JM Exams 2004 - Economics 111 Exam 1 Fall 2004 Prof...

Info iconThis preview shows pages 1–21. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 12
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 14
Background image of page 15

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 16
Background image of page 17

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 18
Background image of page 19

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 20
Background image of page 21
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Economics 111 Exam 1 Fall 2004 Prof Montgomery Answer all questions. Explanations may be brief. 105 points possible. 1. (30 points) Consider a small country with 3 factories. Each factory can produce guns or butter or both. The table below reports, for each factory, the potential output per hour for each good, and the number of hours of production per week. number of guns pounds of butter hours of production that could be that could be per week produced per hour produced per hour factory I 4 4 80 factory 2 3 5 40 factory 3 10 6 40 a. Derive and plot the (weekly) production possibilities curve for each factory. [HINT2 Graphs don’t need to be perfect, but should be clearly labeled, and you should give the horizontal and vertical intercept on each graph.] Comparing factories 2 and 3, which factory has the comparative advantage at producing butter? b. Factory production in this country is determined by a government official. He has currently ordered factory I to split its production time evenly between the two goods (spending 40 hours/week producing each good), while ordering factories 2 and 3 to produce only butter for 40 hours/week. Is this plan efficient? Briefly explain. Holding constant the country’s current production of guns, what is the maximum amount of butter that could have been produced? How should you set production at each factory in order to achieve this outcome? 0. The government official now decides that the country should produce 3 guns for every 1 pound of butter. Given this required ratio of guns to butter, what is the maximum number of guns and pounds of butter that can be produced? How would you set production at each factory to achieve this outcome? 2. (15 points) Suppose that com is an inferior good, that wheat is a substitute for corn, and that fertilizer is a factor used in corn production. For each of the following cases, what will be the effect on the supply and demand for corn, and the equilibrium price and quantity of corn? Illustrate each case with an appropriate supply-and-demand diagram. [HINTz Obviously, you’ve been given no numerical information. I’m merely looking for qualitative effects] a. An increase in consumer income. b. An increase in the price of wheat. c. A decrease in the price of fertilizer. 3. (30 points) A consumer spends her income on goods 1 and 2. Both goods are normal goods for this consumer. Suppose that, as part of a new marketing campaign, the makers of good 1 offer 5 free units of good 1 to any consumer who purchases at least 20 units of good 1. (Consumers can receive the free units only once. Thus, even if she buys 40 or 60 units, the consumer still receives only 5 free units.) a. Draw the consumer’s budget constraint before and after this offer. [HINT: You don’t have enough information to derive the equations for these curves, but your graph should use the information that you were given. Note that the marketing campaign does not alter the price of good 1.] b. If the consumer initially purchased more than 20 units, how will this offer affect the number of units of good 1 that she now purchases (net of the 5 free units)? Briefly explain. Be sure to note any relevant income and substitution effects, and illustrate your answer with a budget constraint / indifference curve diagram. 0. If the consumer initially purchased slightly less than 20 units, how will this offer affect the number of units of good 1 that she now purchases (net of the 5 free units)? Briefly explain. Again, illustrate your answer with the relevant diagram. 4. (30 points) You are the manager of a factory that produces output according to the production function Q=«/—KZ where K is the number of units of capital, and L is the number of units of labor. Further assume that the price per unit labor is w = 1, that the price per unit capital is r = 4, and that the firm has no fixed costs. a. Depending on demand for the firm’s output, you may be instructed by corporate headquarters to produce either Q = 20 or Q = 30 or Q = 40 units of output. For each of these three cases, find the cost-minimizing method of production. [HINT: You can use the equation for each isoquant to solve for the amount of capital that must be hired given some amount of labor. If you solve this problem by constructing a table, you might consider