Answer to Question #115845 in Microeconomics for Nayanjyoti Sarma

Question

Explain mathematically how a producer can obtain his optimum level of output that will maximize the profit of the firm. In a perfectly competitive market, the market orice of a commodity is 3 per unit of output(Q) the totel cost function of the firm is given by
c = 1/3 Q - 4Q2 + 10Q + 10 find the profit maximising output.

Answer 1

In a perfectly competitive market the optimum level of output is calculated from equation P=MC. Marginal cost MC is the first derivative of TC function, so MC=1/3-8Q+10=31/3-8Q. So, 31/3-8Q=3. 8Q=31/3-3=22/3. Q=22/3÷8=22/24.