Economics Homework
1. (7 points) For each of the following production functions, calculate the marginal product
of labor, the marginal product of capital, and the Rate of Technical Substitution (MPL/
MPK). State whether the production function has increasing, constant, or decreasing
returns to scale.
a) Q = 3 K + 4 L
b) Q = 20 K.4 L.5
c) Q = (20K.6 + 30 L.6)2/3
d) Q = 2K + 4L + 6(KL).5
e) ln Q = .2 ln K + .8 ln L + .1 ln K ln L
2. (8 points) Consider the production function
Q = 5 K.3 L.6
This firm faces a wage of $10/unit and a rental price of capital of $30/unit.
a) Show that fk>0 , fL>0, fkk<0, fLL<0, and fkL= fLk>0
b) Derive the total cost function, the marginal cost function, and the average cost function for
this firm when both capital and labor are variable.
c) Derive the total cost function, the marginal cost function, and the average cost function for
this firm when capital is fixed at 2 units. At what quantity does MC=AC in the short-run?
d) At what values are the MC and AC for the short-run function in part d) equal to the long-run
function in part c)?
