Question

Suppose that the total benefit and total cost from a company are given by the following equations: B(Q) = 118.5 + 27.6Q - 1.7Q2 and C(Q) = 63.5 + 11.3Q + 0.6Q2. The marginal net benefit at Q=4 is:

Answer 1

Total benefit B(Q)= 118.5+27.6Q-1.7Q²

Marginal Benefit MB(Q)= dB(Q)/dq

= 27.6 - 3.4Q

Total Cost C(Q)= 63.5 + 11.3Q + 0.6Q²

Marginal Cost MC(Q) = d C(Q)/dq

= 11.3 + 1.2Q

Marginal Net benefit = marginal benefit - marginal Cost

= 27.6 - 3.4Q - (11.3 + 1.2Q)

= 27.6 - 3.4Q - 11.3 - 1.2Q

= 16.3 - 4.6Q

At Q=4

Marginal Net Benefit = 16.3 - 4.6 x 4

= 16.3 - 18.4

= - 2.1

A negative sign indicates that benefits that the consumer is deriving from consuming one additional quantity of the good are decreasing.