Solve the following questions
9. Stock ABC has the following characteristics: . The current price to buy one share is 100. . The stock does not pay dividends. European options on one share expiring in one year have the following prices: Strike Price Call option price Put option price 90 14.6 0.24 100 6.80 1.93 110 2.17 6.81 A butterfly spread on this stock has the following profit diagram. 6 4 2 80 85 90 95 100 105 110 115 120 -2 The continuously compounded risk-free interest rate is 5%. Determine which of the following will NOT produce this profit diagram. (A) Buy a 90 put, buy a 110 put, sell two 100 puts (B) Buy a 90 call, buy a 110 call, sell two 100 calls (C) Buy a 90 put, sell a 100 put, sell a 100 call, buy a 110 call (D) Buy one share of the stock, buy a 90 call, buy a 110 put, sell two 100 puts (E) Buy one share of the stock, buy a 90 put, buy a 110 call, sell two 100 calls. IFM-01-18 Page 6 of 105 10. Stock XYZ has a current price of 100. The forward price for delivery of this stock in 1 year is 110. Unless otherwise indicated, the stock pays no dividends and the annual effective risk-free interest rate is 10%. Determine which of the following statements is FALSE. (A) The time-1 profit diagram and the time-1 payoff diagram for long positions in this forward contract are identical. (B) The time-1 profit for a long position in this forward contract is exactly opposite to the time-1 profit for the corresponding short forward position. (C) There is no comparative advantage to investing in the stock versus investing in the forward contract. (D) If the 10% interest rate was continuously compounded instead of annual effective, then it would be more beneficial to invest in the stock, rather than the forward contract.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. Anna consumes two goods: milk (measured in gallons) and a composite good (measured in dollars). Let Xm represent the gallons of milk that Anna consumes in a given month and let Xc represent her expenditures on the composite good in a given month. Anna's preferences over consumption bundles (Xm,Xc) are summarized by the utility function: U (Xm,Xc) = Xm XE . 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 Anna buys, the grocery store reduces its price from $1 per gallon to $0.50 per gallon, up to a maximum number 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 intersects the axes and determine the coordinates of the kink point. (c) [15 pts.] Suppose now that the price of milk is again Pm = $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 (i.e., 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 Xb = m - 2pb + Pw where X denotes the gallons of beer he demands per month, Po is the dollar price of a gallon of beer, Pw 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 answer. [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) [5 pts.] Suppose that the price of a bottle of wine is Pw = $10, and the price of a gallon of beer is po = $15. What is the relative price of a gallon of beer 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 facing 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 buy. (f) [5 pts.] By definition, a lump sum subsidy to a consumer does not affect his/her consumption behavior
