Question

Suppose a firm can use either Capital (K) or Labor (L) in a production process. The firms Production function is given by Q = 5L + 15K. The price of Capital is $20 per unit and the price of Labor is $8 per unit.

a) (4 points) What is the firm’s Total Cost function?

TC(Q) = ____________________________

b) (8 points) Suppose the firm is producing 30 units of output (Q = 30). Using a graph, draw the firm’s isoquant for Q = 30. Also, on the same graph, draw the isocost line associated with the total cost of producing Q = 30. Your graph should be accurate and carefully labeled. Please put the units of Capital (K) on the vertical axis, and the units of Labor (L) on the horizontal axis. Make sure to clearly indicate the cost-minimizing combination of Labor and Capital that the firm should use, and to clearly label both the isocost line and the isoquant.

Answer 1

a) A firm's total cost function is wL+rK where w= wage and r= price of capital

Total cost function = 8L + 20K

b) The production function is Q = 5L + 15K.

- Q = 54 + 15k = 30 If w= 0: K =2 . If k=0, 4= 6 Hence, the two points for our is ocast line is (0, 2) and (6,0). Cest minimization is at MPL - w - MPK But, in our case, we do not get an equilibrium point where the above condition holds, se, the isocost and the isoquant does not intersect at =30 capital Isoquant 8=30. Isocast Labour L) 6