increasing labor in increments of 10 units.] For each case, give the optimal number of units of K and L that you would hire, and the total cost that you would incur. Using this information, plot the total cost curve and marginal cost curve for your factory. Does this factory have increasing, decreasing, or constant marginal costs? b. Suppose that the price of labor (w) rises. Qualitatively (using the relevant graph without doing any more numerical computation), how would this affect the cost- minimizing method of production at each output level? How would this affect the total cost and marginal cost curves? Econ 111 Exam 1 Fall 2004 Solutions la. [10 pts] Let g represent the number of guns, b represent the pounds of butter, and tg and tb represent time spent in the production of each good. For factory I, g = 4tg and b = 4th and tg + tb = 80. Substituting the first two equations into the time constraint, we obtain g/4 + b/4 = 80, which can be rewritten as g = 320 —- b, which is the equation for factory 1’s PPC. Equations for the PPC’s for factories 2 and 3 can be derived in the same way. Thus, we obtain the PPCs: g = 320 — b for factory I g = 120 — (3/5)b for factory 2 g = 400 — (5/3)b for factory 3 Plotting these PPCs, we obtain g g 400 320 factory I factory 2 factory 3 120 320 b 200 b 240 b [Note that, even without solving for the equations for the PPCs, you could have found the intercepts very easily by multiplying potential output by hour by the number of hours of production for each factory. For example, factory 2 could produce at most 3x40 = 120 guns and 5x40 = 200 pounds of butter.] Comparative advantage is determined by the relative slopes of the PPCs, so factory 2 has the comparative advantage at producing butter. b. [10 pts] This plan is not efficient. Comparing factories l and 3, factory 3 has the comparative advantage at producing guns. So factory I should never produce guns unless factory 3 is already completely specialized in gun production. Given that factory 3 is currently producing all butter, it would be more efficient to shift the production of guns from factory I to factory 3. Given the current (inefficient) plan, total gun production is 4x40 = 160 and total butter production is 4x40 + 200 + 240 = 600. If production of the 160 guns was shifted from factory I to factory 3, then factory 3 could still produce 144 pounds of butter. Factories 1 and 2, now specialized completely in butter production, could produce 320 + 200 pounds of butter. In this way, the country could produce 160 guns and 664 pounds of butter. 1c. [10 pts] Comparing the slopes of the PPCs, efficiency requires that any production of guns should first be assigned to factory 3, and then (after factory 3 is completely specialized) to factory 1, and then (after factory I is completely specialized) to factory 2. If factory 3 specialized in guns while factories 1 and 2 specialized in butter, the ratio of guns to butter would be (400)/(320+200) = .769. Given the required ratio of 3, we would need to produce more guns. If factories 3 and 1 specialized in guns while factory 2 specialized in butter, the ratio of guns to butter would be (400 + 320)/200 = 3.6. So now we need to produce fewer guns. Thus, faCtory 3 should specialize in guns, factory 2 should specialize in butter, and factory I should produce some of each. More precisely, factory I should produce b pounds of butter where b is given by (400 + (320 — b))/(2OO + b)) = 3. Solving this equation, we find that factory 2 should produce b = 30 pounds of butter (and hence g = 320 — 30 = 290 guns). Thus, total production of guns is 400 + 290 = 690, total production of butter is 200 + 30 = 230, and the ratio of guns to butter is 690/230 = 3. [Note that parts b and c might also have been approached graphically, using the country’s overall PPC. The overall PPC is found by “adding” the factory PPCs in the same manner that we added the husband’s and wife’s PPCs to find the overall household PPC in class. Note that the overall PPC is not linear; the slope of each segment corresponds to the slope of an individual PPC. Given the country’s overall PPC, parts b and c essentially asked you to find the point on this PPC that satisfies some condition (the condition g = 160 in part b; the condition g = 3b in part c). Graphically, 840 400 g=160 200 520 760 butter Q1* Q0* Q If corn is an inferior good, an increase in consumer income will shift the demand curve to the left, decreasing equilibrium price from P0* to P1* and decreasing quantity from Q0* to Q1*. 2b. [5 pts] Q0* Q1* Q If wheat is a substitute for corn, an increase in the price of wheat will shift the demand for corn to the right, increasing price from P0* to P1* and increasing quantity from Qo* to Q1*- 2c. [5 pts] 620* Q:1* Q If fertilizer is a factor used in corn production, an decrease in the price of fertilizer will reduce the marginal costs of farmers, shifting the supply curve downwards, decreasing price from P0* to P1* and increasing quantity from Qo* to Q1*. 