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2. A perfectly competitive firm has a production function f(X1, X2) = xX2. Input prices are given by w, = 1 and w2 = 32. a. Does this production function exhibit decreasing, constant, or increasing returns to scale? (1 pt) b. In the short run, input factor 2 is fixed at X2 = 16 and the firm chooses the optimal input quantity x ; to minimize the cost of producing output y = 32. Derive x1. (1 pt) c. Calculate the costs cs associated with the above short-run solution. (1 pt) d. In the long run, the firm chooses the optimal input quantities x] and x2 to minimize the cost of producing output y = 32. Write the Lagrangian function for this firm's long-run cost minimization problem. (1 pt) e. Derive the first-order conditions for this firm's long-run cost minimization problem. (3 pt) f. Solve the above first-order conditions to derive the optimal input quantities x; and x2. (2 pt)Question # 02 Use the information given and show in a table format how value added method is used to Calculate GDP. 1. A forester chops down 200 trees and sells them @ N$50 each to the coal factory on a farm. The coal factory processes these trees into coals and sells the coal @ N$20 000 to the coal wholesaler's. The coal wholesaler's goes to the market and sell 500 bags of coal's @N$100 each to pick n Pay. Pick n Pay sells the 500 bags of coal's @ N$150 each to its customers. According to this example, how much value added do the coals contribute to the GDP?Question # 02 Use the information given and show in a table format how value added method is used to Calculate GDP. 1. A forester chops down 200 trees and sells them @ N$50 each to the coal factory on a farm. The coal factory processes these trees into coals and sells the coal @ N$20 000 to the coal wholesaler's. The coal wholesaler's goes to the market and sell 500 bags of coal's @N$100 each to pick n Pay. Pick n Pay sells the 500 bags of coal's @ N$150 each to its customers. According to this example, how much value added do the coals contribute to the GDP?An individual begins her working life at date twith no non-human wealth. Her labour income grows at rate 9 per year. assumed to be 3% (or 0.03) per annum: thus her income in year t + j is y\"; = 3&(1 + g. Her income is received at the end of each year so that the present value of income received in year t + j is '{1::j+1, where r is the constant real rate of interest assumed to be 5% (0.05) per annum. Assume an innite planning horizon and assume that she consumes her permanent income. Calculate the ratio of consumption to income at the start of her working life. Briey discuss why her consumption will initially be substantially greater than her income. #2 You are given the following information. The current dollar/euro exchange rate is $1.5 per euro. A U.S. basket that costs $100 would cost 60 euro (or the equivalent of 90$) in the euro area. For the next year, the Fed is predicted to keep U.S. inflation at 2% and the ECB is predicted to keep euro area inflation at 1%. The speed of convergence to absolute PPP is 15% per year. Wha#2 You are given the following information. The current dollar/euro exchange rate is $1.5 per euro. A U.S. basket that costs $100 would cost 60 euro (or the equivalent of 90$) in the euro area. For the next year, the Fed is predicted to keep U.S. inflation at 2% and the ECB is predicted to keep euro area inflation at 1%. The speed of convergence to absolute PPP is 15% per year. Wha(20 points) The market inverse demand curve is P(y) = 10 - 2y, and a monopolist's cost curve is y2 + 2. (a) What output level y maximizes the monopolist's revenue? What output level y maximizes the monopolist's profit? Identify which of the two output levels is lower, and explain why using economic intuition. (b) Suppose a second firm with cost curve y + 2 is considering entering the market. If after entry, the firms would compete a la Cournot, what would be the Cournot- Nash equilibrium output levels y1 and y2 of firms 1 and 2? What would be the equilibrium profits for each firm? Will firm 2 choose to enter the market? (c) Suppose that if firm 2 enters, both firms collude, choosing output levels that maxi- mize total profits and then split the profits equally between them. What would be the profits to each firm? Will firm 2 choose to enter the market in this case?(20 points) The market inverse demand curve is P(y) = 10 - 2y, and a monopolist's cost curve is y2 + 2. (a) What output level y maximizes the monopolist's revenue? What output level y maximizes the monopolist's profit? Identify which of the two output levels is lower, and explain why using economic intuition. (b) Suppose a second firm with cost curve y + 2 is considering entering the market. If after entry, the firms would compete a la Cournot, what would be the Cournot- Nash equilibrium output levels y1 and y2 of firms 1 and 2? What would be the equilibrium profits for each firm? Will firm 2 choose to enter the market? (c) Suppose that if firm 2 enters, both firms collude, choosing output levels that maxi- mize total profits and then split the profits equally between them. What would be the profits to each firm? Will firm 2 choose to enter the market in this case