Suppose that the total benefit and total cost from a continuous activity are, respectively, given by...

Suppose that the total benefit and total cost from a continuous activity are, respectively, given by the following equations: B(Q) = 50 + 18Q – 2Q^2 and C(Q) =40 + 6Q.

(i) What is the equation for the net benefits?

(ii) What is the equation for the marginal net benefits.

(iii) What level of Q maximizes net benefits?

Expert Solution

(i)

Net Benefit(NB) = total Benefit(B) - Total Cost(C)

Thus, NB = 50 + 18Q – 2Q² - (40 + 6Q)

=> NB = 10 + 12Q – 2Q² ----------------Net Benefit

(ii)

Marginal Net Benefit(MNB) = d(NM)/dQ = 12 - 2*2Q

=> MNB = 12 - 4Q ------------------Marginal net benefit

(iii)

Maximize : NB = 10 + 12Q – 2Q²

First Order condition :

d(NB)/dQ = 0 or MNB = 0 => 12 - 4Q = 0 => Q = 3

Thus, Net Benefit will get maximized when Q = 3

Rahul Sunny answered 2 years ago

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