When you go to the store to buy a blue shirt, does it ever cross your mind that you'll have an influence on the price of that shirt? Do you wonder if you'll be able to decide how many blue shirts the store will have? If you answered "no" then you're just like the rest of us. But who does decide how much to charge for the blue shirts, or how many to make and send to stores? And how do they make these decisions? The answer is more interesting than you might think. Keep reading this article on Profit Maximization to find out why.
Profit Maximization Definition
Why do businesses exist? An economist would tell you categorically that they exist to make money. More specifically, they exist to make profits. But how much profit do businesses want to make? Well, the obvious answer is the right one - the greatest amount of profit possible. So how do businesses determine how to make maximum profits? Simply put, profit maximization is the process of finding the production output at which the difference between revenues and cost is the largest.
Profit maximization is the process of finding the level of production that generates the maximum amount of profit for a business.
Before we go into details of the process of profit maximization, let's set the stage so that we agree on some fundamental ideas.
A business's profit is the difference between the revenue and the economic costs of the good or service that the business provides.
\(\hbox{Profit}=\hbox{Total revenue}-\hbox{Total Economic Cost}\)
What exactly is the economic cost? We'll simplify this idea going forward by just referring to "Cost", but the economic cost is the sum of the explicit and implicit costs of an activity.
Explicit costs are costs that require you to physically pay money.
Implicit costs are the costs in dollar terms of the benefits a business could have realized by doing the next best alternative.
Let's take the blue shirt business for example. The explicit costs include the costs of the materials required to make blue shirts, the machines required to make the blue shirts, the wages paid to the people needed to make the blue shirts, the rent paid for the building where the blue shirts are made, the costs to transport the blue shirts to the store, and... well you get the idea. These are the costs the blue shirt business has to pay money for directly.
But what are the implicit costs facing the blue shirt company? Well, the implicit costs include things like the next best use of the material used to make the shirts (maybe scarves), the next best use for the machines used (renting the machines out to another business), the wages paid to the people making the shirts (maybe you outsource this process to an existing shirt manufacturer and avoid hiring people altogether), the next best use for the building you're paying rent for (maybe you could turn it into a restaurant), and the time the owners of the blue shirt business spend starting and running the business.
Think of implicit costs as the opportunity costs of the resources required to make provide the good or service in question.
In economics, profit is the difference between total revenues and total economic costs, which we now know includes implicit costs. For simplicity, you can assume that when we talk about costs, we mean economic costs.
Profit is total revenue minus total cost
\(\hbox{Profit}=\hbox{Total revenue}-\hbox{Total Cost}\)
Stated another way, profit is the difference between the quantity of a good or service sold (Qs) multiplied by the price it's sold at (P), minus the quantity of a good or service that is produced (Qp) multiplied by the costs incurred in providing that good or service (C).
\(\hbox{Profit}=(Q_s\times P)-(Q_p\times C)\)
Types of Profit Maximization
There are two types of profit maximization in general:
- short-run profit maximization
- long-run profit maximization
Take perfect competition as an example:
Short-run profit maximization occurs at the point where marginal revenue equals marginal costs for as long as the competitive marketplace allows a positive profit, and before the perfect competition has reduced prices.
In the long run, therefore, as firms enter and exit this market, profits are driven to the point of zero maximum profit.
To learn more about profit maximization in perfectly competitive markets - check our explanation on Perfect Competition!
Profit Maximization Formula
There's no straightforward equation for the profit maximization formula, but it is calculated by equating the marginal revenue (MR) to the marginal cost (MC), which represents the additional revenue and cost incurred from producing one additional unit.
Profit will be maximized at the point of production and sales where Marginal Revenue = Marginal Cost.
Continue reading to understand how economists find the profit-maximizing output of production!
How to Find Profit-Maximizing Output?
So how exactly do businesses find the profit-maximizing quantity? The answer to this question is determined by the use of a key economic principle called marginal analysis. Follow our example to find out how to do it!
Marginal Analysis is the study of the trade-off between the costs and benefits of doing a little bit more of an activity.
When it comes to running a business, marginal analysis comes down to deciding the best possible trade-off between the costs and revenues associated with making a little bit more of a good or service. In other words, a profit-maximizing business will continue to make its product or service until the point where making one more unit is equal to the cost of making one more unit.
