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Draw an isoquant representing Y = 140 for each of the following ca and K denotes units of capital. A. Y = Min (2L, 7K). Find the TRS at L = 80 and K = 20

Draw an isoquant representing Y = 140 for each of the following ca and K denotes units of capital. A. Y = Min (2L, 7K). Find the TRS at L = 80 and K = 20

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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**Title: Understanding Isoquants in Production** To explore the concept of isoquants in production, consider the scenarios below where \( L \) denotes the number of workers and \( K \) denotes units of capital. We aim to draw an isoquant representing \( Y = 140 \) for each case. **Case A: Perfect Complements** Given: \( Y = \text{Min} (2L, 7K) \) Task: Find the TRS (Technical Rate of Substitution) at \( L = 80 \) and \( K = 20 \). This case represents a situation of perfect complements where output depends on the minimum of a linear combination of labor and capital. Here, the isoquant will reflect a right-angle (L-shaped) path due to the fixed proportions of inputs needed. **Case B: Linear Combination** Given: \( Y = 2L + 7K \) Task: Find the TRS. In this scenario, the production function is a linear combination of labor and capital. The isoquant will appear as a straight line since the inputs can be perfectly substituted at a constant rate. The TRS in this case is determined by the ratio of the coefficients of labor and capital in the production function. --- **Graphs and Diagrams Explanation:** - **Isoquant for Perfect Complements (Case A):** The graph will show an L-shaped curve. The 'corner' of the L will correspond to the optimal mix of labor and capital, which is essential for producing the desired level of output. Beyond this point, increasing one input without the other won't increase output. - **Isoquant for Linear Combination (Case B):** The graph will depict a straight line with a constant negative slope. This constant slope represents the TRS, indicating a constant rate at which one input can be substituted for another while maintaining the same output level.
Transcribed Image Text:**Title: Understanding Isoquants in Production** To explore the concept of isoquants in production, consider the scenarios below where \( L \) denotes the number of workers and \( K \) denotes units of capital. We aim to draw an isoquant representing \( Y = 140 \) for each case. **Case A: Perfect Complements** Given: \( Y = \text{Min} (2L, 7K) \) Task: Find the TRS (Technical Rate of Substitution) at \( L = 80 \) and \( K = 20 \). This case represents a situation of perfect complements where output depends on the minimum of a linear combination of labor and capital. Here, the isoquant will reflect a right-angle (L-shaped) path due to the fixed proportions of inputs needed. **Case B: Linear Combination** Given: \( Y = 2L + 7K \) Task: Find the TRS. In this scenario, the production function is a linear combination of labor and capital. The isoquant will appear as a straight line since the inputs can be perfectly substituted at a constant rate. The TRS in this case is determined by the ratio of the coefficients of labor and capital in the production function. --- **Graphs and Diagrams Explanation:** - **Isoquant for Perfect Complements (Case A):** The graph will show an L-shaped curve. The 'corner' of the L will correspond to the optimal mix of labor and capital, which is essential for producing the desired level of output. Beyond this point, increasing one input without the other won't increase output. - **Isoquant for Linear Combination (Case B):** The graph will depict a straight line with a constant negative slope. This constant slope represents the TRS, indicating a constant rate at which one input can be substituted for another while maintaining the same output level.
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