A firm manufactures widgets according to the production function Q = 8L1/4 K3/4, where Q is the number of skis made, K is the amount of capital, and L is the amount of labor employed. The firm is currently producing Q =400 using L = 50 and K = 50. The factor price of labor (w) is $5 and the factor price of capital (r) is $12. The firm suspects that it is not minimizing the cost of producing Q = 400 and has hired you, a student taking a course with the most famous economist in campus, to help it understand the nature of its inefficiency.
a) At the current level of production (Q = 400) what are the marginal productivities of Labor and Capital respectively?
MPL =
MPK =
b) What are the current cost of production for the company?
TC =
c) In order to minimize the costs of production the company should use more Capital or Labor
d) In order to miminize costs of production the company should use the following input ration: K = AnswerL
e) Say the company wanted to continue use the same total costs as to when K and L = 50, and instead produce more output. How much output can the company produce?
Q2 =