How does a firm determine what price to charge for its product and what quantity to produce so that it will obtain the greatest amount of profit?

The marginal cost of production and marginal revenue are economic measures used to determine the amount of output and the price per unit of a product that will maximize profits.

A rational company always seeks to squeeze out as much profit as it can, and the relationship between marginal revenue and the marginal cost of production helps them to identify the point at which this occurs. The target, in this case, is for marginal revenue to equal marginal cost.

Key Takeaways

• When it comes to operating a business, overall profits and losses matter, but what happens on the margin is crucial.
• This means looking at the additional cost versus revenue incurred by producing just one more unit.
• According to economic theory, a firm should expand production until the point where marginal cost is equal to marginal revenue.

Calculating Marginal Cost of Production

Production costs include every expense associated with making a good or service. They are broken down into two segments: fixed costs and variable costs.

Fixed costs are the relatively stable, ongoing costs of operating a business that are not dependent on production levels. They include general overhead expenses such as salaries and wages, building rental payments, or utility costs. Variable costs, meanwhile, are those directly related to and those that vary with production levels, such as the cost of materials used in production or the cost of operating machinery in the process of production.

Total production costs include all the expenses of producing products at current levels. As an example, a company that makes 150 widgets has production costs for all 150 units it produces. The marginal cost of production is the cost of producing one additional unit.

For instance, say the total cost of producing 100 units of a good is $200. The total cost of producing 101 units is $204. The average cost of producing 100 units is $2, or $200 ÷ 100. However, the marginal cost for producing unit 101 is $4, or ($204 - $200) ÷ (101-100).

Reaching Optimum Production

At some point, the company reaches its optimum production level, the point at which producing any more units would increase the per-unit production cost. In other words, additional production causes fixed and variable costs to increase. For example, increased production beyond a certain level may involve paying prohibitively high amounts of overtime pay to workers. Alternatively, the maintenance costs for machinery may significantly increase.

The marginal cost of production measures the change in the total cost of a good that arises from producing one additional unit of that good.

The marginal cost (MC) is computed by dividing the change (Δ) in the total cost (C) by the change in quantity (Q). Using calculus, the marginal cost is calculated by taking the first derivative of the total cost function with respect to the quantity:

M C = Δ C Δ Q where: M C = Marginal cost Δ = Dividing the change C = Total cost Q = Change in quantity \begin{aligned}&MC=\frac{\Delta C}{\Delta Q}\\&\textbf{where:}\\&MC=\text{Marginal cost}\\&\Delta=\text{Dividing the change}\\&C=\text{Total cost}\\&Q=\text{Change in quantity}\end{aligned} ​MC=ΔQΔC​where:MC=Marginal costΔ=Dividing the changeC=Total costQ=Change in quantity​

The marginal costs of production may change as production capacity changes. If, for example, increasing production from 200 to 201 units per day requires a small business to purchase additional equipment, then the marginal cost of production may be very high. In contrast, this expense might be significantly lower if the business is considering an increase from 150 to 151 units using existing equipment.

A lower marginal cost of production means that the business is operating with lower fixed costs at a particular production volume. If the marginal cost of production is high, then the cost of increasing production volume is also high and increasing production may not be in the business's best interests.

Calculating Marginal Revenue

Marginal revenue measures the change in the revenue when one additional unit of a product is sold. Assume that a company sells widgets for unit sales of $10, sells an average of 10 widgets a month, and earns $100 over that timeframe. Widgets become very popular, and the same company can now sell 11 widgets for $10 each for a monthly revenue of $110. Therefore, the marginal revenue for the 11th widget is $10.

The marginal revenue is calculated by dividing the change in the total revenue by the change in the quantity. In calculus terms, the marginal revenue (MR) is the first derivative of the total revenue (TR) function with respect to the quantity:

M R = Δ T R Δ Q where: M R = Marginal revenue Δ = Dividing the change T R = Total revenue Q = Change in quantity \begin{aligned}&MR=\frac{\Delta TR}{\Delta Q}\\&\textbf{where:}\\&MR=\text{Marginal revenue}\\&\Delta=\text{Dividing the change}\\&TR=\text{Total revenue}\\&Q=\text{Change in quantity}\end{aligned} ​MR=ΔQΔTR​where:MR=Marginal revenueΔ=Dividing the changeTR=Total revenueQ=Change in quantity​

For example, suppose the price of a product is $10 and a company produces 20 units per day. The total revenue is calculated by multiplying the price by the quantity produced. In this case, the total revenue is $200, or $10 x 20. The total revenue from producing 21 units is $205. The marginal revenue is calculated as $5, or ($205 - $200) ÷ (21-20).

How Can Marginal Revenue Increase?

Marginal revenue increases whenever the revenue received from producing one additional unit of a good grows faster—or shrinks more slowly—than its marginal cost of production. Increasing marginal revenue is a sign that the company is producing too little relative to consumer demand, and that there are profit opportunities if production expands.

Let's say a company manufactures toy soldiers. After some production, it costs the company $5 in materials and labor to create its 100th toy soldier. That 100th toy soldier sells for $15, meaning the profit for this toy is $10. Now, suppose the 101st toy soldier also costs $5, but this time can sell for $17. The profit for the 101st toy soldier, $12, is greater than the profit for the 100th toy soldier. This is an example of increasing marginal revenue.

