 |
| ||
| |||
|
| Math Central | Quandaries & 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.
Harley
| ||
| ||
| ||
 |
 |
|
Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.