Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN: 9781305506381
Author: James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher: Cengage Learning
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Question
Chapter 7, Problem 6E
a)
To determine
To find:The value of marginal revenue product.
b)
To determine
To find:The value of marginal factor cost production.
c)
To determine
To find:The value of L that maximize profit.
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A competitive firm uses two variable factors to produce its output, with a production function y = min{ x1, x2 }.The price of x1 is w1 = $8 and the price of x2 is w2 = $5. Due to a lack of warehouse space, the company cannot use more than 10 units of x1. The firm must pay a fixed cost of $80 if it produces any positive amount but doesn't have to pay this cost if it produces no output. What is the smallest integer price that would make a firm willing to produce a positive amount?
A firm has the following Cobb-Douglas production function: q=(L^α)(K^1-α)0<α < 1 is a parameter. Suppose in the short run K = 1. The rental rate of a unit of K is $10, and the wage rate of a unit of L is $20.(a) Derive the marginal cost of the firm (expressed in terms of α and q).(b) Derive the average variable cost of the firm (expressed in terms of α and q).(c) Derive the cost function of the firm.
Suppose the total cost function for a firm is given by C = q(v + 2/vw + w).
a) Use Shephard's lemma to compute the contingent demand functions for inputs k and l.
b) Use your results from part (a) to compute the underlying production function for q.
c) Compute the elasticity of substitution between inputs k and l.
Chapter 7 Solutions
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
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Similar questions
- (a) Find the conditional input demand function for inputs 1 and 2, as well as the cost function for this firm. (b) What is the firm's marginal cost when it is producing y units of output?arrow_forward2 Short-Run Cost Consider a firm with the Cobb-Douglas production function F (K, L) = K 1/3 L1/2 Suppose the firm currently has 64 units of capital. The wage rate is 32 per unit and the rental rate of capital is 8 per unit. (a) Determine the short-run cost function C(Q). (b) Determine the marginal cost function and average total cost function. (c) Determine the quantity at which average total cost is minimized. (d) Sketch a graph of the MC and ATC functions, indicating the efficient scale on the graph. Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.arrow_forwardThe manager of Don Teeta Company Limited hires labour (L) and rents capital equipment (K) in a very competitive market. Currently, the wage rate of labour is GH¢2 per hour and capital is rented at GH¢5 per hour, the unit price of the product is GH¢0.75 and total cost of production is GH¢1,000. Suppose the firm's production function (Q) is as folows: Q = 14K05L05+ 10 Determine the optimal input usage and the maximum profit.arrow_forward
- The long-rung production function of a competitive firm is f(L,K)= L1/3K 1/2 , where L is the amount of labor and K is the amount of capital. The cost per unit of labor is w and the cost of capital is r, which is the interest rate. The price per unit of output is p. (A. What are the returns to scale of this production function? (B. Find the long-run profit maximizing levels of capital, labor and output.arrow_forwardA firm has the following production function: q= f (Z1, Z₂) = 2₁%2₂³ a. Solve for the firm's cost minimization problem using the Lagrangean method. Verify using the Varian Method. b. Solve for the firm's conditional demand function (simplify) c. Derive the firm's cost function (simplify)arrow_forward
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