PROFIT MAXIMIZATION IN ECONOMICS: EVERYTHING YOU NEED TO KNOW

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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

QuantT. revenueM RevenueT. costM CostT. 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. 

You know total revenue is price times quantity and the total cost is Average cost times quantity. 

$TR=P\times Q$

$TC=AC\times Q$.

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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