Exercise #1. A firm produces output using the technology y= -KLi, 1,000 where capital, K, is measured in machine-hours, labor, L, is measured in person-hours, and y denotes the yearly output. The hourly wage rate wy = 10, and the hourly rental rate of capital is Wk = 20. (a) Show that this technology displays increasing returns to scale. (b) Compute the marginal products of labor and capital. (c) Suppose that at the end of 1999 the firm has signed a contract to rent K = 1,000 machine hours over the course of the year 2000. Derive the firm's short run cost function in the year 2000. (d) What is the firm's short run marginal cost function? What is the firm's short run average cost function? At which point do these two curves intersect? (e) On a diagram plot the firm's short run average and marginal cost curves. Exercise #2. The aggregate labor supply in the state of Bahnanas is Ls = 2,000w, where w is the hourly wage, measured in Bahnanas $ and L, denotes the number of person- hours supplied by the workers of Bahananas in a year. The aggregate labor demand in the state of Bahananas is La = 12,000 - 2,000w, where La denotes the number of person-hours demanded by the firms of Bahnanas in a given year. (a) Compute the equilibrium hourly wage and the amount of hours worked in a given year. (b) The government of Bahnanas introduces a minimum wage law requiring firms to pay an hourly wage not lower than $4. Compute the equilibrium number of hours worked by the workers of Bahnanas. (c) On a diagram that has the wage rate on the y-axis and the number of hours on the x-axis, plot the labor demand and supply functions and the equilibrium prices and quantities that you found in points (a) and (b). (d) Compute the deadweight loss induced by this policy, and show it on the diagram of point (c). Exercise #3. Short questions. (a) Compute the price and income elasticities of the following demand function I'd (p.m) = 2p (b) A firm produces output, denoted by y, using the following production function y = 10VL, where L represents the labor input, measured in person-hours. The unit price of output is $10. Let w denote the hourly wage rate. Compute and plot on a diagram the inverse labor demand curve for the firm. (c) Explain how it can be possible that as tax rates decrease, government tax revenues increase (i.e. the Laffer curve).Exercise #1. The supply ofprivate apartments for rent around Chill is given by the following function '35 = lm. where Q3 denotes the quantity of apartments supplied in a given year. The yearly demand for apartments is given by QD = 1., mm _ PI. where Q1: denotes the quantity of apartments demanded in a given year and 1] denotes the monthly rent for one apartment. {a} [5 pts.] Find the equilibrium price and quantity in this market. {b} [10 pts.] The university enacts a policy that subsidiaes rent for students that decide to rent a private apartment around CM'U. Specically, the university will subsidize rent by paying 31m to a student every time hefshe shows a receipt of monthly rent payment signed by a landlord. lIEompute the equilibrium prices and quantity in this case. [Hint there wiii ire two prices. One paid by the student out ofhisfher cum pocket, p5, and the other received by the seiner of the apartment, P3r with Pa = P3 l] {c} [1|] pts.] [in a diagram that has quantity of apartments on the x-axis and the monthly rent on the y-axis, draw the inve1se demand and supply curves and mark the equilibrium prices of points {a} and {b}. {d} [15 pts.] Compare the equilibrium in [all with the equilibrium in {h}: i} what is the change in consumer's surplus induced by the policy of the university? ii} \"that is the change in supplier's surplus? iii} How much does the university spend to subsidize rents? iv} \"hat is the deadweight loss induced by this policy? Exercise #2. Consider a rm which produces a single output using two inputs according to the following production function: y = min {2 KL} 1 where y is the rm's output1 K is machinery {measured in machine-hours} and L is labor supply [measured in person-hours}. Let r be the cost of one machine-hour and let to be the wage rate [i.e. the cost of one person-hour}. {a} [ll] pts.] Does the rm's technology exhibit increasing returns to scale? Explain carefully. {b} [5 pts.] In a neat and clear diagram1 draw the isoquant corresponding to output of II] units. Be sure to label important features in the diagram. {c} [1|] pts.] Suppose that r = 16 and w = 4. Determine the rm's cost function mfg}. {d} [10 pts.] Clo a diagram that has costs on the y-axis and output and the x-ain's, plot the rm's cost curve cy}, average cost curve Ay}, and marginal cost curve J'lfC{y}l. Exercise #3. Short questions. To get full credit you should justify your answers. {a} [5 pts.] Show that~ in the short run1 if the price of the xed factor is increased, prots will decrease. {b} [10 pts.] If pJ'rIPl } all, [where p is the output price~ MP1 the marginal product of factor l~ and an the rental rate of factor 1}\" should the rm increase or decrease the amount of factor 1 in order to increase prots? Explain carefully. {c} [III] pts.] If a rm had everywhere increasing returns to scale1 what would happen to its prots if prices remained xed and Hit doubled its scale of operations? Show your work. 19. A monopolist operates in two submarkets. In submarket 1, Eu = 2 and in submarket 2, E = -4. Suppose that C(Q) = 30 in both markets. The profit- maximizing prices for this monopolist are given by a. Pg=2ansz=2 b. P|=23ndP1=3 c. P1=2andPa=5 d)\" Pg=ansz=4 e. None of the above. 