Question

Suppose that the total benefit and total cost from a continuous activity are, respectively, given by the following equations: B(Q) = 100 + 36Q – 4Q2 and C(Q) =80 + 12Q. (Note: MB(Q) = 36 – 8Q and MC(Q) = 12.)(a) Write out the equation for the net benefits.(b) What are the net benefits when Q=1 and Q=5?(c) Write out the equation for the marginal net benefits.

Answer 1

Answer:

A. Net benefits equation 20 + 24q - 4q^2

B. Q(1) = 40 ; Q(5) = 40

C. BE' = 24 - 8q

Explanation:

A. Net benefits:

Benefits equation - Cost equation

[100 + 36q - 4q^2] - [80 + 12q]

100 + 36q - 4q^2 - 80 - 12q

20 + 24q - 4q^2

B. replace Q=1 and Q=5

• For Q= 1

Q(1) = 20 + 24(1) - 4(1)^2

Q(1)= 44 - 4

Q(1) = 4

• For Q= 5

Q(5) = 20 + 24(5) - 4(5^2)

Q(5)= 20 + 120 - 4(25)

Q(5) = 140 - 100

Q(5) = 40

C. Marginal Benefits. First derivative of the equation wrote in section A.

Benefits equation : 20 + 24q - 4q^2

BE' = 24 - 8q