Cost Revenue and Profit Maximization

Cost, Revenue, and Profit Maximization

Before diving headlong into the world of business, let's start with the basics of cost, revenue, and profit maximization.

Costs

In business, there are generally three types of costs:

• Fixed Costs;
• Variable Costs; and,
• Total Costs.

Fixed costs represent the types of costs that are, well, fixed. Fixed costs don't change when the amount of output changes. For example, if you open a lemonade stand business, the knife you use to cut the lemons for your freshly squeezed lemonade is a fixed cost since you don't need more knives the more lemonade you sell. In fact, you will need to buy the knife even if you don't sell any lemonade. Total fixed costs are sometimes also called overhead costs.

In the world of big business, fixed costs can include things like salaries for executives, interest paid on loans, rent for the building your business is in, property taxes, and the machines you need to make your products.

Variable costs, on the other hand, change directly in proportion to the amount of production. In the case of your lemonade stand, lemons would represent a variable cost because the more lemonade you make, the more lemons you will need.

In the business world, variable costs can include things like wages paid to workers who produce your products, the electricity required to operate your machines, the raw materials needed to produce your product, and the cost of shipping your products. Generally speaking, wages paid to workers is a company's largest variable cost.

Total costs are simply the sum of fixed and variable costs.

Revenue

In business, revenue represents the amount of money a company receives in exchange for the products they sell. Generally speaking, a company's total revenue is calculated by multiplying the number of products sold times the price the products were sold for.

In some industries, the price of a product is set and no single firm can change that price. In other industries, a firm can change the price it sells its products for.

Profit

Profit is the difference between a company's total revenue and its total costs at the level of production that it chooses.

Marginal Analysis

Marginal analysis is an important economic and business concept because it looks closely at how things change when a key variable changes by one unit.

For the purposes of this explanation, marginal analysis looks specifically at marginal cost and marginal revenue.

Marginal cost is the change in costs resulting from the production of one more unit of output.

Marginal revenue is the change in revenue resulting from the production (and presumed sale) of one more unit of output.

Take note of these ideas because they are central to the process by which companies maximize their profitability!

Finding Profit-Maximizing Quantity Given Total Cost and Total Revenue

Finding the profit-maximizing quantity of output given total cost and total revenue for a company is most easily understood by using a numerical example.

Table 1 below illustrates the costs and revenues for a hypothetical company we will call Company A, which produces Product A, which sells for $30 per unit.

You might notice that, even before producing a single unit of product A, company A has incurred a cost of $100. That, of course, is company A's fixed cost, or overhead.

If you peruse Table 1 row by row, you'll see that Company A's profit is maximized at $57, at a production level of 9 units.

Profit Maximization Using Total Cost and Total Revenue Curves

The profit-maximizing level of output can also be determined by using the graphical equivalent of a numerical example for output, costs, and revenues by looking at the total cost and total revenue curves on a graph.

Figure 1 illustrates a graphical example of Table 1 for Company A.

Fig. 1 - Total Cost, Total Revenue, and Total Profit Curves

You can see from Figure 1 that the largest distance between Total Revenue and Total Cost occurs at the 9th unit of production. Correspondingly, you can see that the Total Profit curve reaches its peak at the same point.

Profit-Maximizing Level for Costs and Revenue for an Operating Firm

You might be wondering if there is a more sophisticated way to determine the profit-maximizing level for costs and revenue for an operating firm, and if you are, you are correct.

This is where the concept of marginal analysis comes in. More specifically, the concepts of marginal cost and marginal revenue are, in fact, the keys to finding the profit-maximizing level of output.

In its simplest form, the idea is this: a company will maximize its profit at the level of production where the additional revenue of producing one more unit of output is exactly equal to the additional cost of producing that unit. The idea is that whenever an additional unit of production generates more revenue than the cost incurred, then that unit of output can only increase profits. Conversely, if an additional unit of production incurs a greater cost than the revenue generated, then that unit of output can only decrease profit.

This is why marginal analysis is so important. It tells companies exactly when to keep producing, and when to stop producing additional units.

Marginal Revenue and Marginal Cost Approach to Profit Maximization

The marginal revenue and marginal cost approach to profit maximization is a foundational one and is always true. That is to say, no matter what market characteristics are like, or the type of competition a company is in, it is always true that profits will be maximized at the point of production where Marginal Revenue (MR) is equal to Marginal Cost (MC).

Consider Table 2 below.

Now, rather than examining each row to see where you can find the largest number under the Profit column, try something else. Try to find the point where MR is equal to MC instead. Note that 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 producing additional units at the first instance where MR < MC.

You might notice that, at the 9th unit of output, MR is $30 and MC is $28. Technically speaking, at this output Company A has still generated slightly more revenue than it has costs. However, if Company A continues and produces a 10th unit of output, you'll see that at this level of production MR is $30 but MC is $37, which means that Company A's profits have decreased relative to the 9th unit. Therefore, producing 9 units of output is the very best that Company A can do in terms of maximizing profits.

Marginal Revenue Marginal Cost and Profit Maximization Graph

Let's now look at a graphical representation of Company A's costs, revenues, and profits. This time, however, instead of looking at Total Costs, Total Revenues, and Total Profit, we will only look at the MR and MC curves.

Figure 2 below shows only 2 curves, Company A's MR curve and its MC curves.

Fig. 2 - Profit MaximizationUsing Marginal and Marginal Revenue Curves

You'll probably first notice that the MR curve isn't a curve at all, but rather a straight line. That is because Company A is a price-taker and must accept the market price for Product A. As a result, the additional revenue associated with every additional unit of output is constant at $30.

That said, you might also have noticed that the point where the MC curve meets the MR curve is exactly at the 9th unit of output, which is the profit-maximizing level of production.

So you see, rather than creating and examining elaborate tables and graphs, all we need to do is graph MR and MC, identify where they meet, and presto! Profit is maximized!