Question

1. (10 pts.) Your firm's research department has estimated your total revenues to be R(Q) = 3,000 - 8Q2 and your total costs to be C(Q) = 100 + 2Q

1. What are the net benefits when Q=100? Q=200?

2. What are the marginal net benefits when Q=100? Q=200?

3. What level of Q maximizes net benefits?

4. What is marginal net benefit at the level of Q that maximizes net benefit? Marginal revenue? Marginal cost?

Answer 1

Here, i am assuming that the question is :

Your firm's research department has estimated your total revenues to be R(Q) = 3,000 - 8Q² and your total costs to be C(Q) = 100 + 2Q²

a) Net benefit at Q = 100

3000*100 -8*(100)² - [100 +2*100²]

= 199900

Net benefit at Q = 200

3000*200 -8*(200)² - [100 +2*200²]

199900

b) Marginal benefit (MB) = d(R(Q))/dQ = 3000 - 16Q

At Q = 100,

MB = 3000-16*100 = 1400

At Q = 200,

MB = 3000 - 16*200 = -200

c) Q maximize where MB = MC ( marginal cost)

MC = d(C(Q))/dQ = 4Q

3000-16Q = 4Q

3000 = 20Q

Q = 150

d) When Q= 150, net benefits are $224,900.

Marginal benefit = 3000- 16*150 = 600

MC = 4*150 = 600