Consider a competitive firm with a Cobb-Douglas Production function: Y = f(K, L) = KL. Let...
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Consider a competitive firm with a Cobb-Douglas Production function: Y = f(K, L) = KL. Let P be the price of output, W the wage, and R the rental rate on capital. (a) Prove that this production function exhibits diminishing marginal products. (b) Prove that the production function exhibits decreasing returns to scale for any z > 1. (c) Solve the profit maximization problem and find expressions for labor demand, capital demand, and the supply of output. (d) Plot the labor demand curve when P = 1, R = 1. Plot the supply curve when W = R = 1. (e) Solve the cost minimization problem and find expressions for conditional labor demand and conditional capital demand. (f) Find the minimized cost function from (e). (g) Suppose that W = R = 1 and suppose that fixed costs are equal to FC = 4. Find and plot Average fixed costs (AFC), Average Variable costs (AVC), Average Total Cost (ATC), and Marginal costs (MC). Consider a competitive firm with a Cobb-Douglas Production function: Y = f(K, L) = KL. Let P be the price of output, W the wage, and R the rental rate on capital. (a) Prove that this production function exhibits diminishing marginal products. (b) Prove that the production function exhibits decreasing returns to scale for any z > 1. (c) Solve the profit maximization problem and find expressions for labor demand, capital demand, and the supply of output. (d) Plot the labor demand curve when P = 1, R = 1. Plot the supply curve when W = R = 1. (e) Solve the cost minimization problem and find expressions for conditional labor demand and conditional capital demand. (f) Find the minimized cost function from (e). (g) Suppose that W = R = 1 and suppose that fixed costs are equal to FC = 4. Find and plot Average fixed costs (AFC), Average Variable costs (AVC), Average Total Cost (ATC), and Marginal costs (MC).
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a To prove that the CobbDouglas production function exhibits diminishing marginal products we need to show that the marginal product of each input decreases as we increase the amount of that input whi... View the full answer
Related Book For
Microeconomics An Intuitive Approach with Calculus
ISBN: 978-0538453257
1st edition
Authors: Thomas Nechyba
Posted Date:
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