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5. Jorge has an idea for a new product to help Econ 3101 students graph 3 dimensional functions (like utility functions and production functions!). Jorge has figured out that to produce these devices, he needs capital and labor according to the following production function: F(K,L) = 15K^3/5L^2/5 (a) For now assume flexible capital and labor. Identify the elasticity of substitution for Jorge's production function. (2 points) (b) Suppose in the short run he can only get 2 units of capital. Set up and solve the cost minimization problem for Jorge's product in the short run. What are the short run values for inputs and what is the short run minimized cost? (4 points) (c) Suppose Jorge realizes that Econ 3101 students are very interested in his product because it helps them with the problem sets. All the student interest makes Jorge consider producing the product for the long run. Let capital and labor both freely move. Setup and solve the long run cost minimization problem for the optimal level of capital, labor, and the minimized cost.3. Consider a competitive firm which uses three inputs K (capital), L (labor), and A (land) to produce output y. The input prices are (wk = 2, wL - 1, wx = 4) and the output price is p = 1. The firm faces the following production function: f (K, L, A) = A ( VL + VK). In the short-run, the firm's land level is fixed at A, but can choose labor and capital as it wishes. In the long-run, the firm can also vary its land level. First, derive the short-run cost function given A. Then, use the short-run cost function to derive the long-run cost function. Hint: Use an approach similar to the example in class, where the profit-maximization problem can be decomposed into two steps. Here try to decompose the long-run cost minimization problem into two steps.]A Firm uses capital and labor to produce steel. The production function is CobbDouglas, Y = AK ^(1/3) L ^(2/3) , where K is capital stock and L is number of workers employed. A is a measure of technology level (total factor productivity), and we currently assume A =1. Capital is a fixed input and cannot be adjusted in the short run. Labor is a variable input and can be adjusted. Suppose the input prices for capital and labor are WK = 1, WL = 2. The firm needs to produce 100 units of steel, Y = 100, which is determined by the market demand. a. Suppose in the short run, the number of capital is fixed at K = 196. Solve for the short-run total cost function. What is the total cost to produce 100 units of steel? b. In the long run, both capital and labor can be adjusted. Solve for the long-term optimal usage of capital and labor to produce 100 units of steel.Assume the market demand and market supply functions for pears in the United States are given by QU = 36 - 3p and Q = =6 + 4p, respectively. p represents the price of pears. a) Find producer and consumer surplus when the market is in equilibrium. bl Suppose the federal government introduces a price ceiling of $5.50. a. Compute and graphically show the impact of the program on producer surplus. b. Calculate and graphically show the impact of the program on consumer surplus. C. How does the government implement the program? d. What is the deadweight loss of this policy? (calculate and show graphically)