In: Economics
1. A firm produces 100 units of good A at a total cost of $1,500 and separately 200 units of good B at a cost of $2,000. By combining the production of A and B, it is possible to produce the same quantities of A and B respectively at a combined total cost of $2,238. Compute the economies of scope experienced by this firm.
Hint: Write your answer to two decimal places.
2. Suppose we are given a profit function Q = 12L.5K.5 . The price of labor is $6 per unit and the price of capital (K) is $15 per unit. The firm is interested in the optimal mix of inputs to minimize the cost of producing any level of output Q. In the optimal mix the ratio of labor to capital is ____ .
Hint: Write your answer to two decimal places. When discussing ratios the convention is "ratio of a to b" is
a/b"
3. A firm’s long-run average cost curve is estimated by the equation: LAC = 1,000 – 1.6Q + .005Q2 . What is the lowest price per unit sold that would prevent the firm from shutting down in the long run?
Hint: Write the answer to two decimal places.
1) Total cost (separate) = A + B = 1000 + 1500 = 3500
Total cost (actual) = 2238
Economies of scope = (3500 - 2238)/3500 = 0.36
2) For optimal mix: MPL/w = MPK/r
MPL = dQ/dL = 6(K/L)0.5
MPK = 6(L/K)0.5
MPL/MPK = K/L = 6/15
L/K = 2.5
3) lowest price = min ATC
ATC = 1000 - 1.6Q + 0.005Q2
ATC is minimum when d(ATC)/dQ = 0
0.01Q = 1.6
Q = 160
lowest price = 1000 - 1.6 x 160 + 0.005 x 1602 = 872