How is marginal revenue related to the marginal cost of production?

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 maximize its profit, and the relationship between marginal revenue and the marginal cost of production helps to find the point at which this occurs. The point at which marginal revenue equals marginal cost maximizes a company's profit.

Production costs include every expense associated with making a good or service. These costs are broken down into fixed costs and variable costs. Fixed costs are the relatively stable, ongoing costs of operating a business that are not dependent on production levels. Fixed costs include general overhead expenses like salaries and wages, building rental payments or utility costs. Variable costs are those directly related to, and 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 product at current levels:  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 example, 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).

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, the 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, or the maintenance costs for machinery may significantly increase.

The marginal cost of production measures the change in total cost of a good that arises from producing one additional unit of that good. The marginal cost (MC) is calculated by dividing the change (Δ) in the total cost (TC) 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: MC = ΔTC/ΔQ. 

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 business equipment, then the marginal cost of production may be very high. However, this expense may 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.

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 each month. 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 11^th 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 is the first derivative of the total revenue function with respect to the quantity: MR = dTR/dQ. 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).

When marginal revenue and the marginal cost of production are equal, profit is maximized at that level of output and price. In terms of calculus, the relationship is stated as: ΔTR/ΔQ = ΔTC/dQ. For example, 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 the marginal revenue is greater than the marginal cost, the firm is not producing enough goods and should increase its output until profit is maximized.

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 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 100^th toy soldier. That 100^th toy soldier sells for $15. Profit for this toy is $10. Now, suppose the 101^st toy soldier also costs $5, but this time can sell for $17. The profit for the 101^st toy soldier, $12, is greater than the profit for the 100^th toy soldier. This is an example of increasing 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 expected marginal revenue begins to fall, a company should take a closer look at the cause. It could be from 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 so it can keep its product line fresh. It could either add additional products or additional features to its existing products to increase the expected decline in marginal revenue.

If a company believes it will be unable to increase its marginal revenue once it's expected to decline, the company will need to look at both its marginal revenue and marginal cost of producing an additional unit of its good or service, and it should 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. (For related reading, see: How does the law of diminishing returns affect marginal revenue?)

Although they sound similar, marginal revenue is not the same as 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.

It represents the incremental increase in the benefit to a consumer brought on by consuming one additional unit of a good or service. Marginal benefit 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. He goes to a local furniture store and purchases a table for $100. Since he only has one dining room, he wouldn't need or want to purchase a second table for $100. He might, however, be enticed to purchase a second table for $50, since there is 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 11^th widget is $3, and the widget company is willing to sell the 11^th 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.

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 optimal output is where marginal benefit is equal to marginal cost, any other cost is irrelevant. So marginal analysis also tells managers what not to consider in 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 1,001^sttoy. If it will cost $12.50 to make the 1,001^sttoy, but it will only sell for $12.49, the company should stop production at 1,000.

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.