Answer to Question #24706 in Economics of Enterprise for Mohamed Abdi

Question

Question 7 Consider the following short-run production function (where L = variable input, Q =
output):
Q = 6L3 – 0.4L3
a. Determine the marginal product function (MPL).
[1 marks]
b. Determine the average product function (APL).
[1 marks]
c. Find the value of L that maximizes Q.
[1 marks]
d. Find the value of L at which the marginal product function takes on its maximum
value.
[1 marks]
e. Find the value of L at which the average product function takes on its maximum
value.
[1 marks]
[TOTAL: 5 MARKS]

Answer 1

Consider the following short-run production function (where L = variable input, Q = output): Q= 6L3 – 0.4L3
a.Determine the marginal product function (MPL).
MPL = Q' = 16.8L2
b.Determine the average product function (APL).
APL = Q/L = 5.6L2
c.Find the value of L that maximizes Q.
Q = max, when Q' = MPL = 0, L = 0
d.Find the value of L at which the marginal product function takes on its maximum
MPL = max, when MPL' = 0, 33.6L = 0, L = 0
e.Find the value of L at which the average product function takes on its maximum value.
APL = max, when APL' = 0, 11.2L = 0, L = 0