profit 'asvhe would if he acted as a Cournot oligopolist. ' b. will produce at most as much Output as he would if he acted as a Cournot oligopolist- c. will produce at least as much output as he would if he acted as a Bertrand oligopolist. ' d. will make at least as much proﬁt as he would if he was a monopolist in the market. 6. none of the above. ' 4. A monopolist is able to practice third degree price discrimination between two markets. The demand function in the first market is q = 500 — 2p and the demand function in the second market is q = 1500 —_6p. To maximize his proﬁts, he should: a. charge a higher price in the second market than in the first. b. charge a higher price in the ﬁrst market than in thesecond. c. charge the same price in both markets. (1. sell only in one of the two markets. e. none of the above. 5. Suppose that in Hong Kong, the cost of operating a taxi is \$2000 a week. Suppose that if x taxis operate in the city, the total weekly revenue from the taxis in the city is \$1000(26x — x2). If there are no restrictions on entry and new taxis enter the market until there is no proﬁt to be made by a new entrant, then the number of taxis in the city will be x1. If the number of taxis in the city is regulated to maximize total profits,_the number of taxis in the city will be x; where - a. x; = 24 ande = 24. b. x; =12 ande =10. ox; = 24 ande = 12. d. x1 :28 and x2 = 16 6. None of the above. 6. Which of the following is not required for efﬁciency in and economy with production and exchange: a. The allocation of consumption goods is on a contract curve in the commodity space. b. The allocation of production factors is on a contract curve in the input space. c. Production of outputis on the production possibility frontier. d. Each consumer’s consumption bundle is on his production possibility frontier. 6. None of the above (i.e. all are necessary). i- B. Explain whether the following statements are True, False or Uncertain. (10 points each) ’ ' 1- The CPI (a Laspeyres price index) will overestimate the reduction in the cost of living in times of deﬂation. ’ » ~ . 2. Suppose oil companies in Hong Kong are colluding members of a joint-proﬁt maximizing cartel. Then, other things being the same, a reduction in the import tax on gasoline would not result in a reduction’in price of gasoline. 3. A ﬁrm has two Variable factors and a production function ﬁx,y) _= (2x + 4y)m. The technical rate of substitution between x and y is constant. 4. China currently imposes tariffs on many imported goods. Suppose the Chinese government now instead auctions off quotas for importing a commodity and determines the total import quotas to equal the quantity that would be imported under the tariff. Then, given an upward sloping supply curve, the proceeds to the government from the sale of import quotas will equal the amount it would collect under the tariff. I C. Long Questions: 1. The Spanish movie Los Lunes al Sol (Mondays in the Sun) is about a number of shipbuilders who have lost their jobs when the the shipyard was closed. In the movie, one worker remarks that with lower-cost international competition (particularly from South Korea), closure was inevitable. Another counters that the union actually was willing to accept lower wages so that the firm could be competitive, but the ﬁrm insisted on closing the yard because it wanted to build condominiums on the waterfront real estate. Suppose the concessions that the union was willing to make could have brought wages for Spanish workers down to the Korean level, and that there is no difference in shipbuilding ’ technology between the two countries. a.(6 points) If competing Korean ﬁrms have been economically profitable (in the sense that they are making non—negative profits), would it have been profitable for the shipyard to continue production? ' b.(7 points) Suppose the Spanish government steps in and tells the ﬁrm that the shipyard cannot be redeveloped for other uses. Would it then be proﬁtable for the shipyard to ' continue production? c.(7 points) Suppose instead the Spanish government dictates‘that the shipyard cannot be closed without the consent of the union (which supposedly represents the interest of all workers). Will the shipyard be closed in this case? Why or why not? 2. Attendance at the Chicago-Bulls’ home games depends on the number‘of games the team wins per season and on the price of the tickets. Suppose the demand for tickets for the Bulls’ home games is ' ' 43 = NB (20 “173) where qB = the number of tickets (in hundred thousands) sold per year, 19;; is the price per ticket to a Bulls game, and N3 = the percentage of games won by the Bulls. The team can increase the number of games it ‘wins by hiring better players. Let CB represents the team’s expenditure (in million dollars) on players’ salaries. Over the relevant range, marginal cost of selling an extra ticket is zero. I a. (12 points) Suppose if the team spends CB on players, then it will win a fraction .7 -— l/CB of its games.(where CB > 1/.7). If you were the owner of the Bulls, what are your choice variables? How much will you spend on players? What will be the price that you Charge for tickets and how many will be sold? What will be the winning percentage of the Bulls? b. (18 points) Suppose instead of the winning ratio speciﬁed in part a, the fraction of games that the Bulls‘win depends on the other teams’ spending on players as well.. Suppose, for simplicity, that there is only one other team, the Lakers, in the league, which faces the following demand for tickets for their home games: ' qL = NL (20 —PL), where qL = the number of tickets to Lakers home games, pL 2 price per ticket to a Lakers game, and NL = the percentage of games won by the Lakers. If the Lakers- spend CL on ‘ players, then the winning ratio of each team is given by ' ' 1 N, = C/( C3 + CL), 1': B,L. Derive each team’s reaction function, given the other teams’ spending on players, and calculate each team’s profit maximizing ticket price, spending on players and winning ratio of each term in a Nash equilibrium. - End of Paper - ...
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