Question #24706

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]

Expert's answer

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

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

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