ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN: 9780190931919
Author: NEWNAN
Publisher: Oxford University Press
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Consider a Cobb-Douglas production function with three inputs. K is capital (the number of machines), N is labor (the number of workers), and H is human capital (the number of college degrees among the workers). The production function is Y = AKiNiHi 1. Show that the production function exhibits constant retums to scale. 2. Derive an expression for the marginal product of labor. How does an increase in the amount of human capital affect the marginal product of labor? 3. Derive an expression for the marginal product of human capital. How does an increase in the amount of human capital affect the marginal product of human capital? 4. What is the income share paid to labor? What is the income share paid to human capital? In the national income accounts of this economy, what should of total income do you think workers appear to receive? (Hint: consider where the return to human capital shows up.) 5. An unskilled worker eams the marginal product of labor whereas a skilled worker eams the marginal product of labor plus the marginal product of human capital. Using your answers to Parts 2 and 3, find the ratio of the skilled wage to unskilled wage. How does an increase in the amount of human capital affect this ratio? Explain. 6. Some people advocate funding of college scholarships as a way of creating a more egalitarian society. Others argue that scholarships help only those who are able to go to college. Do your answers to the preceding questions shed light on this debate? 7. Provide the growth accounting equation for the production function with three inputs.
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Transcribed Image Text:Consider a Cobb-Douglas production function with three inputs. K is capital (the number of machines), N is labor (the number of workers), and H is human capital (the number of college degrees among the workers). The production function is Y = AKiNiHi 1. Show that the production function exhibits constant retums to scale. 2. Derive an expression for the marginal product of labor. How does an increase in the amount of human capital affect the marginal product of labor? 3. Derive an expression for the marginal product of human capital. How does an increase in the amount of human capital affect the marginal product of human capital? 4. What is the income share paid to labor? What is the income share paid to human capital? In the national income accounts of this economy, what should of total income do you think workers appear to receive? (Hint: consider where the return to human capital shows up.) 5. An unskilled worker eams the marginal product of labor whereas a skilled worker eams the marginal product of labor plus the marginal product of human capital. Using your answers to Parts 2 and 3, find the ratio of the skilled wage to unskilled wage. How does an increase in the amount of human capital affect this ratio? Explain. 6. Some people advocate funding of college scholarships as a way of creating a more egalitarian society. Others argue that scholarships help only those who are able to go to college. Do your answers to the preceding questions shed light on this debate? 7. Provide the growth accounting equation for the production function with three inputs.
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Step 1: Define production function
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Step 2: Show constant returns to scale
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Step 3: Determine marginal product of labor
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Step 4: Determine marginal product of human capital
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