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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: Applications, Strategies and Tactics (MindTap Course List)
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:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter7: Production Economics
Section: Chapter Questions
Problem 3E
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2. 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 PL = w for capital and labour respectively. Find the firm's conditional input demands. (d) Now suppose that the firm's contract with the upstream retailer is coming to an end and they are considering whether to extend it or not. The retailer will purchase 1000 chairs per day at £50 per chair. If the firm does not extend their contract then they can sell their chairs locally and will 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 contract with the national retailer? (Note: Assume the firm can only sell to either the market or the retailer)
Transcribed Image Text:2. 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 PL = w for capital and labour respectively. Find the firm's conditional input demands. (d) Now suppose that the firm's contract with the upstream retailer is coming to an end and they are considering whether to extend it or not. The retailer will purchase 1000 chairs per day at £50 per chair. If the firm does not extend their contract then they can sell their chairs locally and will 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 contract with the national retailer? (Note: Assume the firm can only sell to either the market or the retailer)
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