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Exercise #1. A firm produces output using the technology y = 7 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 un = 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 = 2,000ur, 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 Im Id (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).Part III Exercise #1. [10 pts.] A monopolist has an inverse demand curve given by p(y) = 12-y and a cost curve given by c(y) = y". Describe how to determine its profit-maximizing level of output. and compute it. Show your work: to receive full credit you should show how you compute the optimal quantity of output. Exercise #2. [15 pts.] You are the manager of a new amusement park that has monopoly power over the service it offers: roller coaster rides. You have figured that the park will attract 1,000 people per day, and each person will take a = 50- 50p rides, where p is the price of a ride. The marginal cost of a ride is essentially zero. (a) If admission to the park were free and you had to choose the profit maximizing price of a ride p', which value would you set? (b) Suppose now that you can use a two-part tariff, i.e., you can set a price for admission to the park, and another one for each roller coaster ride, Which admission fee and price of a ride would you choose? Show your work: to receive full credit you should show how you compute the optimal prices. Exercise #3. [20 pts.] Your company has monopoly over product H. It sells it in the UK and in the US. The cost function for your firm is c(q) = 10q. Your marketing department has identified the UK and the US demand curves for H to be qUS = 50,000 - 2,000pus qUK = 10,000 - 500PUK, where qus and quy represent the quantities demanded by US and UK consumers respectively, and pus and puk the (US dollar) prices charged for the product in the US and in the UK, respectively. (a) If you were to charge the same price in both countries, how many units of H should you sell, and what price should you charge in order to maximize your company's profits? (b) If you could charge different prices in the US and the UK what prices would you choose and how many units would you sell in the US and how many in the UK? Exercise #4. [20 pts.] A company sells product A in a competitive market. Its long-run cost function is given by c(y) = y'+ 10 for y > 0 c(y) = 0 for y = 0, where y represents the quantity of good A. (a) What is the lowest price at which this company will supply a positive amount of product A in the long-run? (b) Suppose that the market price for A is p = 2v10, and that 100 firms are operating in this market in the long-run. What is the equilibrium market demand for the product? Part II Exercise #5. [17 pts.] The rental price of machinery K (measured in machine-hours) is $10 per hour, while the hourly wage rate for labor, L (measured in labor-hours), is $6. Find the cost function associated with the following technology: y = 10K + L, where K represents machinery (measured in machine-hours) and L labor (measured in labor-hours). Part I Exercise #6. [18 pts.] John likes books and restaurant meals. His utility function is u(Th, I'm) = (15)02 (1m)04, where as represents the quantity of books that John "consumes" in a month, and I'm the amount of restaurant meals that he consumes. Suppose that both books and restaurant meals are perfectly divisible goods. The relative price of books in terms of restaurant meals is 0.4, i.e., buying a book costs 40% of the price of a restaurant meal. The nominal price of a restaurant meal is $40. John's income is $1,000 per month. Compute the quantity of books and restaurant meals that John consumes in a month.Exercise #4. [20 pts.] A company sells product A in a competitive market. Its long-run cost function is given by c(y) = 13 + 10 for y > 0 c(y) = 0 for y = 0, where y represents the quantity of good A. (a) What is the lowest price at which this company will supply a positive amount of product A in the long-run? (b) Suppose that the market price for A is p = 2v10, and that 100 firms are operating in this market in the long-run. What is the equilibrium market demand for the product? Part II Exercise #5. [17 pts.] The rental price of machinery K (measured in machine-hours) is $10 per hour, while the hourly wage rate for labor, L ( measured in labor-hours), is $6. Find the cost function associated with the following technology: y/ = 10K + L. where K represents machinery ( measured in machine-hours) and L labor (measured in labor-hours). Part I Exercise #6. [18 pts.] John likes books and restaurant meals. His utility function is u (Th, I'm) = (15)"- (2m)4, where r, represents the quantity of books that John "consumes" in a month, and 2m the amount of restaurant meals that he consumes. Suppose that both books and restaurant meals are perfectly divisible goods. The relative price of books in terms of restaurant meals is 0.4, i.e., buying a book costs 40% of the price of a restaurant meal. The nominal price of a restaurant meal is $40. John's income is $1,000 per month. Compute the quantity of books and restaurant meals that John consumes in a month.Exercise # 1. Anna consumers two goods: milk (measured in gallons) and a composite good (measured in dollars). Let X represent the gallons of milk that Anna consumes in a gives mouth and let Me represent her expenditures on the composite good in a given month. Anna's preferences over consumption bundles (Xm,X2) are summarized by the utility function: U (Xm.X) = Xm X . Anna's monthly income is $400. Let Pm denote the dollar price of a gallon of milk. (a) [10 pts.] Suppose that Pm - $1. What is Anna's optimal consumption bundle? Show your work. Illustrate your answer with a neat and clear diagram showing Anna's budget line and indifference curves. Label the points at which the budget line intersects the axes and identify the optimal bundle. (b) [10 pts ] Suppose now that the local grocery store where Anna regularly shops decides to introduce a discount on milk. Specifically, for each gallon of milk that Amma buys, the grocery store reduces its price from $1 per gallon to $0.50 per gallon, up to a maximum manber of 50 gallons of milk per month. If Anna buys more than 50 gallons she has to pay the regular price on every gallon beyond the 50-th. In a neat and clear diagram, graph Anna's budget line. Label the points at which the budget line inteases is the axes and determine the coordinates of the kink point. (c) [15 pts.) Suppose now that the price of milk is again Am = $1 (there are no discounts anymore). Due to a shortage of milk, the price of milk increases from $1 to $2. Describe how to compute the extra income that must be given to Anna in order to compensate her for this increase in the price of milk (Le, the compensating variation) Here you are not asked to compute this amount. Simply show which steps you would take to compute it.] Exercise # 2. John has the following demand function for beer * = m- 2 + PM where * denotes the gallons of beer he demands per month, Pe is the dollar price of a gallon of beer, Py is the dollar price of a bottle of wine, and m denotes John's income (a) [5 pts.] Is beer an ordinary good in this case? Motivate your answers. Notice: no credit will be given to yeso type of answers. In order to get credit you need to explain your answer.] (b) [5 pts.] Is beer a substitute for wine in this case? Motivate your answer. [Notice: no credit will be given to yeso type of answers. In order to get credit you need to explain your answer.] (c) 15 pts ] Suppose that the price of a bottle of wine is py = $10, and the price of a gallon of beer is po = $15. What is the relative price of a gallon of bees in terms of bottles of wine? (d) [10 pts.] Suppose that m = $100 and that pw = $10 Compute the loss in John's consumer surplus that occurs when the price of a gallon of beer increases from $15 to $20. Support your analysis with a graph representing John's demand curve and his loss in consumer's surplus. Remember that to draw a demand curve you need to place p, on the y-axis and x, on the x-axis.] (e) [10 pts.] From point (d) you can see that the loss in consumer's surplus can be decom- posed into two subregions, whose shapes are respectively rectangular and triangular. How can you interpret each of these two subregions? Exercise # 3. Consider the following statements and say whether they are true or false and why. To get credit you should provide a clear justification for your answers. (a) [10 pts.] If two goods are perfect complements the consumer will be just as well off faxing a quantity tax as an income tax. (b) (5 pts.] If the price of one good increases the demand for that good always decreases. (c) [5 pts. ] The marginal rate of substitution measures the rate at which the market is willing to substitute one good for the other. (e) [5 pts.] An indifference curve represents the collection of all bundles that a consumer can bury (f) [5 pts.] By definition, a lump sum subsidy to a consumer does not affect his/her consumption behavior