## Elasticity: A Measure of Response

### The Price Elasticity of Demand

### Elasticity: A Measure of Response

#### Start Up: Raise Fares? Lower Fares? What's a Public Transit Manager To Do?

Imagine that you are the manager of the public transportation system for a large metropolitan area. Operating costs for the system have soared in the last few years, and you are under pressure to boost revenues. What do you do?

An obvious choice would be to raise fares. That will make your customers angry, but at least it will generate the extra revenue you need – or will it? The law of demand says that raising fares will reduce the number of passengers riding on your system. If the number of passengers falls only a little, then the higher fares that your remaining passengers are paying might produce the higher revenues you need. But what if the number of passengers falls by so much that your higher fares actually reduce your revenues? If that happens, you will have made your customers mad and your financial problem worse!

Maybe you should recommend *lower* fares. After all, the law of demand also says that lower fares will increase the number of passengers. Having more people use the public transportation system could more than offset a lower fare
you collect from each person. But it might not. What *will* you do?

Your job and the fiscal health of the public transit system are riding on your making the correct decision. To do so, you need to know just how responsive the quantity demanded is to a price change. You need a measure of responsiveness.

Economists use a measure of responsiveness called elasticity. **Elasticity** is the ratio of the percentage change in a dependent variable to a percentage change in an independent variable. If the dependent variable is *y*,
and the independent variable is *x*, then the elasticity of *y* with respect to a change in *x* is given by:

A variable such as *y* is said to be more elastic (responsive) if the percentage change in *y* is large relative to the percentage change in *x*. It is less elastic if the reverse is true.

As manager of the public transit system, for example, you will want to know how responsive the number of passengers on your system (the dependent variable) will be to a change in fares (the independent variable). The concept of elasticity will help you solve your public transit pricing problem and a great many other issues in economics. We will examine several elasticities in this chapter – all will tell us how responsive one variable is to a change in another.

### LEARNING OBJECTIVES

- Explain the concept of price elasticity of demand and its calculation.
- Explain what it means for demand to be price inelastic, unit price elastic, price elastic, perfectly price inelastic, and perfectly price elastic.
- Explain how and why the value of the price elasticity of demand changes along a linear demand curve.
- Understand the relationship between total revenue and price elasticity of demand.
- Discuss the determinants of price elasticity of demand.

We know from the law of demand how the quantity demanded will respond to a price change: it will change in the opposite direction. But how *much* will it change? It seems reasonable to expect, for example, that a 10% change in the price
charged for a visit to the doctor would yield a different percentage change in quantity demanded than a 10% change in the price of a Ford Mustang. But how much is this difference?

To show how responsive quantity demanded is to a change in price, we apply the concept of elasticity. The **price elasticity of demand** for a good or service, *e*_{D}, is the percentage change in quantity
demanded of a particular good or service divided by the percentage change in the price of that good or service, all other things unchanged. Thus we can write

Because the price elasticity of demand shows the responsiveness of quantity demanded to a price change, assuming that other factors that influence demand are unchanged, it reflects movements *along* a demand curve. With a downward-sloping
demand curve, price and quantity demanded move in opposite directions, so the price elasticity of demand is always negative. A positive percentage change in price implies a negative percentage change in quantity demanded, and vice versa. Sometimes
you will see the absolute value of the price elasticity measure reported. In essence, the minus sign is ignored because it is expected that there will be a negative (inverse) relationship between quantity demanded and price. In this text, however,
we will retain the minus sign in reporting price elasticity of demand and will say "the absolute value of the price elasticity of demand" when that is what we are describing.

### Heads Up!

Be careful not to confuse elasticity with slope. The slope of a line is the change in the value of the variable on the vertical axis divided by the change in the value of the variable on the horizontal axis between two points. Elasticity is the ratio of the percentage changes. The slope of a demand curve, for example, is the ratio of the change in price to the change in quantity between two points on the curve. The price elasticity of demand is the ratio of the percentage change in quantity to the percentage change in price. As we will see, when computing elasticity at different points on a linear demand curve, the slope is constant – that is, it does not change – but the value for elasticity will change.

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