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 Y^ss = √(K^ssL) , 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 = 1.21L on the Solow diagram.

c. What are the algebraic and numeric outcomes for the short-run level of output, that is, Y^ss in terms of K^ss 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 Challenge question you will need to use the steady state condition ϒY = ϒK to show this result.

f. Derive output per worker in the initial steady state (use Y₀^ss from part a and divide by the labor force); output per worker in the short run (use Y^ss from part c and divide by the new labor force); and output per worker in the long run (use Y^ss 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. Bonus: What is the value for the new steady state level of capital stock in this country?