Suppose that the total benefit and total cost from a continuious activity are re

ID: 1093170 • Letter: S

Question

Suppose that the total benefit and total cost from a continuious activity are respectively, given by the following equations:

B (Q)= 100+36Q - 4Q2

C (Q)= 80+12Q

Note: MB (Q)= 36-8Q, and MC (Q)= 12.

Write out the equation for the net benefit.

What are the net benefits when Q=1? and Q=5?

Write out the equation for marginal net benefit.

What are the marginal net benefits when Q=1? and Q=5?

What level of Q maximizes net benifets?

At that level of Q maximize net benefit, what is the level of marginal net benefit?

N(Q) = B(Q)-C(Q) = 20+24Q-4Q^2

WHEN Q=1

N(1) = 20+24-4 = 40

WHEN Q=5

N(5) = 20 + 120 - 100 = 40

MNB(Q) = d(N(Q))/dQ = 24-8Q

WHEN Q=1

MNB(1) = 24-8 = 16

WHEN Q=5

MNB(5) = 24-40 = -16

SETTING MNB(Q) = 24-8Q =0 AND SOLVING FOR Q WE SEE THAT NET BENEFITS ARE MAXIMISED WHEN

Q=3

WHEN NET BENEFIT ARE MAXIMISED AT Q=3 , MARGINAL NET BENEFITS ARE 0 . THAT IT

MNB(3) = 24-8*3 = 0

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