The Rapid Transit Corporation in a city has estimated the following Cobb-Douglas production function using monthly observations for the past two years: an = 2.303 + 0.41nK + 0.6lnL + 0.21n G Where Q is the number of bus miles driven, K is the number of buses the firm operates, L is the number of bus drivers it employs each day, and G is the gallons of gasoline it uses. With respect to the above results, answer the following questions: (a) Estimate (1 if K = 200, L = 400, and G = 4000. (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 = 4000. Are they 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 percent, one at a time? (e) Determine the economies of 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 percent? (f) Suppose the firm operates 200 buses per day with 400 drivers and uses 4000 gallons of gasoline. The rental price of a bus is $40 per day, the wage rate of a driver is $30 per day, and the price of gasoline if $1 per gallon. Determine whether the firm is using the optimal combination of capital, labor, and gasoline