2. A firm’s production function is given by:Q = 10KLThe unit capital and labour costs are 2 and 1 pounds respectively. The firm is contracted to produce2000 units.(a) Write out the optimisation problem of the firm. (b) Express this problem using a Lagrangian function. (c) Find values of K and L which fulfil the contract with minimal cost to the firm. (d) Calculate the total cost to the firm.
2. A firm’s production function is given by:Q = 10KLThe unit capital and labour costs are 2 and 1 pounds respectively. The firm is contracted to produce2000 units.(a) Write out the optimisation problem of the firm. (b) Express this problem using a Lagrangian function. (c) Find values of K and L which fulfil the contract with minimal cost to the firm. (d) Calculate the total cost to the firm.
Economics (MindTap Course List)
13th Edition
ISBN:9781337617383
Author:Roger A. Arnold
Publisher:Roger A. Arnold
Chapter21: Production And Costs
Section21.4: Costs Of Production: Total, Average, Marginal
Problem 1ST
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2. A firm’s production function is given by:
Q = 10KL
The unit capital and labour costs are 2 and 1 pounds respectively. The firm is contracted to produce
2000 units.
(a) Write out the optimisation problem of the firm.
(b) Express this problem using a Lagrangian function.
(c) Find values of K and L which fulfil the contract with minimal cost to the firm.
(d) Calculate the total cost to the firm.
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