Derive the factor demands given prices of factors
Econometrics
The output of the Ofce is measured by the number of forms lled by the employees. It can be described by a function y = 10 min (l; k) ; where l is the amount of labor, and k is the number of computers used
a. Solve the long-run cost minimization problem and derive the factor demands given prices wl and wk. Derive the cost function.
b. Suppose that the Ofce can hire skilled labor h that can ll the forms without using computers. The output of the Ofce that hires h skilled labor, l unskilled labor and k computers is equal to y = l + 10 min (h; k) :
Solve the long-run cost minimization problem and derive the factor demands given prices of factors, wl; wh and wk. Hint: denote ws = wl + wk as the price of computer-based forms.
c. For what levels of prices the Ofce will hire the skilled labor? For what levels of prices the Ofce will rent any computers?
d. Characterize returns to scale (i.e., are they increasing, decreasing, or constant).
