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{"ops":[{"insert":"Consider the Cobb\u2013Douglas production function"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"Y = \u03b21L\u03b22K\u03b23 (1)"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"where Y = output, L = labor input, and K = capital input. Dividing (1) through by"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"K, we get"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"(Y\/K) = \u03b21(L\/K)\u03b22K\u03b22+\u03b23\u22121 (2)"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"Taking the natural log of (2) and adding the error term, we obtain"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"ln (Y\/K) = \u03b20 + \u03b22 ln (L\/K) + (\u03b22 + \u03b23 \u2212 1) ln K + ui"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"where \u03b20 = ln \u03b21."},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"a. Suppose you had data to run the regression (3). How would you test the hypothe-"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"sis that there are constant returns to scale, i.e., (\u03b22 + \u03b23) = 1?"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"b. If there are constant returns to scale, how would you interpret regression (3)?"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"c. Does it make any difference whether we divide (1) by L rather than by K?"},{"insert":"\n"}]}

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