Consider the CobbDouglas production function Y = 1 L 2 K 3 ......................(1) where Y = output, L = labor input, and K =

Consider the Cobb–Douglas production function

Y = β₁L^β2K^β3 ......................(1)

where Y = output, L = labor input, and K = capital input. Dividing (1) through by K, we get

(Y/K) = β₁(L/K)^β2K^β2+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 + u_i ......................(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?