- I Ii Iii 1 2 V Iv Essay Question 1 What Are The Assumptions Of A Perfectly Competitive Market Why Are The Impli 1 (260.08 KiB) Viewed 7 times
I. II. III. 1. 2. V. IV. ESSAY
QUESTION 1. What are the assumptions of a perfectly competitive market? Why are the implication of these assumptions in the optimization process of a single firm? What does this mean for aggregation of individual level supply and demand into one market? (15 pts) 3. Does this firm's marginal product of labor ever diminish? Use calculus, words, and the necessary concept to answer this
question. (2 pts) 4. What is this firm's maximum average product of labor? Use calculus, words, and the necessary concept to answer this
question. (2 pts) SHORT RUN PRODUCTION 1. A firm's short-run production function is given by q = 5L¹/2 + 3L - 6. [Note: The amount of capital used by this firm has been fixed at some constant value.] (Total 8 pts) Find this firm's average product and marginal product of labor functions. (2 pts) Does this firm's average product of labor ever diminish? Use calculus, words, and the necessary concept to answer this
question. (2 pts) PROPERTIES OF AN ISOQUANT. A firm's production function is given by q = 2KL + K + L for L> 0 and K > 0. (4 pts) 1. Show that this firm's isoquants are downward sloping. Use calculus, words, and the necessary concept to answer this
question. (2 pts) 2. Show that this firm's isoquants are strictly convex. Use calculus, words, and the necessary concept to answer this
question. (2 pts) RETURNS TO SCALE. Consider the production function given by q = L0.5+ K0.5. Suppose both labor and capital change by the proportion t > 1. (5 pts) 1. What is the proportion change in output? (1.5 pts) 2. Based on your answer in 1 and the necessary concept, what degree of returns to scale does this production function exhibit? (1 pt) What is the elasticity of substitution for this production function? (2.5 pts) 3. LONG RUN PRODUCTION FUNCTION 1. A firm's long-run production function is given by q = 2(10.5 + 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)
VI. 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) LONG RUN COST FUNCTION 1 A firm sells its output, q, in a perfectly competitive market at a price of p per unit. Suppose this firm's long run total cost function is C = 40q-q² +q³. (6 pts) 1. Find the long run average cost and long run marginal cost functions of a typical firm in this market. (1 pt) 2. Currently, the market demand for this firm's product is Q = 884-8p. Assume that the industry in which this firm sells its output is a constant cost industry and entry and exit are allowed. (5 pts) a. What is the long run equilibrium market price and market output? Show and briefly explain the basis for your answer. (3 pts) b. How much output does each firm produce when the market is in long run equilibrium? Show and briefly explain the basis for your answer. (1 pt) c. How many firms will be in this market at the long run? Show and briefly explain the basis for your answer. (1 pt) BONUS [MAX 4 pts]. Explain what the envelope theorem is and how it is applied to short-run and long-run cost curves.