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Change the production function used in the chapter to reflect the contribution of labor in the production process. As with capital, labor also has diminishing returns, so let Y = √√KL. Now suppose that immigration reform leads to an increase in this country's labor force. a) Begin with a country in a steady-state condition at yss = √KSL and let KSS equal 400 and L = 100. What is the steady-state level of output? b) Show the short-run effects of a 21% increase in the amount of labor available for use in this country such that L₁ = 1.214 on the Solow diagram. c) What are the algebraic and numeric outcomes for the short-run level of output, that is, yss in terms of KSS and L? d) Show the new steady-state level of output on the diagram. e) Demonstrate whether this country will be able to produce 21% more output with a 21% increase in the labor supply. Show this result algebraically. As illustrated in question 8.1, you will need to use the steady-state condition Y = 8K to show this result. f) Derive output per worker in the initial steady state (use Yoss from part a and divide by the labor force); output per worker in the short run (use Y₁ss from part c and divide by the new labor force); and output per worker in the long run (use Y₁ss from part e and divide by the new labor force). g) Are the citizens of this country made worse or better off in the long run by a new immigration policy such as this; that is, how does the new long-run level of output per worker compare with the initial level of output per worker? h) What is the value for the new steady-state level of capital stock in this country?

Change the production function used in the chapter to reflect the contribution of labor in the production process. As with capital, labor also has diminishing returns, so let Y = √√KL. Now suppose that immigration reform leads to an increase in this country's labor force. a) Begin with a country in a steady-state condition at yss = √KSL and let KSS equal 400 and L = 100. What is the steady-state level of output? b) Show the short-run effects of a 21% increase in the amount of labor available for use in this country such that L₁ = 1.214 on the Solow diagram. c) What are the algebraic and numeric outcomes for the short-run level of output, that is, yss in terms of KSS and L? d) Show the new steady-state level of output on the diagram. e) Demonstrate whether this country will be able to produce 21% more output with a 21% increase in the labor supply. Show this result algebraically. As illustrated in question 8.1, you will need to use the steady-state condition Y = 8K to show this result. f) Derive output per worker in the initial steady state (use Yoss from part a and divide by the labor force); output per worker in the short run (use Y₁ss from part c and divide by the new labor force); and output per worker in the long run (use Y₁ss from part e and divide by the new labor force). g) Are the citizens of this country made worse or better off in the long run by a new immigration policy such as this; that is, how does the new long-run level of output per worker compare with the initial level of output per worker? h) What is the value for the new steady-state level of capital stock in this country?

Essentials of Economics (MindTap Course List)
Essentials of Economics (MindTap Course List)
8th Edition
ISBN:9781337091992
Author:N. Gregory Mankiw
Publisher:N. Gregory Mankiw
Chapter17: Production And Growth
Section17.1: Economic Growth Around The World
Problem 1QQ
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Change the production function used in the chapter to reflect the contribution of labor in the production process. As with capital, labor also has diminishing returns, so let Y = √√KL. Now suppose that immigration reform leads to an increase in this country's labor force. a) Begin with a country in a steady-state condition at yss = √KSL and let KSS equal 400 and L = 100. What is the steady-state level of output? b) Show the short-run effects of a 21% increase in the amount of labor available for use in this country such that L₁ = 1.214 on the Solow diagram. c) What are the algebraic and numeric outcomes for the short-run level of output, that is, yss in terms of KSS and L? d) Show the new steady-state level of output on the diagram. e) Demonstrate whether this country will be able to produce 21% more output with a 21% increase in the labor supply. Show this result algebraically. As illustrated in question 8.1, you will need to use the steady-state condition Y = 8K to show this result. f) Derive output per worker in the initial steady state (use Yoss from part a and divide by the labor force); output per worker in the short run (use Y₁ss from part c and divide by the new labor force); and output per worker in the long run (use Y₁ss from part e and divide by the new labor force). g) Are the citizens of this country made worse or better off in the long run by a new immigration policy such as this; that is, how does the new long-run level of output per worker compare with the initial level of output per worker? h) What is the value for the new steady-state level of capital stock in this country?
Transcribed Image Text:Change the production function used in the chapter to reflect the contribution of labor in the production process. As with capital, labor also has diminishing returns, so let Y = √√KL. Now suppose that immigration reform leads to an increase in this country's labor force. a) Begin with a country in a steady-state condition at yss = √KSL and let KSS equal 400 and L = 100. What is the steady-state level of output? b) Show the short-run effects of a 21% increase in the amount of labor available for use in this country such that L₁ = 1.214 on the Solow diagram. c) What are the algebraic and numeric outcomes for the short-run level of output, that is, yss in terms of KSS and L? d) Show the new steady-state level of output on the diagram. e) Demonstrate whether this country will be able to produce 21% more output with a 21% increase in the labor supply. Show this result algebraically. As illustrated in question 8.1, you will need to use the steady-state condition Y = 8K to show this result. f) Derive output per worker in the initial steady state (use Yoss from part a and divide by the labor force); output per worker in the short run (use Y₁ss from part c and divide by the new labor force); and output per worker in the long run (use Y₁ss from part e and divide by the new labor force). g) Are the citizens of this country made worse or better off in the long run by a new immigration policy such as this; that is, how does the new long-run level of output per worker compare with the initial level of output per worker? h) What is the value for the new steady-state level of capital stock in this country?
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