Question

Q2. Suppose you are given the following Cob-Douglas Production Y; = B1X2 X3 exp(ui) for i = 1, 2, ...,n, where B1, B2 and Bzare population parameters and the Ui are IID (0,02). Note that: Y; routput, X2i =labor input, Xzi =capital input, exp = base of the natural logarithm. (a) Transform the above non-linear model, Yį = B2X2 X : exp(ui) to a linear model (b) How do you the interpret B2? (c) How do you the interpret By? (d) Suppose the sum (B2+B3)=1, how do you interpret this result? (e) Are the variables linear and does this affect the linearity of the regression model?

Answer 1

B2 B3 (a) Yi- ß, X29 x 39 explui) Taking Natural log (Roth sides ) in B2 B3 intis In (B, X 29 x 31 exp cuis) inyo = Inßit B2 inx2 + 83 in xzi tui (1) (b) differenticite equation (1) wort x2i dinyi - Br Jin X2i = dinti - tri xri Jinxai ix2 Ti Bz represents Partial elasticity of yo with Respect to that is the X28. elasticity. OR % Change in Average value of ye for % Change in xp when yzo held constant - Lohere = (c.) differ Similarly for xzi B3 = Re Presents Pao tial elasticity of yi with Respect to X30 % in Avg. value of vi Jor to change in Xi When X2i held constant OR

(d)- Br+ B2 = 1 that is Pao tial Sole Cocyficient Sum = 1 So, there is constant Returns to scale. (C) variables are not linear. Yes this agject the dinearity of Regsession model