Question

Consider a producer facing the following cost function MC(q,w)=100+q Assuming the fixed cost are 5000 and rhe output price is 100 find maximum profit

Answer 1

By the definition of the total revenue, we get:

$$TR=PQ=100Q.$$

Let's find the marginal revenue:

$$MR=\dfrac{dTR}{dQ}=\dfrac{d}{dQ}(100Q)=\$100.$$

The profit maximizing level of output will be when MR=MC:

$$100+Q=100,$$ $$Q=0.$$

Let's write the TC function:

$$TC=FC+VC=5000+\int MC(Q)dQ,$$ $$TC=5000+\int (100+Q)dQ=5000+100Q+0.5Q^2.$$

By the definition of the profit, we have:

$$\pi=TR-TC=100Q-5000-100Q-0.5Q^2,$$ $$\pi=100\cdot0-5000-100\cdot0-0.5\cdot(0)^2=-\$5000.$$