# Relationship between marginal revenue and cost at the point of profit maximization

### Marginal revenue and marginal cost (video) | Khan Academy

The point at which marginal revenue equals marginal cost When marginal revenue and the marginal cost of production are equal, profit is maximized at In terms of calculus, the relationship is stated as: ΔTR/ΔQ = ΔTC/dQ. When marginal revenue is equal to marginal cost, profit is maximized. should strive to reach the point where marginal revenue equals marginal cost to get the. The monopolist's profit maximizing level of output is found by equating its marginal revenue with its marginal cost, which is the same profit maximizing conditi. equals marginal cost (point c)—and then looking at the demand curve to find the.

This point can also be illustrated using the diagram for the marginal revenue—marginal cost perspective. A change in fixed cost would have no effect on the position or shape of these curves. The profit maximization conditions can be expressed in a "more easily applicable" form or rule of thumb than the above perspectives use.

The additional units are called the marginal units.

Moreover, one must consider "the revenue the firm loses on the units it could have sold at the higher price" [6] —that is, if the price of all units had not been pulled down by the effort to sell more units. These units that have lost revenue are called the infra-marginal units.

Thus the optimal markup rule is: Marginal cost is positive. Thus Q1 does not give the highest possible profit. Markup is smaller when demand is more elastic.

### Markup Pricing: Combining Marginal Revenue and Marginal Cost

Markup is zero when the demand curve is perfectly elastic: Their current markup, in other words, was about 79 percent: It was clear that they could do better by increasing their price A Pricing Algorithm To summarize, a manager needs two key pieces of information when determining price: We have shown that the profit-maximizing price is a markup over the marginal cost of production.

If a manager does not know the magnitude of marginal cost, she is missing a critical piece of information for the pricing decision. Once a manager knows marginal cost, she should then set the price as a markup over marginal cost.

But this should not be done in an ad hoc manner; the markup must be based on information about the elasticity of demand. Given these two pieces of information, a manager can then use the markup formula to determine the optimal price. But if you change the price, both marginal cost and the elasticity of demand are also likely to change. A more reliable way of using this formula is in the algorithm shown in Figure 6. The five steps are as follows: At your current price, estimate marginal cost and the elasticity of demand.

Calculate the optimal price based on those values.

## Profit maximization

If the optimal price is greater than your actual price, increase your price. Then estimate marginal cost and the elasticity again and repeat the process. If the optimal price is less than your actual price, decrease your price. If the current price is equal to this optimal price, leave your price unchanged. They had found that based on current marginal cost and elasticity, the price could be raised. But as they raised the price, they knew that the elasticity of demand would probably also change.

An elasticity of 2 means that the markup should be percent to maximize profits. Shifts in the Demand Curve Facing a Firm So far we have looked only at movements along the demand curve—that is, we have looked at how changes in price lead to changes in the quantity that customers will buy. Firms also need to understand what factors might cause their demand curve to shift. Among the most important are the following: Changes in household tastes.

Starting around or so, low-carbohydrate diets started to become very popular in the United States and elsewhere. For some companies, this was a boon; for others it was a problem. For example, companies like Einstein Bros. As more and more customers started looking for low-carb alternatives, these firms saw their demand curve shift inward. Consider Lexus, a manufacturer of high-end automobiles.

As an example of the costs that a monopolist might face, consider the data in Table. The first two columns of Table represent the market demand schedule that the monopolist faces. As the price falls, the market's demand for output increases. The third column reports the total revenue that the monopolist receives from each different level of output. The fourth column reports the monopolist's marginal revenue that is just the change in total revenue per 1 unit change of output.

The fifth column reports the monopolist's total cost of providing 0 to 5 units of output. The sixth and seventh columns report the monopolist's average total costs and marginal costs per unit of output. The eighth column reports the monopolist's profits, which is the difference between total revenue and total cost at each level of output.