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How do I determine the per-worker production function, y = f (k) of the production function...

How do I determine the per-worker production function, y = f (k) of the production function Y = K1/3 L2/3?

I know I must divide both sides by L, labor. This gives me y = (K1/3L2/3)/L. Where do I go from here?

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Answer #1

Y=K^1/3*L^2/3

Y/L=k^1/3*L^2/3)/L

Y/L=K^1/3*L^-1/3

Y/L=(K/L)^1/3

So output per worker(y),

y=k^1/3,where y is output per worker and k is capital per worker.

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