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Suppose that a certain factory output is given by the Cobb-Douglas production function Q(K, L) = 60K¹/3 [2/3 units, where K is the level of capital and L the size of the labor force need to maximize the factory's output. If a unit of labour costs $100, unit of capital $200, and $200,000 is budgeted for production (d) Write down the first-order conditions. (e) Determine how many units should be expended on labour and how many units should be expended on capital in order to maximize production. (f) What is the maximum production level?

Suppose that a certain factory output is given by the Cobb-Douglas production function Q(K, L) = 60K¹/3 [2/3 units, where K is the level of capital and L the size of the labor force need to maximize the factory's output. If a unit of labour costs $100, unit of capital $200, and $200,000 is budgeted for production (d) Write down the first-order conditions. (e) Determine how many units should be expended on labour and how many units should be expended on capital in order to maximize production. (f) What is the maximum production level?

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 10E
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Suppose that a certain factory output is given by the Cobb-Douglas production function Q(K, L) = 60K ¹/3 12/3 units, where K is the level of capital and L the size of the labor force need to maximize the factory's output. If a unit of labour costs $100, unit of capital $200, and $200,000 is budgeted for production (d) Write down the first-order conditions. (e) Determine how many units should be expended on labour and how many units should be expended on capital in order to maximize production. (f) What is the maximum production level? (g) Use the bordered Hessian to prove that the level of production is indeed maximized.
Transcribed Image Text:Suppose that a certain factory output is given by the Cobb-Douglas production function Q(K, L) = 60K ¹/3 12/3 units, where K is the level of capital and L the size of the labor force need to maximize the factory's output. If a unit of labour costs $100, unit of capital $200, and $200,000 is budgeted for production (d) Write down the first-order conditions. (e) Determine how many units should be expended on labour and how many units should be expended on capital in order to maximize production. (f) What is the maximum production level? (g) Use the bordered Hessian to prove that the level of production is indeed maximized.
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