Answer to Question #143492 in Macroeconomics for Eric

Question

1. A firm has the following production function Q=K1/3L2/3. It will produce 80 units of output and faces prices for labour and capital as capital follows: w=10, r=15.
a. Show whether the production function exhibits decreasing, increasing or constant returns to scale?
b. Find the cost minimizing bundle of labour and capital
c. Explain what the prisoners dilemma means.

Answer 1

a. The production function exhibits decreasing returns to scale.

b. The cost minimizing bundle of labour and capital is at the levels of capital and labor such that the marginal product of labor divided by the wage (w) is equal to the marginal product of capital divided by the rental price of capital (r).

$MPK = 1/3×(L/K)^{2/3},$

$MPL = 2/3×(K/L)^{1/3},$

0.5×L/K = 15/10,

L = 3K,

$Q = K^{1/3}×3K^{2/3} = 80,$

K = 26.67 units, L = 80 units.

c. The prisoner's dilemma is a paradox in decision analysis in which two individuals acting in their own self-interests do not produce the optimal outcome. The typical prisoner's dilemma is set up in such a way that both parties choose to protect themselves at the expense of the other participant.