# PROFIT MAXIMIZATION IN ECONOMICS: EVERYTHING YOU NEED TO KNOW

One feature that is shared by all firms is profit maximization.

Profit maximization is the short-run or long-run process whereby a firm determines the output and price level that will earn the maximum profit by comparing revenue and cost.

A firm will maximize profit when it is producing at the output where marginal revenue is equal to marginal cost.

The intuition is that total profit will be at a maximum when marginal profit is zero.

Marginal profit is the difference between marginal revenue and marginal cost.

This means marginal profit will be zero when marginal revenue equals marginal cost and the firm will, therefore, be maximizing profit.

The accompanying table illustrates the relationship between marginal profit and total profits

 Quant T. revenue M Revenue T. cost M Cost T. profit Marginal profit 1 240 240 300 300 -60 -60 2 440 200 360 60 80 140 3 600 160 440 80 160 80 4 720 120 560 120 160 0 5 800 80 700 140 100 -60 6 840 40 840 140 0 -100 7 840 0 1120 280 -140 -140 8 800 -40 1480 360 -680 -720

The above table is a schedule for an imperfectly competitive firm. Marginal revenue is derived by dividing the change in total revenue by the change in output.

Marginal cost is derived by dividing the change in total cost by the change in output.

Marginal profit is easily gotten by subtracting marginal cost from marginal revenue.

In the 3rd unit, the firm would be making a profit of 160. This is, however, not the ideal quantity, as the firm would not be making the maximum profit.

So, production is expanded further to the 4th unit. At this output, the firm will be maximizing profit as marginal revenue is equal to marginal cost.

If the firm decided further expand production above the profit maximization, the firm will suffer economic loss.

### Is revenue-maximizing the same as profit-maximizing profit?

In economics, maximizing revenue is not same as the maximizing profit.

A firm can be maximizing revenue yet not maximizing profit. Remember profit is not solely determined by revenue, rather it is determined by both revenue and cost.

This is clearly illustrated in the above-mentioned table. In the seventh unit, the firm was earning the highest revenue (840) and therefore maximizing revenue.

However, This didn't translate to maximizing profit as the firm was earning an economic loss of 140. This can be largely attributed to the somewhat exponential rise in total cost.

Another reason is that the marginal revenue of producing the seventh unit is lesser than the marginal cost of producing the units

This perhaps explains why a firm will produce at the point where marginal revenue equals marginal cost and not where total revenue is largest.

Under specific conditions, however,  the revenue-maximizing quantity may be the same as the profit-maximizing quantity. This is the case of a production process where the total cost is constant.

And you know the total cost will be constant when there is no variable cost. In other words, the total cost will be constant if all costs are fixed as is always the case with zero output.

As you will know in the next heading, the point where marginal revenue equals marginal cost is not always the profit-maximizing point.

### Is the quantity where marginal revenue equals marginal cost always the profit-maximizing point?

Sometimes, the output where marginal revenue equals marginal cost may not be the profit-maximization output, rather, it may be the loss minimization output.

The idea is entirely based on the price and average cost relationship.

$TR=P\times Q$

$TC=AC\times Q$.

So, when Price is greater than the average cost at the output where marginal revenue equals marginal cost, it means total revenue is greater than total cost, and therefore, the firm is maximizing profit.

This is illustrated below

 Q A.Cost Price Revenue Cost Profit M. Revenue M. Cost 1 300 240 240 300 -120 240 300 2 180 220 440 360 80 200 60 3 147 200 600 440 160 160 80 4 140 180 720 560 160 120 120 5 140 160 800 700 100 80 140 6 140 140 840 840 0 40 140 7 160 120 840 1120 -280 0 280 8 185 100 800 1480 -640 -40 340

From the above tabular representation, the marginal revenue equals marginal cost at the 4th.

At that unit, the price of 180 is greater than the average cost (140). Therefore, the firm is said to be maximizing profit at the fourth unit.

Conversely, when the average cost is greater than the price at the output where marginal revenue equals marginal cost, it means the total cost is greater than total revenue, and therefore, the firm is minimizing loss.

Below is a theoretical example of a firm minimizing loss

 Q A. Cost Price Revenue Cost Profit M. Revenue M. Cost 1 360 240 240 360 -120 240 360 2 250 220 440 500 -60 200 140 3 220 200 600 660 -60 160 160 4 205 180 720 820 -100 120 160 5 198 160 800 990 -190 80 170 6 194 140 840 1164 -324 40 174 7 192 120 840 1344 -504 0 180 8 191 100 800 1528 -728 -40 184

As can be visualized, marginal revenue equals marginal cost at the 3rd unit. However, the firm is not earning profit at this unit, rather, it is suffering economic loss.

The average cost is greater than the price. Hence, the firm is said to be minimizing loss at the 3rd unit.

To summarize, Whether a firm maximizes profit or minimizes loss at the quantity where marginal revenue equals marginal cost is highly dependent on the relationship between price and average cost.

If the price is greater than the average cost at the quantity where marginal revenue equals marginal cost, then the firm will be maximizing profit.

However, if the average cost is greater than the price at the quantity where marginal revenue equals marginal cost, then the firm will be minimizing loss

We will be using the idea of profit-maximization to analyze perfect competition here.

Also, we shall be learning how to maximize profit via cost functions in the next post.

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