Question

e Do Part e f) Do Part f g) Do Part g (ign dified R2) Q2. Suppose you are given the following Cob-Douglas Production Y = 3,x3x3 expl) for i = 1, 2, ..n, where 31. 3, and Bare population parameters and the u, are IID (0,0%) Note that: Y =output, X2i =labor input, X3i ==capital input, exp = base of the natural logarithm. (a) Transform the above non-linear model, Y; exp(-) to a linear model 5) How do you the interpret B,? (c) How do you the interpret Bz? (d) Suppose the sum (B+B2)=1, how do you interpret this result? (e) Are the variables linear and does this affect the linearity of the regression model?

Answer 1

Gren a - Yo B, 2 x heu Taking log on both sides, we get log Cri) = log B & B log Xit & logtzi + we This is a linear model as we can treat the variables log (Yi) = y. i log B, a bilogy - this Log xz & Rze and we get Hence we can equation ② is a linear model in yo, ai, ai, b, b) let us use the a operator on both sides of equation 1, we get a log Yi o + B 2 log (X2i) + 0 + 0 a Xzi = $ = 2/4 - Labour dasticity of output X2

PAGE NO. DATE c) we can do similar analysis as part b by using the a operator to go B. Milli = Capital elasticity of output 900 let us assume B₂ + B = 100 = (ar - Hence we can say that the given products function follows a constant returns to scale (CRS) T aXzi/xgi e If we follow as per oquation , we can see that we have successfully converted I the given model into a log-log model I which is linear in nature. This does not I affect the linearity of the model in any way as yo is a libear combination of Hi and Hai"