3a. [8 pts] 3b. [12 pts] III Ill-ll. Initially, the consumer’s budget constraint is given by the solid line. Given the market campaign, the lower part of the budget constraint shifts outward by 5 units, so that the budget constraint follows the solid line until x1 = 20, and then follows the dotted curve. Because good 1 is a normal good, the quantity of good 1 consumed will rise (from a to b). However, subtracting the 5 free units, the quantity of good 1 purchased will actually fall (from a to b—5). Intuitively, because good 2 is also a normal good, the consumer must be purchasing more good 2, and hence spending less on good 1. The marketing campaign generates a pure income effect because it causes a parallel shift of the budget constraint. There is no substitution effect because relative prices have not changed. 3c. [10 pts] If the consumer initially purchased slightly less than 20 units, she will probably now be at a corner solution — buying just enough good 1 to receive the 5 free units. Thus, there is an increase in both consumption (from a to 25) and purchase (from a to 20) of good 1. a 20 25 x1 4a. [20 pts] Given the required production level Q, we may rewrite the production function as K = Q2/ L to obtain K as a function of L. For each possible level of L, we can then determine required capital (K = Q2 / L) and the total cost (TC = wL + rK = L + 4K). For the three cases under consideration, Q=2o Q=30 Q=40 L K TC L K. TC L K TC 10 40 170 10 90 370 10 160 650 20 20 100 20 45 200 20 80 340 30 1333 8333 30 30 150 30 5333 24333 40 1o 80* 40 225 130 40 40 200 50 8 82 50 18 122 50 32 178 60 666 8666 60 15 120* 60 2666 16666 70 12.86 121.43 70 22.86 161.43 80 1L25 125 80 20 160* 90 17.77 161.11 100 16 164 The asterisks denote the minimum total cost in each table. Thus, your cost-minimizing production plans would be Q=20 —) L=40,K=10,TC=80 Q=30 -—) L=60,K=15,TC=120 Q=40 —> L=80,K=20,TC=16O The total cost curve gives TC as a function of Q (given that the firm is using the cost- minimizing method of production). The marginal cost curve shows the slope of the TC curve at each level of Q. $ Tch) $ 160 120 80 4 MC(Q) 20 30 40 Q Q Given that MC = ATC/AQ = 40/ 10 = 4, this factory has constant marginal costs. 4b. [10 pts]- An increase in the wage would cause the factory to substitute toward capital. Plotting an isoquant (with K on the horizontal axis and L on the vertical axis), this increase in w would cause the isocost curves to become flatter, and the factory would move along the isoquant from a to b. Both total costs and marginal costs would be higher at each output level, so those curves would both shift upwards. Q constant K [It would have been possible to use calculus to solve part a. The plant manager’s problem is to choose K and L to minimize wL + rK given Q = VKL . where w, r, and Q are constants. Substituting the constraint (rewritten as K = QZ/L) into the objective function (wL + rK), the problem becomes choose L to minimize wL + rQZ/L. Differentiating with respect to L, we obtain the condition w — rQZ/ L2 = 0 which can be rewritten as L = Q JH—w . In the current problem, r/w = 4, so this becomes L = 2Q which implies K = Q2/2Q = (1/2)Q and thus TC = wL + rK = (1)(2Q) + (4)(1/2)Q = 4Q. The marginal cost function MC(Q) = TC’(Q) = 4.] Economics 111 Exam 2 Prof Montgomery Fall 2004 Answer all questions. Explanations can be brief. 100 points possible. 1. [18 points] Suppose that a hospital is a monopsonist, being the only employer of nurses in the local labor market. Further assume that the market supply curve for nurses is upward sloping, while the hospital’s demand curve for nurses is downward sloping. (Recall that the height of the labor demand curve reflects the value of the marginal product of labor — that is, the firm’s monetary gain from the last worker hired.) a) Using a graph, explain how the hospital determines the optimal number of nurses to hire and the wage paid. [HINT: Your graph should be clearly labeled, and should show the supply curve, demand curve, and marginal cost of labor curve.] Is the marginal cost of labor curve above, below, or the same as the supply curve? Explain. b) Using your graph, compare the outcome that would have been generated by a competitive market to the outcome chosen by the monopsonist. Is the wage higher or lower under monopsony? Is the number of workers hired higher or lower under monopsony? Is total surplus (producer surplus + worker surplus) higher or lower under monopsony? Identity any deadweight loss on your graph. 