Question

Subject: Managerial Economics

Assume that total benefits are B(Q) = 24Q – 2Q² and total costs are C(Q) = 4 + Q²

2.1 Find the value of Q that maximizes net benefits. Find marginal net benefits.

2.2 Explain the following graph

Answer 1

Marginal Benefits = dTB/dQ = 24 - 4Q

Marginal Costs = dC/dQ = 2Q

For benefits max

MB=MC

24-4Q = 2Q

6Q = 24

Q = 4, at Q = 4 MB=MC, so net benefits are maximised at Q= 4 units

Net Benefits(NB) = Total Benefits - Total Costs = 24Q-2Q^2 - (4+Q^2) = 24Q - 2Q^2 - 4 - Q^2

-3Q^2 + 24Q - 4

Marginal Net Benefits = d(NB)/dQ = -6Q + 24 =

6Q = 24, Q = 24/6 = 4 units

Total Benefits at Q=4 = 24*4-2*(4)^(2) = 64

Total Costs at Q = 4 = 4+(4)^(2) = 20

Net Benefits = 64-20 = 44