Balancing the Scales of Marginal Revenue

For any given amount of consumer demand, marginal revenue tends to decrease as production increases. In equilibrium, marginal revenue equals marginal costs; there is no economic profit in equilibrium. Markets never reach equilibrium in the real world; they only tend toward a dynamically changing equilibrium. As in the example above, marginal revenue may increase because consumer demands have shifted and bid up the price of a good or service.

It could also be that marginal costs are lower than they were before. Marginal costs decrease whenever the marginal revenue product of labor increases—workers become more skilled, new production techniques are adopted, or changes in technology and capital goods increase output.

When marginal revenue and the marginal cost of production are equal, profit is maximized at that level of output and price:

M R = Δ T R Δ Q M C = Δ C Δ Q E q . = M R = M C \begin{aligned}MR&=\frac{\Delta TR}{\Delta Q}\\\\[-9pt]MC&=\frac{\Delta C}{\Delta Q}\\\\[-9pt]Eq.&=MR=MC\end{aligned} MRMCEq.​=ΔQΔTR​=ΔQΔC​=MR=MC​

Example

For instance, a toy company can sell 15 toys at $10 each. However, if the company sells 16 units, the selling price falls to $9.50 each. The marginal revenue is $2, or ((16 x 9.50) - (15 x10)) ÷ (16-15). Suppose the marginal cost is $2.00; the company maximizes its profit at this point because the marginal revenue is equal to its marginal cost.

When marginal revenue is less than the marginal cost of production, a company is producing too much and should decrease its quantity supplied until marginal revenue equals the marginal cost of production. When, on the other hand, the marginal revenue is greater than the marginal cost, the company is not producing enough goods and should increase its output until profit is maximized.

When Marginal Revenue Starts to Fall

When expected marginal revenue begins to fall, a company should take a closer look at the cause. The catalyst could be market saturation or price wars with competitors.

If this is the case, the company should plan for this by allocating money to research and development (R&D), so it can keep its product line fresh. Should a company believe it will be unable to increase its marginal revenue once it's expected to decline, management will need to look at both its marginal revenue and the marginal cost of producing an additional unit of its good or service, and plan on maintaining sales volume at the point where they intersect.

If the company plans on increasing its volume past that point, each additional unit of its good or service will come at a loss and shouldn't be produced.

Marginal Revenue vs. Marginal Benefit

Although they sound similar, marginal revenue is not the same as a marginal benefit. In fact, it's the flip side. While marginal revenue measures the additional revenue a company earns by selling one additional unit of its good or service, marginal benefit measures the consumer's benefit of consuming an additional unit of a good or service.

Marginal benefit represents the incremental increase in the benefit to a consumer brought on by consuming one additional unit of a good or service. It normally declines as more of a good or service is consumed.

For example, consider a consumer who wants to buy a new dining room table. They go to a local furniture store and purchase a table for $100. Since they only have one dining room, they wouldn't need or want to purchase a second table for $100. They might, however, be enticed to purchase a second table for $50, since there is an incredible value at that price. Therefore, the marginal benefit to the consumer decreases from $100 to $50 with the additional unit of the dining room table.

Tying the two together, let's go back to our widget-maker example. Let's say a customer is contemplating buying 10 widgets. If the marginal benefit of purchasing the 11th widget is $3, and the widget company is willing to sell the 11th widget to maximize its consumer benefit, the marginal revenue to the company would be $3 and the marginal benefit to the consumer would be $3.

Marginal Analysis

All these calculations are part of a technique called marginal analysis, which breaks down inputs into measurable units. First developed by economists in the 1870s, it gradually became part of business management, especially in the application of the cost-benefit method—the identification of when marginal revenue is greater than marginal cost, as we've been explaining above.

According to the cost-benefit analysis, a company should continue to increase production until marginal revenue is equal to marginal cost. If the optimal output is where the marginal benefit is equal to marginal cost, any other cost is irrelevant. So marginal analysis also tells managers what not to consider when making decisions about future resource allocation: They should ignore average costs, fixed costs, and sunk costs.

For example, a toy manufacturer could try to measure and compare the costs of producing one extra toy with the projected revenue from its sale. Suppose that, on average, it has cost the company $10 to make a toy. The average sales price over the same period is $15.

This doesn't necessarily mean that more toys should be manufactured, however. If 1,000 toys were previously manufactured, then the company should only consider the cost and benefit of the 1,001sttoy. If it will cost $12.50 to make the 1,001st toy, but will only sell for $12.49, the company should stop production at 1,000.

The Bottom Line

Manufacturing companies monitor marginal production costs and marginal revenues to determine ideal production levels. The marginal cost of production is calculated whenever productivity levels change. This allows businesses to determine a profit margin and make plans for becoming more competitive to improve profitability.

The best entrepreneurs and business leaders understand, anticipate, and react quickly to changes in marginal revenues and costs. This is an important component in corporate governance and revenue cycle management.

What determines what prices a firm will charge?

How does the firm determine what quantity to produce?

How do firms determine price and output?

How a monopoly firm determines the price and and level of output that maximizes its profits?