Problem 1. (30 marks) Suppose that in a city there are 100 identical self-service gasoline stations selling the same type of gasoline. The total daily market demand function for gasoline in the market is QD = 60,000 - 25,000P, where P is expressed in dollars per gallon. The daily market supply curve is Os = 25,000P for P > $0.60 (Via ofSi elli ge Jil you die displayall ol ,by). (A) Determine algebraically the equilibrium price and quantity of gasoline. (B) Draw a figure showing the market supply curve and the market demand curve for gasoline, and the demand curve and the supply curve of one typical firm in the market on the assumption that the market is nearly perfectly competitive. (C) Explain why your figure of the market and the firm in part (B) is consistent. (D) Suppose that now the market is monopolized (e.g., a cartel is formed that determines the price and output as a monopolist would and allocates production equally to each member). Draw a figure showing the monopolist's equilibrium output and price. (Hint: the market supply curve becomes the MC curve of the monopolist.) (E) How many gasoline stations would the monopolist operate? (F) Can we say that the monopoly leads to a less efficient use of resources than perfect competition?Problem 2. (30 marks) The Rapid Transit Corporation in a city has estimated the following Cobb-Douglas production function using monthly observations for the past two years: In Q = 2.303+ 0.40 in K + 0.60 In L + 0.20 in G I-statistic: (3.40) (4.15) (3.05) R' = 0.94 where O is the number of bus miles driven, K is the number of buses the firm operates, & is the number of bus drivers it employs each day, and G is the gallons of gasoline it uses. The numbers in parentheses below the estimated coefficients are the f-statistic values. With respect to the above results, answer the following questions: (a) Estimate Q if K = 200, _ = 400, and G = 4,000. (b) Rewrite the estimated production function in the form of a power function. (c) Find the marginal product of capital, labor, and gasoline at K = 200, L = 400, and G = 4,000. Are the MPr, MPz, and MPG positive? Are they diminishing? Why? (d) Find the value of the output elasticity of K, L, and G. By how much does output increase by increasing each input by 10%, one at a time? (c) Determine the economies of scale (or returns to scale) in production. By how much does output increase if the firm increases the quantity used of all inputs at the same time by 10%? (f) Suppose that the firm operates 200 buses per day, with 400 drivers, and uses 4,000 gallons of gasoline, and the rental price of a bus (r) is $40 per day, the wage rate of a driver (w) is $30 per day, and the price of gasoline (g) is $1 per gallon. Determine whether the firm is using the optimal combination of capital, labor, and gasoline. (g) If the firm operated 200 buses with 400 drivers and used 4,000 gallons of gasoline per day, and the average bus ride is 1 mile, what price would the firm have to charge for a bus ride in order to maximize profits? (h) Are the estimated coefficients of the Cobb-Douglas production function statistically significant at the 5% level? How much of the variation in O does the estimated regression explain