# Revenue maximizing price and quantity relationship

### Elasticity, Total Revenue, and the Linear Demand Curve - Wolfram Demonstrations Project

Calculate the following, assuming that Night Timers maximizes profit: a. For example, in this one, the quantity and price relationship Q. An equivalent perspective relies on the relationship that, for each unit sold, marginal profit. When you increase prices, you know quantity will fall, but by how much? The first thing to note is that revenue is maximized at the point where elasticity is about the relationship between the price elasticity of demand and revenue is TRUE?.

Markup is smaller when demand is more elastic. 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. 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. The optimum quantity Q is the same as the optimum quantity in the first diagram. If the firm is operating in a non-competitive market for its output, changes would have to be made to the diagrams. For example, the marginal revenue curve would have a negative gradient, because it would be based on the downward-sloping market demand curve.

In an environment that is competitive but not perfectly so, more complicated profit maximization solutions involve the use of game theory.

## How to Find the Revenue Maximizing Price

Case in which maximizing revenue is equivalent[ edit ] In some cases a firm's demand and cost conditions are such that marginal profits are greater than zero for all levels of production up to a certain maximum. Marginal revenue equals zero when the total revenue curve has reached its maximum value.

- Elasticity, Total Revenue, and the Linear Demand Curve
- solving for price, quantity, revenue, and costs
- Profit maximization

An example would be a scheduled airline flight. The marginal costs of flying one more passenger on the flight are negligible until all the seats are filled. The airline would maximize profit by filling all the seats. It appears in Figure 4 as the area of a rectangle whose bottom left corner is the origin and top right corner is a point on the demand curve. The top left and bottom right corners equal price and quantity respectively.

It is also clear in the above Figure that the total revenue varies as we move along the demand curve. Marginal revenue is defined as the change in total revenue that occurs when we change the quantity by one unit.

The marginal revenue is thus the slope of the total revenue curve in Figure 5. At quantity zero, the marginal revenue is equal to the priceselling the first unit adds one times the price of that unit to the total revenue. As quantity increases the marginal revenue falls because as we add successive units not only is the price of the last unit lower than the price of the previous unit but all previous units have to be sold at this lower price.

Marginal revenue for each quantity sold is given in Figure 5 as the distance between the thick line and the horizontal axis at that quantity. This distance is equal to the slope of the total revenue curve at that quantity.

The marginal revenue curve thus crosses the horizontal axis at the quantity at which the total revenue is maximum. Past the mid-point of a straight line demand curve, the marginal revenue becomes negative. Why is marginal revenue important?

### Elasticity, Total Revenue and Marginal Revenue

This question is best answered by way of example. Consider the market for fresh eggs in a locality. Suppose that the government permits producers to establish an Egg Marketing Board with the power to set the price of eggs to the consumer and allocate output quantities to all individual producers.

Purchases of eggs from outside the local area are prohibited. This situation is shown in Figure 6.