(30 total points) suppose a firm’s production function is given by q = l1/2*k1/2. the marginal product of labor and the marginal product of capital are given by: mpl = 1/ 2 1/ 2 2l k , and mpk = 1/ 2 1/ 2 2k l . a) (12 points) if the price of labor is w = 48, and the price of capital is r = 12, how much labor and capital should the firm hire in order to minimize the cost of production if the firm wants to produce output q = 18?
l=9, k = 36
Let a firm's production function= Q = L1/2*K1/2.
Price of labor is given as, w = 48
Price of capital is given as, r = 12
Formula for Cost, c = w*l + 12*k
When we put the value of Q as 10 om the first equation, we get
18 = L1/2*K1/2
Thus, k = 324/l which is out first equation.
c= 48*l + 12*k where we place the value of k we got from first equation.
c = 48*l +12*(324/l)
After calculation of above equation, we will get l = 9
k (from first equation)= 324/9 = 36