### What is the labor share and capital share of output

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Consider the following technology F(K,L) = (AK^?)(L^(1??)) where K is the level of capital, L is the level of labor or hours worked, A is a efficiency parameter and ?  (0, 1)

(a) Write down the firms problem in the long-run. Note the price for capital and labor are respectively, r and w. (Normalize the price of output to be 1 so that w and r are in real terms).

(b) Does this production function depict constant return to scale? Prove it.

(c) What are the marginal productivities of capital and labor? Are they decreasing in each factor?

(d) What is the labor share and capital share of output?

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