2. [32 points] Consider a market with demand curve p = 360 — 3Q. a) Suppose that this market is monopolized by a firm that can produce costlessly (and hence has zero marginal costs). Derive the monopolist’s optimal quantity, the price it charges, and the profit that it receives. b) Now suppose that two firms (a “duopoly”) face this market demand. Both firms choose quantities simultaneously, and then price adjusts to clear the market given the total quantity produced (Q = Q1 + Q2). Assume that both firms can produce costlessly. Derive each firm’s optimal quantity, the market price, and the profit received by each firm. 0) Now suppose that three firms (a “triopoly”) face this market demand. All firms choose quantity simultaneously, and then price adjusts to clear the market given the total quantity produced (Q = Q1 + Q2 + Q3). Assume that all firms produce costlessly. Derive each firm’s optimal quantity, the market price, and the profit received by each firm. [HINT: You should first derive the reaction function for one firm, viewing the quantities chosen by other firms as constants. Deriving all 3 reaction functions, you would have a system of 3 equations with 3 unknowns. But recognizing the symmetry of the problem (which implies that all firms will choose the same quantity in equilibrium), you could simply use any one reaction function along with the condition that Q = Q2 = Q3 = (1/3)Q.] d) Intuitively, what happens to each firm’s optimal quantity, the market price, and the profit received by each firm as the number of firms becomes very large? 3. [18 points] Political scientists sometimes view rulers (e. g., kings or dictators) as revenue maximizers who attempt to extract as much wealth as possible from their subjects. In a country governed by this kind of ruler, suppose that an entrepreneur can decide either to undertake or not undertake a new business venture. If the entrepreneur does undertake this venture, she would earn revenue = 4 and incur cost = 1. If she does not, she earns revenue = 0 and incurs cost = 0. Further suppose that, after the entrepreneur makes her choice, the ruler can either confiscate all of the entrepreneur’s revenue or else confiscate half of the entrepreneur’s revenue. The entrepreneur’s payoff is equal to the amount of revenue not confiscated by the ruler, minus any cost incurred. The ruler’s payoff is equal to the amount of revenue confiscated from the entrepreneur. a) Use a game-tree diagram to show the possible sequences of actions and the resulting payoffs for each player. [Payoffs should be written in the form (payoff for entrepreneur, payoff for ruler).] Using backward induction (“rollback”), explain what outcome will occur in this game. Further explain how the outcome could be more efficient if the players were able to make credible commitments to take (or not to take) some actions. b) Conceptually, how and why might the outcome of the game (without commitment) change if there was (infinitely) repeated interaction between the ruler and entrepreneur? 4. [20 points] An insurance company is deciding whether to offer dental insurance to 6000 university employees, and if so, the yearly price (p) at which the company should offer the insurance. Suppose there are three types of employees: 1000 “high use” employees who would each be willing to buy insurance if p S $1,500, and would each generate expected costs of $1,300 for the insurance company; 3000 “medium use” employees who would each be willing to buy insurance if p .<. $1,000, and would each generate expected costs of $800for the company; 2000 “low use” employees who would each be willing to buy insurance if p 5 $500, and would each generate expected costs of $400 for the company. While the insurance company might be able to distinguish between these different types of employees (perhaps by requiring dental exams before issuing policies), the company has been told by the university that it cannot charge different prices to different employees. Thus, if the company offers insurance at all, every employee must be offered insurance at the same price p. Each employee would then decide for themselves whether or not to buy at this price. For each price p that the company might set, determine the company’s expected cost per policyholder. What price maximizes profit (= price — expected cost) per policyholder? What price maximizes total profit (= expected profit per policyholder X number of policyholders)? Should the firm offer insurance? At what price? Which employees benefited from the university’s rule that the company could not set different prices? Which employees were hurt? 5. [12 points] The city council has recently debated whether to outlaw smoking in all bars and restaurants. Some proponents have argued that regulation is necessary because restaurant workers are harmed by second—hand smoke. What alternative solution would be suggested by the Coase Theorem? Why is (or isn’t) this solution viable? Econ 111 Exam 2 Fall 2004 Solutions 