Problem 2 Assume that total benefits for a given level of ou

Problem 2 Assume that total benefits for a given level of output are given as B(Q) = 200 + 25Q + 6Q2, and that C(Q) = 70 + 10Q. 1. Write out the net benefit equation 2, What are the net benefits when Q = 1 ? And Q-6? 3. Write out the equation for marginal benefits. 4. What are the marginal net benefits when Q = 1 ? And Q=5? 5. What is the level of Q that maximizes net benefits? 6. Given the value of Q that maximizes net benefits, what is the value of marginal net benefits?

Solution

B(Q)=200+25Q+6Q²

C(Q)=70+10Q

Answer:- Net Benefit = B(Q)-C(Q) =200+25Q+6Q² -70-10Q =130+15Q+6Q²

Answer:- Net benefit when Q=1

NB(1) =130+15*1+6*1*1 = 130+15+6=151

Net benefit when Q=5

NB(5) =130+15*5+6*5*5 = 130+15+6=355

Answer:- MB(Q) =d/dq(200+25Q+6Q²) =25+12Q

MC(Q)=d/dq(70+10Q)=10

Thus, MNB(Q) =25+12Q-10 =15+12Q

Answer:- MNB (1) =15+12*1 =27

MNB(5)=15+12*5 =75

Answer:- For maximizing net benefit

MB(Q)= MC(Q)

25+12Q=10

12Q=-15

Q=-1.25

Answer:- MNB=15+12*(-1.25)=0