Suppose that the following production function is given: @ = min(, L}. 3 a-) (6 points) For the above production function, find the elasticity of substitution? Find the Returns to Scale. b-) (8 points) Using the above production function; find the labor demand and capital demand as functions of output (Q), price of labor (w) and price of capital (r). Does the Law of Demand hold for each input? Are these inputs normal or inferior inputs in the production process? Are inputs complements or substitutes? Why? c-) (10 points) Find the cost function for the above production function. Verify the properties of the cost function. d-) (8 points) Suppose that a firm wants to produce 36 units of output and w=1, 1=1. Find long run total cost. Suppose now that wage goes up to 2. Find the new long run total cost. Does firm substitute capital for labor? What is the percentage of cost saving relative to the case where firm is not able to substitute? e-) (4 points) Suppose that w=1, 1=1 and a firm has fixed amount of capital K = 108 in short run (SR). Find the short run total cost, average total cost and marginal cost. What would be the short run total cost of producing 36 units. Compare your answer with long run total cost in part d. How and why are they different