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11. (18 Points) Consider a market with two horizontally differentiated firms, X and Y. Each has a constant marginal cost of $20. Demand functions are Qx = 100 - 2Px + Py Qy = 100 - 2Py + Px a) (10 Points) Calculate the Bertrand equilibrium in prices in this market. b) (8 Points) Draw the best response function diagram corresponding to your solution.Consider market for masks. Not everyone values the mask equally: marginal private benet is 100 Q and marginal private costs are given by 20 (per Q). Given that wearing masks will help reduce spread of virus, marginal benet to others is 1130 = 50 (per Q). o 3.. Draw the marginal private benet (MPB) marginal social benet (MSB), marginal private cost (MPG), and marginal social cost (MSG) curves on a graph. labeling clearly the axes and intercepts. Pay close attention to what is on the Xiaxis and yiaxis. _ ' o b. What is the equilibrium amount of masks? What is the eicient level? 0 c. What is the deadweight loss (D'WL) caused by the externality? Shade in the area. of the DWL on the graph from part (a). What is the welfare gain from moving to the efcient level of Q? o d. For which good is a market absent in this case? Government solution: Suppose the government steps in and decides to correct the externality by subsi dizing masks. o e. Suggest a Pigouvian tax that would induce the efcient consumption. What is the optimal tax rate per unit, and how much subsidy is needed? Market solution: The Cease theorem states that \"the eicient outcome should occur regardless of which party has the property rights,\" implying that the market can potentially solve externalities by itself (no need for the government to step inl). o f. Interpret the Cease theorem in the context of this question. What are ways in which the Cease theorem could fail? Give some examples in the context of this question. I 1 Externalities Problem 1 Answer questions (a) and (b) for each of the following four examples: 1. Smoking by individuals; 2. Toxic waste production by firms; 3. R&D by a high-tech firm; and 4. Individual vaccination against communicable illness. (a) Is there an externality? If so, describe it, including references to whether it is positive or negative, and whether it is a consumption or production externality. (b) If there is an externality, does it seem likely that private markets will arise that allow this externality to be internalized? Why or why not? Problem 2 Brookhaven has two regions. In Stony Brook, the marginal benefit associated with pollution cleanup is AB - 300 - 100, while in Port Jefferson, the marginal benefit associated with pol- lution cleanup is MB - 200 - 40. Suppose that the marginal cost of cleanup is constant at $12 per unit. What is the optimal level of pollution cleanup in each of the two regions? Problem 3 The private marginal benefit associated with a product's consumption is PAD - 360 - 49 and the private marginal cost associated with its production is PAC - 60. Furthermore, the marginal external damage associated with this good's production is MD - 20. To correct the externality, the government decides to impose a tax of 7 per unit sold. What tax T should it set to achieve the social optimumn?A perfectly competitive firm has a Cobb-Douglas production function f (X1, X2) = X1X2. Suppose that input prices are w1 = 1 and W2 = 1. The firm wants to find the cheapest way of producing y = 32. a. Suppose that in the short run the quantity of input factor 2 is fixed at X2 = 8. Solve the firm's short-run cost minimization problem to derive the optimal input quantity x1. b. Derive the corresponding costs Cs of producing y = 32 in the short run. c. Now consider the long run, in which both input factors are variable. Set up the Lagrangian function for this firm's long-run cost minimization problem. d. Derive the first-order conditions of the above long-run cost minimization problem. e. Solve the above first-order conditions to derive the optimal input quantities x1 and X2. f. Derive the corresponding costs c* of producing y = 32 in the long run.2. Currently, Krona has currently no compensation scheme for workers infected with the disease and you are advising the government on the introduction of such a scheme (suppose for this exercise that there are no other unemployment or sick benefits and this would most likely concern any future disease). Model the economy with identical individuals who earn a wage of 500 while working and 0 when sick with the disease. With probability q, the individuals get sick with the disease and cannot work. When sick, individuals would receive a sickness compensation s from the government. To finance the scheme, when working individuals pay lax of (500*t) where t is the tax rate. u(c) = c1/$ denotes the individuals utility from consumption of c in any given state. a) Write down the individual's expected utility as function of s, q and t. [3 marks] b) What is the government's budget constraint for an actuarially fair compensation scheme; write down what is balanced government budget in terms of s, q and t. [2 marks] c) Find the value of compensation s that maximizes individuals expected utility, assuming a balanced budget. [6 marks] d) What is the tax rate t required to finance the compensation maintaining a balanced budget? Discuss very briefly the intuition (2 sentences). [4 marks] e) Discuss briefly the merits of the introduction of such a disease specific compensation scheme, including a brief discussion of moral hazard. [5 marks] 41. Refer to Table 2. {a} What was the quoted ask price [in dollars] for the 8.?5s of 2020'? Assume par value = 310.000. You can ignore accrued interest. {b} What cash ows would you receive if you bought this bond on August 13, 2006 and held it to maturity? Specify amounts and timing [by month]. {c} Suppose you buy $10 million (par value] of the 4.125s of 2008 and sell short $10 million [par value] of the 3.253 of m. You hold each trade until the bond matures. What cash flows would you pay or receive? Specify amounts and timing. You can ignore any fees or margin requirements for the short sale. Table 2: Treasury Prices and Yields, August 3. 2005 assayed Bonds and Notes: 3.25 . 5.09% 4.125 . : 4.39 6.0 . 4.92 5.25 . 4.86 4.375 . 4.88 12.5 . 4.86 3.?5 . 5.11 3.125 . 5.11 Strips: 5.08% 4.93 4.91 4.80 4.8? 4.92 5.05 42. Refer again to Table 2. {a} What were the l. 2, 3. 4. 6 and 10-year spot interest rates? {b} What was the forward interest rate from August 2007 to August 2003? From August am to August 2010? {c} The 8.75s of August 2020 will pay a coupon in August 2010. What was the PV of this payment in August 2\"? (d) 'What did the slope of the term structure imply about future interest rates? Ex- plain briey. Fall 2003 Page 20 of 36 Express your answers to (a) and (h) as effective annual interest rates. 43. Refer again to Table 2. Use the quoted yield on the August 2012 note to calculate the preseut value for the cash payments on the August 2012 note. Assume that the rst note coupon comes exactly six months after August 13. 2006. Note: The quoted yields are rounded. Your PV may not match the Asked Price exactly. 44. Lu August 2006 you learn that you will receive a $10 million inheritance in August 2007. You have committed to invest it in Treasury securities at that time._ but worry that interest rates may fall over the next year. Assume that you can buy or sell short any of the Treasuries in Table 2 at the prices listed in the table. {a} How would you lock in a one-year interest rate from August 2007 to August sues? What transactions \"mild you make in August 2008? Show how the transactions that look in the rate. (h) Suppose you wanted to lock in a 5-year interest rate from August 2007 to August 2012. How does your answer to part a change