Underlying these ideas is the law of diminishing returns for the supply of the good or service.
The law of diminishing returns states that the output generated by adding labor (or any other factor of production) to a fixed amount of capital (machinery) (or another fixed factor of production) will eventually begin producing diminishing output.
As you can imagine, if you were the owner of the blue shirt business, and you hired one person to work the shirt-making machine, that person would only be able to produce so much output. If the demand is there, you would hire a second person, and together your two employees would produce more shirts. This logic would continue until you hired so many people that they would be waiting in line for their turn to use the shirt-making machine. Clearly, this would not be optimal.
Figure 1 depicts the law of diminishing marginal returns in a visual way as follows:
Fig. 1 - Diminishing marginal returns
As you can see from Figure 1, adding more labor inputs at the beginning generates increasing returns. However, there comes a point - Point A - where those returns are maximized on the margin. In other words, at point A, the trade-off between one more unit of labor generates one more unit of blue shirts. After that point, the returns from adding units of labor generate less than one blue shirt. In fact, if you keep hiring units of labor, you'll get to a point where you're not producing any additional blue shirts at all.
Now that we've covered the Law of Diminishing Returns, we can go back to our profit-maximizing formula.
As the owner of the blue shirt business, and as well versed economist with an understanding of marginal analysis, you know that profit maximization is the ideal outcome. You're not entirely sure where that is yet, however, so you start by experimenting with different levels of output because you know that you have to reach the point where the revenue of producing one more shirt is equal to the cost of producing that shirt.
Profit will be maximized at the point of production and sales where Marginal Revenue = Marginal Cost.
\(\hbox{Max Profit: } MR=MC\)
Let's look at Table 1 to see how your experimentation plays out.
Table 1. Profit Maximization for the Blue Shirt Company Inc.
| Blue Shirt Business |
|---|
| Quantity of Blue Shirts (Q) | Total Revenue (TR) | Marginal Revenue (MR) | Total Cost (TC) | Marginal Cost (MC) | Total Profit (TP) |
| 0 | $0 | $0 | $10 | $10.00 | -$10 |
| 2 | $20 | $20 | $15 | $7.50 | $5 |
| 5 | $50 | $30 | $20 | $6.67 | $30 |
| 10 | $100 | $50 | $25 | $5.00 | $75 |
| 17 | $170 | $70 | $30 | $4.29 | $140 |
| 30 | $300 | $130 | $35 | $2.69 | $265 |
| 40 | $400 | $100 | $40 | $4.00 | $360 |
| 48 | $480 | $80 | $45 | $5.63 | $435 |
| 53 | $530 | $50 | $50 | $10.00 | $480 |
| 57 | $570 | $40 | $55 | $13.75 | $515 |
| 60 | $600 | $30 | $60 | $20.00 | $540 |
| 62 | $620 | $20 | $65 | $32.50 | $555 |
| 62 | $620 | $0 | $70 | - | $550 |
| 62 | $620 | $0 | $75 | - | $545 |
| 62 | $620 | $0 | $80 | - | $540 |
| 62 | $620 | $0 | $85 | - | $535 |
You might have noticed a couple of things about Table 1.
First, you might have noticed that the total revenue for the blue shirts is simply the quantity of shirts produced multiplied by $10. That's because we have assumed that this is a perfectly competitive industry, such that all shirt-making businesses are price-takers. In other words, no one shirt-making business can influence the equilibrium price of shirts, so they all accept the price of $10.
In perfect competition, all firms are price-takers since no single firm is large enough to influence prices. If a firm in perfect competition raises its price by as little as five cents, it would go out of business because no consumer would buy from them.
To learn more about perfectly competitive markets - check our explanation on Perfect Competition!
You might also have noticed that at zero shirt production, there is still a cost. That would be the cost of capital, or the shirt-making machine.
If you have a keen eye, you might have noticed the Law of Diminishing Returns in action by looking at the rate of change Quantity of Blue Shirts. Think of each additional level of output in terms of one additional worker to manufacture blue shirts. When thought of in that way, you can see the effect of diminishing returns.
