Answer to Question #220071 in Microeconomics for Sbuda

Question

Mathematically prove that profit maximizing level of output is obtained where MR=MC

Answer 1

This can be proved as follows:

A firm's profit (π) equals its total revenue(TR) minus its total cost (TC).

$π = TR- TC$

The expression can be written as:

$\frac {∆π}{∆q}=\frac {∆TR}{∆q}- \frac {∆TC}{∆q}$

This means that the rate of change of profit is equal to the difference between the rate of change of total revenue and the rate of change of total cost.

At the profit maximizing output, the rate of change of profit has to be zero because the peak of the profit curve has been reached.

Thus, profit maximization is possible if $\frac {∆π}{∆q}$ is equal to zero.

$0= \frac {∆TR}{∆q}-\frac{∆TC}{∆q}$

$\frac {∆TR}{∆q}= \frac {∆TC}{∆q}$

$\implies MR= MC$