Question

This is a multipart question.

Assume that total benefits for a given level of output are given as B(Q) = 100 + 20Q - 2Q², and that C(Q) = 20 + 10Q. Assume that Q is in thousands units and benefits and costs are in dollars.

1. Write out the net benefit equation:

2. What are the net benefits when Q = 10? Explain result meaning based on the economic theory.

3.Write out the equation for marginal benefits. What is the benefit from selling an additional unit of output?

4. What are the marginal net benefits when Q = 10? Explain result meaning based on the economic theory.

5. What is the level of Q that maximizes net benefits? Given your answer, will you produce Q =10, explain?

Answer 1

Given That B(Q) = 100 + 20Q - 2Q^2

C(Q) = 20 + 10Q

1) Net Benefit = B(Q) - C(Q) = 100 + 20Q - 2Q^2 - 20 - 10Q = 80 + 10Q - 2Q^2

2) At Q = 10,

Net Benefit = 80 + 100 - 200 = -20

Means cost has outweighed the benefit at Q = 10.

3) Net Benefit = 80 + 10Q - 2Q^2

To arrive at Marginal net benefit, we will differentiate the net benefit equation

Marginal Net Benefit = 10 - 4Q

4) At Q = 10

Marginal Net benefit = 10 - 40 = -30

It means that total benefit is decreasing.

5) To maximize the net benefit,

MB(Q) = MC(Q)

20-4Q = 10

4Q = 10

Q = 2.5

From above it is clear that we should not produce 10 units.