1) Note that monopsony is discussed in the appendix to Chapter 12, and that this question could be answered directly from that discussion. a) [12 pts] marginal cost of labor w (wage) labor supply labor demand L* Lc L (number of nurses) The hospital will hire nurses until the marginal cost of labor is equal to the value of the marginal product of labor. Graphically, this point is determined by the intersection of the marginal cost of labor curve and the labor demand curve. Thus, the hospital hires L* nurses and pays the wage w*. As shown on the diagram, the marginal cost of labor curve is above the labor supply curve. Intuitively, to hire an additional nurse, the hospital must not only pay that additional nurse, but also pay more to all the other nurses hired. [Note the analogy to the monopolist’s problem: the marginal revenue curve is below the demand curve because, in order to sell an additional unit, the firm must cut the price sold on all previous units.] b) [6 pts] In a competitive market, price and quantity are determined by the intersection of the supply and demand curves. Using the graph above, the wage would be w° and the quantity of labor supplied would be LC. Thus, both the wage and the quantity of labor supplied is lower under monopsony: w* < wc and L* < LC. Total surplus is also lower under monopsony, since there is deadweight loss equal to the area of the triangle bounded by the demand curve, the supply curve, and the (dotted) horizontal line at L*. 2a) [9 pts] The monopolist would set quantity Q so that MR(Q) = MC(Q) which implies 360 — 6Q = 0 and hence Q = 60 p= 360—3Q = 360—3(60) = 180 n = pQ = (180)(60) = 10,800 b) [10 pts] Taking firm 2’s quantity Q2 as constant, the residual demand curve facing firm 1 is given by p = 360 — 3Q1 — 3Q2. Thus, firm 1’s marginal revenue is equal to MR1 = 360 — 3Q2 — 6Q1. Firm 1 chooses quantity by setting MR1(Q1) = MC1(Q1) which becomes 360 — 3Q2 — 6Q1 = 0. Rewriting this equation, we obtain firm 1’s reaction function: Q, = 60 — (1/2)Q2. In the same way, we can derive firm 2’s reaction function: Q2 = 60 - (1/2)Q1. The Nash equilibrium is determined by the intersection of the two reaction functions. Algebraically, we can substitute one reaction function into the other, obtaining Q = 60 — (1/2)[60 — (1/2)Q1] which implies Q1 = 40 and hence Q2 = 60—(1/2)(40) = 40. Price p = 360—3(40+40) = 120, and profit for each firm is 1: = (120)(40) = 4,800. c) [10 pts] Taking the outputs of firms 2 and 3 as constant, the residual demand curve facing firm 1 is p = 360 — 3Q1 — 3Q2 — 3Q3, and thus firm 1’s marginal revenue is equal to MR1 = — 3Q2 - 3Q} — 1 sets Q1 SO that = MC1(Q1), 360 — 3Q2 — 3Q3 — 6Q1 = 0. Rewriting this equation, we obtain firm 1’s reaction function: Q = 60 — (1/2)Q2 — (1/2)Q3. There are now several ways to solve for the Nash equilibrium. One strategy is to solve for the other two reaction functions. You would then have a simultaneous equation system with 3 equations and 3 unknowns that could be solved to find the Qi’s. Alternatively, given the symmetry of this problem, it is clear that every firm will choose the same quantity in equilibrium. Thus, given Q1 = Q2 = Q3 = (l/3)Q, substitution into firm 1’s reaction fimction yields (1/3)Q = 60 —- (1/2)(1/3)Q — (1/2)(1/3)Q which implies Q = 90 and hence Q1 = Q2 = Q3 = 30. Thus, p = 360 — 3(90) = 90, and profit for each firm is 1t = (90)(30) = 2700. d) [3 pts] As the number of firms continues to rise, the quantity per firm, price, and profit per firm will fall to 0, while total quantity will rise toward 120. Intuitively, this is the outcome that would be generated by a perfectly competitive market (given the assumed market demand curve, and infinitely elastic supply at price p = 0). [Formally, given Coumot competition with n firms, firm 1’s reaction function becomes Q = 60 — (1/2)(Q2+Q3+. . .+Qn). Given the symmetry of the problem, each of the Qi’s will equal Q/n in equilibrium. Substituting into firm 1’s reaction fimction, we obtain Q/n = 60 — (1/2)(n-1)(Q/n) which implies total quantity = Q = (120)[n/(n+1)] market price = p = 360 — 3Q = 360/(n+1) profit per firm = n = 43200/(n+1)2 ] 3a) [12 pts] entrepreneur 0,0 Solving this sequential game using backward induction (“rollback”), we first consider what would happen if the entrepreneur does undertake the new venture. Because he would prefer 4 rather than 2, the ruler would confiscate all of the entrepreneur’s revenue. Thus, the entrepreneur realizes that, if she undertakes the venture, she will receive —1. Because this is worse than 0, the entrepreneur will choose to not undertake the new venture, and both players will receive payoffs of zero. Both players could obtain better outcomes if the ruler could commit to take only half (or, equivalently, if the ruler could commit not to take all) of the entrepreneur’s revenue. Perhaps