Question

Your firm's research department has estimated your total benefits to be TB=300Q-6Q^2 and your Total Cost =4Q^2. What level of Q will yield the maximum benefit?

Answer 1

Firm will get maximum benefit/profit at that level of output when marginal benefit from producing that level of outpit is equal to marginal cost incurred at that level of output.

Total benefit (TB)= 300Q- 6Q^2

Marginal benfit = dTB/dQ = 300-12Q

Total cost (TC)=4Q^2

Marginal cost = dTC/dQ = 8 Q

Maximum benefit will be attained when Marginal benefit = Marginal cost

300-12Q= 8Q

20Q=300

Q=15

Output level (Q)= 15 will yield the maximum benefit to the firm.