When elasticity of demand is inelastic and price goes up what happens to total revenue?

The Elasticity of Demand

If narcotic drugs are legalized, the price of those drugs will fall, and people will buy more of those drugs. If tolls are removed from the New Jersey Turnpike on Christmas weekend, then more people will drive on the New Jersey Turnpike at Christmas. If the prices of plywood and generators and bags of ice and bottles of water go up after a hurricane, then people will buy less plywood and generators and ice and water. If the price of gasoline goes up, then people get upset but they also buy less gasoline.

These are just simple applications of the Law of Demand. As the price of some good or service goes up, the quantity demanded of that good or service will go down (assuming everything else other than price remains constant). And if the price goes down, the quantity demanded goes up.

But what the Law of Demand does not tell us is how much the quantity demanded changes when the price changes. The Law of Demand tells us the direction in which quantity demanded will change, but it does not tell us the magnitude of that change.

In many cases, it's quite important to know the magnitude of the change in quantity demanded. For example: suppose we decide to spend more money and time and personnel and machinery to restrict the flow of illegal drugs into the U.S. We know that this will, at least to some extent, reduce the supply of illegal drugs in the U.S. Therefore, the price of illegal drugs will rise. And the quantity of illegal drugs demanded will therefore fall. But how much will it fall? That's an important question. Suppose that the price goes up but that drug users continue to buy almost as much drugs as before. If they buy nearly the same quantity, but pay a higher price for each hit, it's possible that the total amount of money that drug users spend on drugs could increase. And to get that increased sum, drug users might have to commit more theft, more burglary, more fraud. So the War on Drugs could lead to an increase in the amount of crime.

What we need is something that can tell us the magnitude of changes in quantities as well as the directions of such changes. The concept that we need is called Price Elasticity of Demand.

The Concept of Elasticity

Elasticity is a measure of responsiveness. It tells us how much something changes in response to a change in something else. In Economics, there are many different types of elasticity, and our textbook discusses several of them in Chapter 4. But we will be concerned with only one kind of elasticity, namely the price elasticity of demand. We will refer to this as the elasticity of demand, or more simply, as elasticity. In other words, when we say �elasticity,� we are going to mean �price elasticity of demand.�

The Law of Demand tells us the direction of the change in quantity demanded (whether it's up or down), but elasticity tells us the magnitude of that change.

Price Elasticity of Demand Defined

Price elasticity of demand is defined as the responsiveness of quantity demanded of some good or service to a change in the price of that good or service. Price elasticity of demand tells us how much the quantity demanded changes when the price of that particular good or service changes.

That is, price elasticity of demand tells us whether quantity demanded changes �a lot� or �a little� when price changes.

Of course, �a lot� and �a little� are subjective terms, and they also depend on the context. A $1 change in the price of a refrigerator is not a big deal, but a $1 change in the price of a gallon of gas could be a big deal. So we make the notions of �a lot� and �a little� precise with the following definition:

Price elasticity of demand is defined as the percentage change in quantity demanded divided by the percentage change in price that caused the change in quantity demanded.

The textbook discusses in some detail how to calculate price elasticity of demand, referring to the point price elasticity and the arc price elasticity, but our concern is the concept, not the calculation.

Note that, by definition, price elasticity of demand will always be a negative number: if price goes up (a positive number), quantity demanded will go down (a negative number), and vice versa. So we would be dividing a negative number by a positive number, or a positive number by a negative number � in either case, the result would be a negative number. We will follow the common practice of ignoring the negative sign, and just assume that everybody realizes that the Law of Demand applies. We will always refer to elasticities as positive numbers.

Elastic and Inelastic Demand

It is common to categorize price elasticity of demand into one of two groups: elastic or inelastic.

We say that demand is elastic when quantity demanded changes a lot when the price changes; more precisely, the percentage change in quantity demanded is greater than the percentage change in price. In this case, quantity demanded is very responsive to changes in price.

We say that demand is inelastic when quantity demanded changes just a little when the price changes; more precisely, the percentage change in quantity demanded is less than the percentage change in price. In this case, quantity demanded is not very responsive to changes in price.

The distinction between elastic and inelastic demand is an extremely useful one.

Elasticity and Total Revenue

The most important application of price elasticity of demand is in determining the effect of a change in price on total revenue. Total revenue is the amount paid by buyers and the amount received by sellers. Total revenue is equal to the price of a good or service multiplied by the quantity of that good or service that is purchased. Total revenue is usually used to refer to the amount received by sellers, while the amount spent by buyers is called total spending. Since money spent by buyers is received by sellers, total revenue and total spending are really the same thing.

Suppose that MacDonald's raises the price of a Big Mac � will the total revenue received by MacDonald's increase? It depends.

When the price is raised, there are two separate effects. On one hand, the higher price by itself will raise the seller's total revenue. Remember that total revenue is equal to price times quantity. If price goes up and quantity remains unchanged, total revenue will rise.

But the second effect is that quantity in fact will not remain unchanged. When price goes up, the quantity demanded (and therefore the quantity sold) goes down. And by itself, the lower quantity causes total revenue to go down.

To repeat: by itself, the higher price will increase total revenue. By itself, the reduced quantity will decrease total revenue. So what will happen to total revenue? It depends on which effect � the effect of the higher price or the effect of the smaller quantity � is bigger. And that depends on the elasticity of demand.

