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.)

Instructions: Use a negative sign (-) where appropriate.

a. Write out the equation for the net benefits.

N(Q) = ______________ +________________  Q +________________  Q²

b. What are the net benefits when Q = 1? Q = 5?

Net benefits when Q = 1: _____________
Net benefits when Q = 5: ______________

c. Write out the equation for the marginal net benefits.

MNB(Q) = _____________ +____________  Q

d. What are the marginal net benefits when Q = 1? Q = 5?

Marginal net benefits when Q = 1: ____________
Marginal net benefits when Q = 5: _______________

e. What level of Q maximizes net benefits?

_______________

f. At the value of Q that maximizes net benefits, what is the value of marginal net benefits?

_____________________

Answer 1

(a) Net benefit = B(Q) - C(Q) = 100 + 36Q – 4Q² - (80 + 12Q) = 100 + 36Q – 4Q² - 80 - 12Q = 20 + 24Q - 4Q²

N(Q) = 20 + 24Q + (-4) Q²

(b)

When Q = 1, N(Q) = 20 + (24 x 1) - (4 x 1 x 1) = 20 + 24 - 4 = 40

When Q = 5, N(Q) = 20 + (24 x 5) - (4 x 5 x 5) = 20 + 120 - 100 = 40

(c) Marginal Net benefit = MB(Q) - MC(Q) = 36 - 8Q - 12

MNB(Q) = 24 + (-8) Q

(d)

When Q = 1, MNB = 24 - 8 = 16

When Q = 5, MNB = 24 - (8 x 5) = 24 - 40 = -16

(e)

Net benefit is maximized when MNB(Q) = 0

24 - 8Q = 0

8Q = 24

Q = 3

(f)

When Q = 3, MNB = 0