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.

Write out the net benefit equation:

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

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

  

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

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

Answer 1

Net benefit= benefit - cost

= 100+ 20Q +2Q2 - ( 20+ 10Q)

= 100 + 20Q + 2Q2 - 20 - 10Q

= 80 + 10Q +2Q²

^{net benefit when Q= 10}

^{net benefit= 80 + 10(10) + 2(10)2}

^{= 80+ 100+ 200}

^{= 380}

^{It clearly says that total benefits outweighs the total cost by 380 when the firm produces 10 units of good. If net benefit is negative, then cost outweighs the total benefit.}

^{Marginal benefit = change in total benefit when an additional unit of good is produced.}

^{= 20 + 4Q ( by differentiating total benefit)}

^{Benefit from selling an additional unit of output = marginal benefit}

^{= 20+4Q}

^{Marginal net benefit = 10 - 4Q}

^{When Q=10 = 10-4(10)}

^{= 10 - 40}

^{= - 30}

It means that when marginal net benefit is negative, the total benefit is decreasing or it falls.