Lastly, you might have noticed that there is no specific quantity of shirt production or sales where MR exactly equals MC. In cases like this, you would continue to manufacture and sell shirts as long as MR is greater than MC. You can see that at the quantity of 60 shirts, MR is $30 and MC is $20. Since MR > MC, you would continue to hire one more additional worker and end up producing 62 shirts. Now at 62 shirts, MR is $20 and MC is $32.50. It's at this point that you would stop producing and selling blue shirts. In other words, you would produce and sell blue shirts until the first level of production and sales where MC > MR. That said, it's also at this point where your profits are maximized at $555.
If there is no specific level of output where MR exactly equals MC, a profit-maximizing business would continue producing output as long as MR > MC, and stop at the first instance where MR < MC.
Profit Maximization Graph
Profit is maximized when MR = MC. If we graph our MR and MC curves, it would look like Figure 2.
Fig. 2 - Profit maximization
As you can see in Figure 2, the market sets the price (Pm), therefore MR = Pm, and in the blue shirt market that price is $10.
Conversely, the MC curve initially curves downward before curving upward, as a direct result of the Law of Diminishing Returns. As a result, when the MC rises up to the point where it meets the MR curve, that's precisely where the blue shirt company will set its level of production, and maximize its profits!
Monopoly Profit Maximization
Are you wondering how a business would maximize profits if it was the only player in its market? As it turns out, this is an ideal, albeit often temporary situation for a business in terms of overall profits.
So how does a monopolist maximize its profit? Well, it's a bit more interesting than in perfect competition because in a monopoly the business can set the price. In other words, a monopoly business is not a price-taker, but rather a price-setter.
Therefore, a monopoly has to carefully understand the demand for its good or service and how demand is affected by changes in its price. In other words, how sensitive demand is to changes in price?
Thought of in this way, the demand curve for a product in a monopoly is the demand curve for the company acting as the monopolist, therefore a monopolist has the entire demand curve to work with.
This phenomenon comes with opportunities and dangers. For example, since a monopoly can set the price for its good or service, it also has to deal with the impact a price change has on the entire industry demand. In other words, if the blue shirt company was a monopoly, an increase in price would mean that the marginal revenue generated would be equal to the lost revenue from selling one less unit plus the sum of the price increase that will occur on all prior units of output, but at a reduced total quantity demanded.
While demand looks different for the monopolist, the rule for maximizing profit is the same for both the monopolist and the perfectly competitive firm. As we know, profit maximization occurs at the output where MR = MC. At this level of output, the monopolist sets the price in accordance with the Demand.
Unlike in a perfectly competitive market, where the Blue Shirt company is a price taker and faces a flat marginal revenue curve, a monopolist faces a downward-sloping marginal revenue curve. Therefore, the company finds the point where its MR = MC, and sets the quantity of output at that profit-maximizing level.
Given that, in a monopoly, the Blue Shirt company has the entire demand curve to play with, once it sets its profit-maximizing production quantity, it will then be able to calculate it revenues, costs, and profits from there!
To learn everything you need to know about how a monopoly maximizes profits, check our explanation on Monopoly Profit Maximization!
Profit Maximization - Key takeaways
- A business's profit is the difference between the revenue and the economic costs of the good or service that the business provides.
- Profit maximization is the process of finding the level of production that generates the maximum amount of profit for a business.
- Economic cost is the sum of the explicit and implicit costs of an activity.
- Explicit costs are costs that require you to physically pay money.
- Implicit costs are the costs in dollar terms of the benefits a business could have realized by doing the next best alternative.
- There are two types of profit maximization in general:
- short-run profit maximization
- long-run profit maximization
- Marginal Analysis is the study of the trade-off between the costs and benefits of doing a little bit more of an activity.
- The law of diminishing returns states that the output generated by adding labor (or any other factor of production) to a fixed amount of capital (machinery) (or another fixed factor of production) will eventually begin producing diminishing output.
- Profit Maximization occurs at the level of output where Marginal Revenue equals Marginal Cost.
- If there is no specific level of output where MR exactly equals MC, a profit-maximizing business would continue producing output as long as MR > MC, and stop at the first instance where MR < MC.
- In perfect competition, all firms are price-takers since no single firm is large enough to influence prices. If a firm in perfect competition raises its price by as little as five cents, it would go out of business because no consumer would buy from them.
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