**Exercise 11**Suppose that a firm's production function is:\[ q = 10L^{0.5}K^{0.5} \]Its marginal product functions are:\[ MP_L = 5K^{0.5}/L^{0.5} = 0.5q/L \]\[ MP_K = 5L^{0.5}/K^{0.5} = 0.5q/K \]The cost of a unit of labor, $ w $, is $50 and the cost of a unit of capital, $ r $, is $50. Isoquants for output of 140 and 280 are illustrated in the figure to the right.Initially, the firm is producing 140 units of output and has determined that the cost-minimizing quantities of labor and capital are 14 and 14, respectively.Suppose now that the firm wants to increase output to 280 units. If capital is fixed in the short run, how much labor will the firm require?The firm will now require [ ] units of labor. (Enter your response rounded to two decimal places.)**Graph Explanation:**The graph on the right displays two isoquants representing different levels of production output: 140 and 280 units. The x-axis is labeled "L, Units of labor," ranging from 0 to 112. The y-axis is labeled "K, Units of capital," ranging from 0 to 112. The isoquants show a downward curve, indicating the trade-off between labor and capital while maintaining the specified levels of output. The q = 140 isoquant is closer to the origin compared to the q = 280 isoquant, reflecting the increased input requirement for higher production levels.

Output has increased to 280 units, capital is 14 units. Therefore, q=10L0.5K0.5280=10L0.5(14)0.5…

Suppose that a firm's production function is: 112- q = 10L0.5K0.5 98- Its marginal product functions are: 84- MP, = 5K0.5/L0.5 = 0.5g/L 70- and MPK = 5L0.5/K0.5 = 0.5q/K. 56- The cost of a unit of labor, w, is $50 and the cost of a unit of capital, r, is $50. Isoquants for output of 140 and 280 are illustrated in the figure to the right. 42- 28- Initially, the firm is producing 140 units of output and has determined that the cost-minimizing quantities of labor and capital are 14 and 14, respectively. 14- Suppose now that the firm wants to increase output to 280 units. If capital is fixed in the short run, how much labor will the firm require? q= 280 요후 140 98 0- 14 28 42 56 70 84 112 K, Units of capital

Suppose that a firm's production function is: 112- q = 10L0.5K0.5 98- Its marginal product functions are: 84- MP, = 5K0.5/L0.5 = 0.5g/L 70- and MPK = 5L0.5/K0.5 = 0.5q/K. 56- The cost of a unit of labor, w, is $50 and the cost of a unit of capital, r, is $50. Isoquants for output of 140 and 280 are illustrated in the figure to the right. 42- 28- Initially, the firm is producing 140 units of output and has determined that the cost-minimizing quantities of labor and capital are 14 and 14, respectively. 14- Suppose now that the firm wants to increase output to 280 units. If capital is fixed in the short run, how much labor will the firm require? q= 280 요후 140 98 0- 14 28 42 56 70 84 112 K, Units of capital

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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