Consider the CobbDouglas production function Y = 1 L 2 K 3 ......................(1) where Y =
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Consider the Cobb–Douglas production function
Y = β1Lβ2Kβ3 ......................(1)
where Y = output, L = labor input, and K = capital input. Dividing (1) through by K, we get
(Y/K) = β1(L/K)β2Kβ2+β3−1 ......................(2)
Taking the natural log of (2) and adding the error term, we obtain
ln (Y/K) = β0 + β2 ln (L/K) + (β2 + β3 − 1) ln K + ui ......................(3)
where β0 = ln β1.
a. Suppose you had data to run the regression (3). How would you test the hypothesis that there are constant returns to scale, i.e., (β2 + β3) = 1?
b. If there are constant returns to scale, how would you interpret regression (3)?
c. Does it make any difference whether we divide (1) by L rather than by K?
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