Attached an image 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 theworkers). The production function isY = AKiNiHi1. 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 ofhuman capital affect the marginal product of labor?3. Derive an expression for the marginal product of human capital. How does an increase in theamount 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 thenational income accounts of this economy, what should of total income do you think workersappear 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 themarginal product of labor plus the marginal product of human capital. Using your answers toParts 2 and 3, find the ratio of the skilled wage to unskilled wage. How does an increase in theamount of human capital affect this ratio? Explain.6. Some people advocate funding of college scholarships as a way of creating a more egalitariansociety. Others argue that scholarships help only those who are able to go to college. Do youranswers 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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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 = AKIN H 1. Show that the production function exhibits constant returns 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?

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 = AKIN H 1. Show that the production function exhibits constant returns 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?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.2P

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