Math CentralQuandaries & Queries


Question from a student:

Use the following equation to demonstrate how a firm that produces at MR=MC can also maximize its total profit. The equations to use are

The revenue from the sale of Q items is the price per item, P times the quantity sold Q. The profit is then the revenue minus the total cost TC. Thus the profit p(Q) is given by p(Q) = P x Q - TC
Use your knowledge of calculus to find the value of Q that maximizes p(Q).

The marginal revenue MR is the derivative of revenue as a function of Q.
The marginal cost MC is the derivative of cost as a function of Q.

Verify that the value of Q that maximizes p(Q) also makes MR = MC.


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