# Elasticity

Elasticity refers to the responsiveness of demand or supply to changes in price or income. The usual meaning is the price elasticity of demand, or the responsiveness of the quantity demanded to price. We speak of an elastic demand -- one which is very responsive to price, and which would result in a relatively flat demand curve; and of an inelastic demand -- one not very responsive to price.

The language is a bit awkward. When we say inelastic, we mean the responsiveness is small not non-existent. The terminology perfectly inelastic is sometimes used for a demand which is not at all responsive to price.

The coefficient of elasticity or COE for short is the measure of elasticity.
It is defined as the percentage change in the quantity demanded divided by the percentage change in price.

1. It is in terms of percentage changes, not just "changes". An increase of a dollar is a big percentage change for a newspaper, and will lose them many customers; a dollar increase in the price of a car will not lose many buyers -- yet the newspaper and car demand curves could have the same elasticity. Percentage change calculations are further discussed in the link on the midpoint formula .
2. There is a close connection between the elasticity of demand and the revenue change resulting from a price change. If the COE is greater than 1, it means the percentage change in quantity is greater than the percentage change in price. For example, if the COE is 3, a 10 percent increase in price will lead to a ____ percent decrease in quantity demanded, or to a ____ loss in revenue. (If you can't fill in the blanks, click here for a discussion of percentage change algebra

### Extended elasticity concepts

As well as the price elasticity of demand -- by far the most frequently used elasticity concept -- we can also speak of:
1. the income elasticity of demand
defined as the percentage change in quantity demanded divided by the percentage change in income. Income elasticity can be either positive or negative, so the associated sign is important.
Goods with a negative income elasticity are inferior goods -- as income rises, the quantity of potatoes purchased may fall, so that potatoes would be inferior goods.

Goods with a positive income elasticity are normal goods; if the income elasticity is not simply positive but is greater than one the good is classified as a luxury good.
This terminology makes the economist's definition of inferior and luxury goods depend on observable economic data rather than a subjective judgement.

2. the cross-price elasticity of demand is defined as the percentage change in the quantity of one good when the price of another good changes. Again, the sign can be either positive or negative. If positive, the two goods are substitutes -- when the price of coffee goes up, the quantity of tea also goes up. If negative, the two goods are complements -- when the price of gas goes up, the number of automobiles purchased goes down.

3. the price elasticity of supply is defined as the percentage change in the quantity supplied divided by the percentage change in the price of the good. Normally, the long-run elasticity of supply is greater than the short-run elasticity of supply -- that is, the supply curve will be flatter in the long run than in the short run.

### Elasticity problems

1. Given the following demand schedule:

Demand
PRICE QUANTITY REVENUE
15 10 ____
10 55 ____
5 100 ____

1. Fill in the revenue column; without doing any further computations, is the demand curve elastic or inelastic? Why?
2. Compute the coefficient of elasticity between a price of \$5 and of \$15 using the midpoint formula. If you have forgotten the midpoint formula, review the hypertext link here
2. Answer the above questions for the following demand schedule:

Demand schedule
PRICE QUANTITY REVENUE
100 100 -----
300 90 -----
500 80 -----

3. Given the demand curve Q = 200 - 4P
1. Graph the demand curve, showing exactly where it cuts the axes.
2. How much is demanded at a price of 10 dollars? 11 dollars? 9 dollars?
3. Use the above information to find the elasticity of the curve at a price of \$10, that is between prices of \$9 and \$11. (Note: given a demand curve in algebraic form, we can find the elasticity at a point by raising and lowering the price by a dollar. We then construct a table similiar to the tables in the first two probems and compute the elasticity between the points defined by the given price plus or minus one dollar.)

4. Using the same demand curve, Q = 200 -4P
1. How much is demanded at a price of 40 dollars? at a price of 39 dollars?at a price of 41 dollars?
2. What is the coefficient of elasticity at a price of 40 dollars?
3. How does this compare with the coefficient of elasticity found in the previous problem? Is elasticity the same anywhere along a straight line demand curve? How does it vary with price?

5. Given the demand curve Q = 100 - 1/2 P
1. Can we say it is less elastic than the previous demand curve?
2. Is it less elastic than the previous demand curve at a price of 30 dollars?
3. Is it less elastic than the previous demand curve at a price of one dollar?
4. Does elasticity vary along this demand curve? Explain how -- does elasticity increase or decrease with price? Is this the same as the previous curve?