counterintuitively, the ruler would be better off in this game if he was less powerful — if he was not able to seize all of the revenues for himself. b) [6 pts] If this game was repeated indefinitely, the two players might be able to sustain the good outcome (i.e., entrepreneur undertakes new venture, then ruler confiscates only half). Suppose the entrepreneur undertakes the first new venture, and then continues to undertake new ventures if and only if the ruler has never confiscated all of the revenue on previous ventures. Given that the entrepreneur is following this type of “trigger strategy,” the ruler will prefer to confiscate only half if the present value of his stream of future benefits (= 2 + B2 + [322 + [332 + ...) exceeds the value of confiscating everything today and then receiving no future benefits (= 4). This will occur when the ruler places enough weight on future outcomes — when his discount factor ([3) is close enough to 1. 4) [20 pts] If the company sets p > 1500, no employees will buy insurance. If the company sets price between 1000 and 1500 (i.e., 1000 < p S 1500), only “high use” employees will buy, and expected costs per policyholder will be $1300. If the company sets price between 500 and 1000 (i.e., 500 < p S 1000), both “high” and “medium” employees will buy, and expected coSts per policyholder will be (1000/4000)(1300) + (3 000/4000)(800) = $925. (Note that the expected costs are weighted by the proportion of each type of employee among all employees who will buy.) If the company sets p S 500, all employees will buy, and expected costs per policyholder will be (1000/6000)(1300) + (3000/6000)(800) + (2000/6000)(400) = $750. (Again, expected costs are weighted by the proportion of each type of policyholder.) For each price p, the company’s expected profit per policyholder would be p—Ec(p) where Ec(p) is expected cost given price p (as derived above). Thus, p=500 —) p—Ec(p) = 500—750= —250 I): 1000 —) p—Ec(p) = 1000—925=75 P: 1500 —) p—Ec(p) = 1500—1300=200 Total profit = (profit per policyholder x number of policyholders). Thus, p = 500 —> —250 x 6000 = —1,500,000 p = 1000 —) 75 x 4000 = 300,000 p = 1500 —> 200 x 1000 = 200,000 Yes, the firm should offer insurance at price p = 1000. If allowed to set different prices for different types of consumers, the company would have charged 1500 to high-use employees, 1000 to medium-use employees, and 500 to low-use employees. Thus, the university’s rule benefits high-use employees (increasing each employee’s consumer surplus by 500). [Low-use employees will not buy insurance at price 1000, but aren’t really hurt by the university’s rule, given that the (monopolist) insurance company would have charged them their full willingness to pay.] 5) [12 pts] The Coase Theorem suggests that government regulation is not needed to solve externality problems. Assuming that bargaining is costless, the government merely assigns property rights, and then the parties themselves negotiate an efficient solution. In the present example, smoking by restaurant customers generates negative extemalities for restaurant workers (and for other customers). But rather than simply outlaw smoking in restaurants, the city council might assign property rights to the customers or to the workers (or to the restaurant owners). For instance, if property rights were assigned to workers, the customers would have to pay workers for the right to smoke. Conversely, if the rights were assigned to customers, the workers would have to pay the customers not to smoke. After negotiation, smoking would occur if and only if the disutility to workers is less than the utility to customers. Trying to imagine how this property-rights solution would work in practice, critics of the Coase Theorem might argue that bargaining costs would be prohibitive. Obviously, it would be difficult and time-consuming for customers to negotiate with workers every time they went out to eat. Even more crucially, if smoking affects every customer and worker in the restaurant, any negotiation would need to include all of these parties. On the other hand, if property rights are assigned to restaurant owners (which is essentially the situation before regulation), a “market solution” to the extemality problem may seem more Viable. Each owner could choose whether to allow smoking, adjusting prices and wages accordingly, without need for costly bargaining. (Presumably, owners who allow smoking will need to pay higher wages to attract workers and will thus set higher prices for customers. Given free entry in the restaurant market, customers could choose their preferred combination of smoking/non-smoking and price.) Some economists would argue that government regulation in this case would be overly “paternalistic” because some workers might (rationally?) be willing to inhale second- hand smoke in exchange for higher wages. Economics 111 Fall 2004 Exam 3 Prof Montgomery Answer all questions. 