2. A firm uses capital (K) and labour (L) to produce luxury office chairs. The productiontechnology is given by Q = K³/4L¹/4, where Q is the number of chairs produced.(a) What is the marginal product of capital and the marginal product of labour for thisfirm?(b) Does this production function display decreasing returns to scale, constant returns toscale or increasing returns to scale? Justify your answer.(c) Suppose that the firm has a contract with a national retailer who purchases Q officechairs from them per day. The firm faces prices PK= r and PL = w for capital andlabour respectively. Find the firm's conditional input demands.(d) Now suppose that the firm's contract with the upstream retailer is coming to an endand they are considering whether to extend it or not. The retailer will purchase 1000chairs per day at £50 per chair.If the firm does not extend their contract then they can sell their chairs locally andwill face an inverse demand curve P(Q) = 500 - Q.Assume that r = 16 and w = = 16/3.(i) What is the firm's profit function (Q) if they sell to the local market?(ii) What is the firm's optimal output level if they sell to the local market?(iii) Is the firm better off selling to only the local market or extending the contractwith the national retailer? (Note: Assume the firm can only sell to either themarket or the retailer)

GivenProduction function: ......... (1)Here Q is the number of chairs produced, L…

A firm uses capital (K) and labour (L) to produce luxury office chairs. The production technology is given by Q = K3/4L¹/4, where Q is the number of chairs produced. (a) What is the marginal product of capital and the marginal product of labour for this firm? (b) Does this production function display decreasing returns to scale, constant returns to scale or increasing returns to scale? Justify your answer. (c) Suppose that the firm has a contract with a national retailer who purchases Q office chairs from them per day. The firm faces prices PK = r and p₁ = w for capital and labour respectively. Find the firm's conditional input demands.

A firm uses capital (K) and labour (L) to produce luxury office chairs. The production technology is given by Q = K3/4L¹/4, where Q is the number of chairs produced. (a) What is the marginal product of capital and the marginal product of labour for this firm? (b) Does this production function display decreasing returns to scale, constant returns to scale or increasing returns to scale? Justify your answer. (c) Suppose that the firm has a contract with a national retailer who purchases Q office chairs from them per day. The firm faces prices PK = r and p₁ = w for capital and labour respectively. Find the firm's conditional input demands.

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter7: Economies Of Scale And Scope

Section: Chapter Questions

Problem 7.5IP

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