20. Suppose that the Department of Justice {DOJ} vetoes all mergers that are likely to lead to an increase in price of the product. The market demand function is given by Pm) = 24 - Q. Premerger, the market is competitive and the cost function is given by em} = 160. Post-merger. the market will be controlled by a monopolist and cm) = m. For what values of v. will the DOJ approve this merger? a.* values of 1'. less than or equal to B. b. values of it less than or equal to 12. c. values of x greater than B. d. values ofxless than or equal to 16. e. The 00.] will not approve this merger for any value of it. Part II. Problems (50 points]. Answer both questions. Each question is worth 25 points. Show all of your work to receive partial credit. Please write legibly, be precise with your answers, and remember that economy of presentation is a desirable quality. 1. (25)The competitive firm's marginal cost function is given by MC{q} = 4 1- 2q and its variable costs are given by AVC(q} = 4 + q. a} {6) What is the profit-maximizing level of output for the competitive firm if the market price is equal to 15? If fixed costs were to decrease, how would the firm alter its profit-maximizing level of output? b) (5) What is the producer surplus for this firm at the profit-maximizing level of output? c} {6} What are the firm's average fixed costs if profits are equal to 24? d) (a) How much output should this firm produce if the market price falls to 4? 2. {25)The market demand function is given by Q = 20 - Pr where Q is output and P is price. a} {1}what price would a profitmaximizing monopolist charge if C(Q) = F + 20, where F a U are fixed costs? Determine the monopolist's profits if its average fixed costs in equilibrium are equal to 4? b) (1 D) How much betterp'worse off would consumers be if the competitive outcome prevailed in this market? [Assume the same cost function as in part all c) {5} Suppose now that Q = 1an min{i(, L} is the production function for this L.\" industry. where K is capital. L is labor and the positive integer n is the number of firms participating in this market. In addition, let r= 1 and w = 1. Suppose that the competitive outcome prevails for all n > 1. If consumers could choose the number of firms participating in this market. what value of n would they choose? Provide a clear economic rationale for your answer. Chapter 5 - Problem 3 Suppose a country has a money demand function (M/P) = KY, where k is a constant parameter. The money supply grows by 12 percent per year, and real income grows by 4 percent per year. a. What is the average inflation rate? b. How would inflation be different if real income growth were higher? Explain. c. How do you interpret the parameter k? What is the relationship to the velocity of money? d. Suppose, instead of a constant money demand function, the velocity of money in this economy was growing steadily because of financial innovation. How would that affect the inflation rate? Explain. Chapter 6 - Problem 1 Use the model of the small open economy to predict what would happen to the trade balance, the real exchange rate, and the nominal exchange rate in response to each of the following events. a. A fall in consumer confidence about the future induces consumers to spend less and save more. b. A tax reform increases the incentive for businesses to build new factories. c. The introduction of a stylish line of Toyotas makes some consumers prefer foreign cares over domestic cars. d. The central bank doubles the money supply. e. New regulations restricting the use of credit cards increase the demand for money. Chapter 6 - Problem 2 Consider an economy described by the following equations: Y = C+I+G+NX, Y = 5000, G = 1000, T = 1000, C = 250 + 0.75(Y - T), 1 = 1000 - 50r, NX = 500 - 500E, r= =5 a. In this economy, solve for national saving, investment, the trade balance, and teh equilibrium exchange rate. b. Suppose now that G rises to 1250. Solve for national saving, investment, the trade balance, and the equilibrium exchange rate. Explain what you find. c. Now suppose that the world interest rate rises from 5 to 10 percent, (G is again 1000). Solve for national saving, investment, the trade balance, and the equilibrium exchange rate. Explain what you find. Chapter 6 - Problem 11 A Case Study in this chapter concludes that if poor nations offered better production efficiency and legal protections, the trade balance in rich nations such as the United States would move toward surplus. Let's consider why this might be the case. a. If the world's poor nations offer better production efficiency and legal protection, what would happen to the investment demand function in those countries? b. How would the change you describe in part (a) affect the demand for loanable funds in world financial markets? c. How would the change you describe in part (b) affect the world interest rate? d. How would the change you describe in part (c) affect the trade balance in rich nations