A firm's long-run production function is given by q = 2(105+ K0.5) for L> 0 and K > 0. The price per unit of labor is P3

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A Firm S Long Run Production Function Is Given By Q 2 105 K0 5 For L 0 And K 0 The Price Per Unit Of Labor Is P3 1 (18.81 KiB) Viewed 17 times

A Firm S Long Run Production Function Is Given By Q 2 105 K0 5 For L 0 And K 0 The Price Per Unit Of Labor Is P3 2 (36.68 KiB) Viewed 17 times

A firm's long-run production function is given by q = 2(105+ K0.5) for L> 0 and K > 0. The price per unit of labor is P3 and the price per unit of capital is P2. Use all of this information to answer the following questions. (7 pts) 1. Using all of the above information and the necessary concepts, write the TWO first-order conditions that are necessary to minimize this firm's total cost of producing any given output, given the input prices. [Note: You are not being asked to solve for the optimal L and K in this question.] (1.5 pts)
2. Using your results in part 1, find this firm's conditional demand for labor and conditional demand for capital functions (as functions only of q). Simplify your answers. [Note: You do not need to show that the SOC for a minimum is satisfied. Assume that it is satisfied.] (2 pts) 3. Using your results in part 2, find this firm's long run cost function (as a function only of q). Simplify your answer. (0.5 pt) 4. Using your result in part 3, find this firm's long run marginal cost and average cost functions (as functions only of q). (1 pt) 5. What happens to this firm's long run marginal cost and long run average cost as it produces more output, ceteris paribus? Use your answers in part 4, calculus and words to answer this question. (1.5 pts) 6. What is the relationship between this firm's long run marginal cost and long run average cost as long as it produces positive output levels? Use your answers in part 4 and words to answer this question. (0.5 pt)