Consider how unemployment would affect the Solow growth model. Suppose that output is produced according to the production function Y = Kα [(1 – u)L]1-α where K is capital, L is the labor force, and u is the natural rate of unemployment. The national saving rate is s, the labor force grows at rate n, and capital depreciates at rate δ.
a. Write a condition that describes the golden rule steady state of this economy.
b. Express the golden rule levels of capital per worker, k*G, and output per worker, y*G, as functions of the parameters, s, n, δ, α, and u.
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