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In the Solow growth model, assume that the aggregate production function is Y = zF(K;L), where Y is total output, z is total productivity, K is the total capital input, and L is the total labor input. Suppose that the Cobb-Douglas form for the production function F(K;L) = K aL1-α, where 0
a. Find an expression for the output per worker as a function of the capital–labor ratio.
b. Suppose that the marginal product of capital increases for each level of capital, given the labor input level. What is the effect of this capital productivity increase on the aggregate production function? Show graphically the impact of this productivity increase on the steady-state capital–labor ratio and output per worker. Explain briefly.