5 : Suppose that a firm uses data on its use of capital and labor over time to estimate its own production function and finds: lnQ=1.3+0.2lnK+0.7lnL a. An investor is interested in providing start-up funding for this firm. If w=35 and r=10, what is the most the firm can produce with a budget of $9000? b. Is the short run marginal cost increasing or decreasing in Q? Explain. c. Is the long run average cost increasing or decreasing in Q? Explain. d. What is this firm's cost function in the long run? What is the composition of costs: what percentage of this firm's cost is labor cost? What percentage is capital cost? e. If the firm faces a perfectly elastic demand curve for its product at P, what is the optimal quantity of output produced Q* in the short run when capital is fixed at K0? f. What is the optimal amount of labor hired at this Q* as a function of P, w, K0 and r? What does that make the firm's elasticity of demand for labor with respect to the wage in the short term? g. Suppose the firm faces the same demand curve for its output in the long run when K is flexible. What is the optimal quantity produced then? h. What are the optimal amounts of labor and capital to hire in the long run as a function of P, w and r? i. What is this firm's long-run elasticity of demand for labor with respect to the wage rate? Is it larger or smaller than the elasticity of demand for labor in the short run? j. Use the expressions you found for long run demand for inputs to find the range of P (as a function of w, r and K0) for which you would advise the firm to plan to increase K between the short and long runs