6. (10) The translog cost function is given as k k k 1 logc(w,y) = on + E ailogwi + 5 E E biJ-logwglogwj + logy. {:1 i=1 j=l i.[3) Does this function satisfy linear homogeneity (homogeneous of degree 1} in factor prices. Answer: Not necessarily. Linear homogeneity requires I: l: 2'\" = 1 2b.} = 0. i=1 i=1 Note also that symmetry requires: '3 . 3' ii. [3) The conditional factor demands are not linear in the parameters, but the factor shares are {factor shares are the share of costs that are labor and the share of costs that are fuel. These add up to one, and by convention the translog cost function is estimated with only one factor share (Please use labor for this assignment). The factor shares given by dln{c)/d|n{w| ). Please write down the model in total (i.e., write out w/o summation signs, and put in names for the variables} you would estimate and the implied theoretical restrictions. E Hwy) = 6i + 201111110:- i=1 Please identify the restrictions implied by linear homogeneity, symmetry and, and the cross-equation restrictions between the cost function and the share equation. iii.(4) In the model, what is the returns to scale at the mean value? And, what is the returns to scale for any output level