If demand is inelastic, we know that the increase in price will cause quantity demanded to fall just a little. When price goes up, quantity demanded goes down, but not by much. To be precise, when demand is inelastic, the percentage change in quantity demanded is smaller than the percentage change in price. That means that when demand is inelastic, the price effect will be bigger than the quantity effect. So: if demand is inelastic, the higher price will lead to an increase in total revenue.

If demand is elastic, we know that the increase in price will cause quantity demanded to fall by a lot. When price goes up, quantity demanded goes down, by a lot. To be precise, when demand is elastic, the percentage change in quantity demanded is greater than the percentage change in price. That means that when demand is elastic, the quantity effect will be bigger than the price effect. So: if demand is elastic, the higher price will lead to a decrease in total revenue.

Here is a quick summary of the possibilities:

�        If demand is inelastic, an increase in price will cause total revenue to increase.

�        If demand is inelastic, a decrease in price will cause total revenue to fall.

�        If demand is elastic, an increase in price will cause total revenue to fall.

�        If demand is elastic, a decrease in price will cause total revenue to rise.

The implications

If the demand for a business' product is inelastic, it should raise price, because doing so will cause its total revenue to rise. When price goes up, the higher price on each product sold will more than make up for the small drop in the quantity sold.

If the demand for a business' product is elastic, however, raising price is not a good idea � the higher price will cause such a large drop in quantity demanded that the business' total revenue will actually fall. Reducing price in this case would lead to higher total revenue � the decrease in price would lead to such a large increase in the quantity sold that it would more than offset the lower price received on each one sold.

So then the question becomes, What makes demand elastic or inelastic?

The Determinants of Elasticity

Price elasticity of demand depends upon several factors.

�        Availability of Substitutes

When price goes up, quantity demanded goes down, in part because people will switch away from the now-higher-priced product to a lower-priced alternative. More people will switch away the more alternatives are available. These alternatives are called substitutes. Substitutes are different products that satisfy more or less the same desire. For most people, for example, Pepsi and Coke satisfy the same desire or want.

So: the more substitutes are available, the easier it will be for people to switch to another product when price rises. A small increase in the price of Coke will lead to a large decrease in the quantity of Coke sold, because many people will switch to Pepsi. The more substitutes are available, the more elastic the demand will be.

�        Time Horizon

The longer the time period considered, the more elastic demand will be. The longer the time period considered, the easier it will be for people to switch to alternatives. For example, when the price of gasoline rises, people will buy less gasoline. They may immediately decide to take shorter driving vacations, for example, although they will still buy gas to commute to work and/or school. But if the price of gas remains high for months or years, people will switch to hybrid cars (powered by electricity as well as gas), move closer to their workplace, and take other measures to reduce their consumption of gasoline. That is, the longer the time period we consider, the bigger will be the change in quantity demanded when price changes.

�        Share of Consumers' Budgets

If a product consumes a small share of a person's total spending budget, the demand for that product is likely to have an inelastic demand. That's because changes in price are likely to go unnoticed in this case. For example, most people don't buy salt very often � purchases of salt take up a pretty small share of the budgets of most consumers. If you don't buy salt very often, you're unlikely to know what the price of salt was the last time you bought it. So if price goes up, you probably wouldn't even know it. On the other hand, items that you buy frequently and that make up a large share of your total budget are likely to be much more noticeable when they change price.

Application: Luxury Tax

Early in the presidency of William Jefferson Clinton, the government increased sales taxes on so-called luxury items. An additional 10 percent of the purchase price was added on to price of goods such as yachts, expensive jewelry, fur coats, and personal jets.

The stated goal of this luxury tax was to increase revenue for the federal government without hurting working-class men and women. Did the luxury tax accomplish its goal?

In fact, it did not. The tax raised the price of these luxury items. What did consumers do? They switched away from buying yachts and personal jets. And that hurt the people whose jobs it was to build the yachts and jets.

Application: Cigarette Taxes

States such as North Carolina, Virginia, and Kentucky, which produce large quantities of tobacco, also tend to have low taxes on cigarettes. But in recent years, these states have considered increasing the taxes they charge on cigarette purchases.

Those who call for increasing cigarette taxes argue that such tax increases will accomplish two things. One is that the higher tax, by raising the price of cigarettes (consumers will have to pay the price of cigarettes plus the tax on top of that), will discourage cigarette smoking, particularly among teenagers. The second result will be that the cigarette tax will produce a large amount of revenue for the state government, which can use that increased revenue for health care, education, and other services that government provides.

Do you think that higher cigarette taxes can accomplish both of these goals? Can it accomplish either one?

It can�t accomplish both of those goals at the same time.

The demand for cigarettes is pretty inelastic. As the price goes up, the quantity demanded goes down but only a little bit � it�s apparently pretty hard to switch away from cigarettes to, say, Twinkies. So when we raise the tax on cigarettes, people keep buying cigarettes anyway. So this tax would do a good job of raising money for the government but it doesn�t bring about a very big reduction in smoking.

However, there may be an important difference in elasticity for younger and for older smokers. Apparently, younger smokers have a much more elastic demand for cigarettes than do older smokers. So one thing that a tax on cigarettes may do is to discourage younger people from starting to smoke.

What happens to total revenue when price rises and demand is inelastic?

What happens to total revenue when price increases and demand is elastic?

Does total revenue increase when demand is inelastic?

How does price elasticity affect total revenue?