The output (Q) of a production process is a function of two inputs (L and K) and K is given by the following relationship: Q = 0.50LK− 0.10L2− 0.05K2 The per-unit prices of inputs L and K are $20 and $25, respectively. The firm is interested in maximizing output subject to a cost constraint of $500. Use the lagrangian optimization techniques to find the following: How many units of L and K should be used by the firm? What is the total output of this combination? What is the marginal rate of substitution between L and K?
The output (Q) of a production process is a function of two inputs (L and K) and K is given by the following relationship: Q = 0.50LK− 0.10L2− 0.05K2 The per-unit prices of inputs L and K are $20 and $25, respectively. The firm is interested in maximizing output subject to a cost constraint of $500. Use the lagrangian optimization techniques to find the following: How many units of L and K should be used by the firm? What is the total output of this combination? What is the marginal rate of substitution between L and K?
Economics (MindTap Course List)
13th Edition
ISBN:9781337617383
Author:Roger A. Arnold
Publisher:Roger A. Arnold
Chapter21: Production And Costs
Section21.3: Production
Problem 3ST
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The output (Q) of a production process is a function of two inputs (L and K) and K is given by the following relationship: Q = 0.50LK− 0.10L2− 0.05K2
The per-unit prices of inputs L and K are $20 and $25, respectively. The firm is interested in maximizing output subject to a cost constraint of $500.
Use the lagrangian optimization techniques to find the following:
- How many units of L and K should be used by the firm? What is the total output of this combination?
- What is the marginal rate of substitution between L and K?
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