1Suppose that the total benefit depends on the level Q of a

1.Suppose that the total benefit depends on the level Q of a particular activity with total benefits given by B(Q) = 40Q - Q 2 and total costs given by C(Q) = 300 + 20Q

a. Write out the equation for net benefits.

b. What are net benefits when Q = 3? Show calculations.

c. Write out the equation for marginal net benefits.

d. What are the marginal net benefits when Q = 3

e. Can you infer from your answer to question

f. whether the net benefit function is increasing, decreasing or flat at Q = 3? Explain.

g. What is the marginal cost at Q = 8? Explain.

h. Which level of activity maximizes net benefits? Explain.

i. What are the net benefits at that level of activity? Explain.

Solution

a) Net benefits = total benefits - total costs

Net benefits = [40Q - Q²] - [300+20Q] -

Net benefits = -Q² - 300 + 20Q

b) at Q = 3

Net benefits =  -Q² - 300 + 20Q =-3² - 300 + 20x3

Net benefits = -249

c) Marginal net benefits = d (Net benefits)/dQ

Marginal net benefits =d(-Q² - 300 + 20Q)/dQ

Marginal net benefits = -2Q +20

d) at Q = 3

Marginal net benefits = -2Q+20

Marginal net benefits = -2x3 + 20 = 14

g) Marginal cost = d [ C(Q)]/dQ

MC = d [300+20Q]/dQ

MC = 20