1 00 points possible. Explanations can be brief 1) [15 points] A small economy has three industries producing goods X, Y, and Z. Some of the output of each industry is sold to other industries (as intermediate goods) while the remainder is sold to final consumers. In addition to purchasing goods from other industries, firms in each industry also pay wages to workers. Any profits are paid out to shareholders. The following table lists revenues and costs for each industry. [HINT: Note that purchases are reported in dollars, not units of output] industry X industry Y industry Z revenues: $ 2200 $ 3100 $ 1800 costs: purchases of X $ 500 $ 100 purchases of Y $ 200 $ 600 purchases of Z $ 900 wages $ 1500 $ 400 $ 500 Compute the Gross Domestic Product (GDP) for this economy using (a) the final goods approach, (b) the value-added approach, and (c) the income approach. [HINT: You must give the details of each computation to receive credit for this problem, labeling terms to demonstrate that you understand each approach] 2) [18 points] Define the federal funds rate and the discount rate. Which rate does the Fed set directly? For which rate does the Fed set a target? What action would the Fed take if this rate began to move above the Fed’s target? Explain how this action would affect the rate, using the relevant supply—and-demand graph. 3) [18 points] Consider the full employment model for an open economy. Suppose that an improvement in technology causes the full-employment output level (I7 ) to rise. List the changes (if any) that would occur in macroeconomic flows (given by the edges of the circular flow diagram), the interest rate (r), and the exchange rate (e). Briefly discuss, using the relevant supply—and-demand graphs for the capital and/or foreign-exchange markets. [HINT: Assume that imports depend only on e, while domestic consumption depends positively on Y and negatively on e.] 4) [12 points] Briefly discuss “efficiency wage” models, and then briefly explain why these models are relevant for macroeconomics. 5) [25 points] Consider the unemployment model for a closed economy. Suppose that consumption is C = 15 + (.75)(1-'c)Y private savings are Sp = —15 + (.25)(l-t)Y tax revenue is T = TY investment is I = 40 government spending is G = 90 where T is the tax rate and Y is income. a) Assuming T = .25, solve for the equilibrium level of income. Is the government running a budget surplus or budget deficit? How large is this surplus or deficit? b) Suppose that the government decides to balance its budget by altering its spending (G) while holding the tax rate constant at r = .25. Find the new equilibrium level of income, and the new level of government spending. 0) To balance its budget in a different way, the government might have altered the tax rate (I) while holding its spending constant at G = 80. If the government had balanced its budget in that way, what would have been the equilibrium level of income? What would have been the new tax rate? 6) [12 points] Suppose that the President is more likely to be re-elected when both unemployment is low and inflation is low. Further suppose that voters merely consider current unemployment and inflation, ignoring longer-run impacts of current monetary policy. Using the ADI-AS framework, explain why the Federal Reserve should not be placed under direct presidential control. If the Fed was under the President’s direct control, what actions would you expect a President to take in the short run (while running for re—election) and the long run (after winning re-election, assuming that he wants his party to win the next election)? Econ 111 Exam 3 Fall 2004 Solutions Note: I added 1 extra point to each part of Q1 , so the exam was worth 103 points total. 1a) [6 pts] GDP = sum of value of final goods produced by each industry = (2200-600) + (3100-800) + (1800-900) = 1600 + 2300 + 900 = 4800 b) [6 pts] GDP = sum of value-added by each industry = (2200-200) + (3100-1400) + (1800-700) = 2000 +1700 +1100 = 4800 c) [6 pts] GDP = sum of wages and profits* paid by each industry = (1500 + 500) + (400 + 1300) + (500 + 600) = 2000 +1700 +1100 = 4800 (*recall that profit = revenues - costs) 2) [18 pts] The federal funds rate is the interest rate that banks charge each other for borrowing reserves. The discount rate is the interest rate that the Fed charges when it loans reserves to banks. The Fed sets the discount rate directly, and sets a target for the federal funds rate (currently, in Dec 2004, the target is at 2%). If the federal funds rate began to move above this target, the Fed would increase the supply of reserves by purchasing T-bills. By increasing the supply of reserves, the Fed would cause the federal funds rate to fall back toward