1.9. 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 con dition at yss = VJ(_SSL, and let K55 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

= 1.21L on the Solow diagram.

c. What are the algebraic and numeric out comes for the short-run level of output, that is, y ss in terms of K55 and L?

d. Show the new steady-state level of output on the diagram.

Growth, Capital Accumulation, and the Economics of Ideas: Catching Up vs. Cutting Edge • CHAPTER 8 • 169

e. Demonstrate whether thi country will be able to produce 21% more output with a 21%

increase in the labor supply. Show thi result algebraically. As illustrated in Challenge ques tion 3, you will need to use the teady- tate condition -y Y = oK to show thi re ult.

f.

Derive output per worker in the initial steady state (use Y~ from part a and divide by the labor force); output per worker in the short run (use y~s from part c and divide by the new labor force); and output per worker in the long run (use ~s from parte and di vide by the new labor force).

g. Are the citizen of this country made worse or better off in the long run by a new immigration policy such as this; that is, how doe the new long-run level of output per worker compare with the initial level of output per worker?

h. Bonus: What is the value for the new steady state level of capital stock in this country?