the target level. Graphically, an initial increase in the demand for reserves (from Do to D1) would increase the equilibrium federal funds rate above the target level (say 2%); the Fed would increase the supply of reserves (from Soto S1) to decrease the rate back to the target level. federal funds rate 2% ....................................................................... .. quantity of reserves 3) [18 pts] It may be helpful to refer to the circular flow diagram as you solve this problem. An increase in 7 would increase disposable income, and hence cause domestic consumption (Cd) and private savings (Sp) and tax revenue (T) to rise. [By the assumption given in the hint, imports (M) do not depend on Y.] The increase in T would cause government savings (Sg) to rise. The increases in both Sp and Sg would shift the supply of savings to the right and hence cause the equilibrium interest rate (r) to fall. r sp 4 5g + NCF(r) ——> capital market 1(r) —___—_____—_._————> 8,1 The decrease in the equilibrium interest rate would cause net capital flows (N CF) to decrease, shifting the demand for dollars to the left, thus decreasing the equilibrium exchange rate (6). M(e) foreign exchange market X(e) + NCF(r) $ This decrease in the exchange rate would cause imports (M) to fall and exports (X) to rise. (By the assumption given in the hint, it would also cause Cd to rise further.) 4) [12 pts] Efficiency-wage models assume that worker productivity is an increasing function of the wage. This effect might occur for several reasons: firms paying higher wages may have lower turnover, be more likely to retain hi gher—ability workers, might provide more incentive to keep workers from “shirking,” or might induce greater employee morale (if worker effort depends on the perceived “fairness” of the wage). If productivity depends on the wage, then the optimal wage paid by the firm may not be very responsive to labor-market conditions. Thus, efficiency-wage model may help explain why wages are “sticky,” failing to fall during recessions when unemployment is high. ' 5a) [9 pts] Equilibrium Y is determined by the equation Y = c + 1+ G Y =15 + (.75)(1-.25)Y + 40 + 90 Y = [1/(1—(.75)(1-.25))][15 + 40 + 90] Y= 331.43 Tax revenue is thus T = (.25)(331.43) = 82.86, and the government has a budget deficit equal to G — T = 90 — 82.86 = 7.14. b) [8 pts] A balanced budget requires G = TY. Holding the tax rate fixed at T = .25, the government obtains a balanced budget by setting G = (.25)Y. Equilibrium Y is ' determined by the equation Y = c + I + G Y = 15 + (.75)(1-.25)Y + 40 + (.25)Y Y = [1/(1 — (.75)(1-.25) — .25)][15 + 40] Y = 293.33 In equilibrium, G = 1: Y = (.25)(293.33) = 73.33 c) [8 pts] Again, a balanced budget requires G = TY. Holding spending fixed at G = 90, the government obtains a balanced budget by setting I = 90/Y. Equilibrium Y is determined by the equation Y = C + I + G Y = 15 + (.75)[1-(90/Y)]Y + 40 + 90 Y = 15 + (.75)(Y—90) + 40 + 90 Y = [1/(1—.75)][15 - (.75)(90) + 40 + 90] Y= 310 In equilibrium, T = 90/310 = .29 6) [12 pts] Suppose that the Fed was under direct Presidential control. By adopting a “looser” monetary policy (shifting the Fed’s monetary policy rule downwards), the President could cause the ADI curve to shift to the right. In the very short run, this would cause output to rise (and unemployment to fall) without any immediate effect on inflation. Graphically, on the ADI-AS diagram, the economy moves from point A to point B. Voters (who, by assumption, care only about current inflation and unemployment) would feel better off, and would thus be more likely to re-elect the incumbent President. However, in the longer run (following the election), inflation would begin to rise. Graphically, the economy begins moving up the ADI to point C. To bring inflation back down to its original level, the President would need return to the original “tighter” monetary policy (shifting the Fed’s policy rule back upwards), causing the ADI curve to shift back to the left. This would move the economy from point C to point D. By temporarily inducing a recession (with income below the full-employment level), this tighter monetary policy would gradually bring inflation back down to its original level (hopefully in time for the next election). Thus, direct presidential control of the Fed might lead to “political business cycles” with booms just before elections and recessions during the mid-term. TC TC Z 7T Fed’s rule (tighter) r equilibrium Y given r % (looser) ...
View Full Document

This note was uploaded on 08/08/2008 for the course ECON 111 taught by Professor Montgomery during the Spring '08 term at University of Wisconsin.

Page1 / 21

JM Exams 2004 - Economics 111 Exam 1 Fall 2004 Prof...

This preview shows document pages 1 - 21. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online