Demand and elasticity

Revised on 8/29/96

The 3 laws of demand.
Elasticity is a useful summary measure of demand.
Price elasticity measures the responsiveness of demand to price changes.
A rule of thumb for calculating elasticity.
The difference between a shift of the demand curve and a movement along the demand curve. Changes in income and changes in the prices of related goods shift the demand curve.
Price elasticity is related to marginal revenue, and to total revenue.
Discussion Questions

The three laws of demand

First Law of Demand: As price increases, the quantity demanded decreases.
Second Law of Demand: The longer the time after a price change, the greater the effect on the rate of demand (quantity consumed per period).
Third Law of Demand: As price increases, goods that were not considered close substitutes at lower prices become closer substitutes.
Example: sugar and HFCS (high fructose corn syrup). HFCS was invented in the 1970's as a substitute for sugar, whose price was kept artificially high (about twice the world price) by price controls and import quotas administered by the Department of Agriculture and supported by Archer Danields Midland. As a caloric sweetener, it is a perfect substitute for sugar in soft drinks. In the graph below, the price of sugar is always above the price of HFCS, making the demand for HFCS very inelastic. If the government should ever decide to stop supporting the price of sugar, the price of sugar would fall to the price of HFCS, and the demand for HFCS would become very elastic.
This example is taken from
- Froeb, Luke and Gregory Werden, "The Reverse Cellophane Fallacy in Market Delineation," Review of Industrial Organization, 7 (1992) 241-247.

Other things that affect demand for a product, besides price:

Increases in income generally increase the demand curve (shifts demand up or to the right).
An increase in the price of a substitute increases demand.
An increase in the price of a complement decreases demand.
Changes in taste can increase or decrease the demand curve.

Perhaps the most common summary statistic associated with a demand curve is the elasticity.
price elasticity=(%change in quantity demanded)/(%change in price)
income elasticity=(%change in quantity demanded)/(%change in income)
- A negative income elasticity means that the good is inferior.
- A positive income elasticity means that the good is normal.
cross price elasticity of good one with respect to the price of good two=(%change in quantity of good one)/(%change in price of good two)
- A positive cross price elasticity means that the good is a substitute.
- A negative cross price elasticity means that the good is a complement.
advertising elasticity=(%change in quantity)/(%change in advertising)
There are two ways to compute % changes:
Arc price elasticity (arithmetic)={(q1-q2)/(q1+q2)}/{(p1-p2)/(p1+p2)}
Example: suppose that when the price changes from $10 to $8, the quantity changes from 1 to 2. In this example, the arc elasticity between the prices of $10 and $8 is [(1-2)/(1+2)]/ [(10-8)/(10+8)]=-3
Point price elasticity (calculus), (dq/dp)/(q/p)
If demand is described by the equation q=10-2*p, the elasticity at a price of 1 and a quantity of 8 is (-2)1/8=-.25

First law of demand: price elasticities are negative.
Second law of demand: in the long run, demand curves become more price elastic, |e| increases.
Third law of demand: as price increases, demand curves become more price elastic, |e| increases.

Graphical computation of elasticity
Elasticity for a linear demand curve
If you assume that demand can be approximated by a linear function, you can use the formula, e=p/(pmax-p) to elicit individual elasticities from consumers. Simply ask what they currently pay for the product (p) and how high price would have to be for them to stop consuming the product (pmax).

Marginal revenue is the extra revenue that comes from selling one more item.
MR=delta(PQ)=delta(P)Q+delta(Q)P= P(1-1/|e|) (note: delta means "change in")
Note that the marginal revenue is less than the price. P=MR for a perfectly elastic demand curve. This means you can sell as many items as you want at the current price. However, MR is less than price for a downward sloping demand curve because in order to sell more, you have to lower the price.
As long MR is positive, you can increase total revenue by selling more (by lowering the price).
Note that MR is positive if and only if elasticity is greater than one. In other words, as long as demand is elastic, you can increase total revenue by selling more, or equivalently, by lowering price.
Note that in the table above, revenue is maximized by selling only two items. This illustrates the same trade off we saw in bargaining between higher revenues and lower quantity sold.

As a grocery store manager, you alternate pickle promotions between Heinz and Vlasic. On a promotion week, the price of the promoted product drops by 25% and quantity increases by 300%. Does this mean that the elasticity of demand for pickles is -12? (Hint there are two complicating factors here.)
The Mayor of DC must have thought that demand for gasoline was inelastic, because he tried raising the sales tax on gasoline to raise more tax revenue. Instead, tax revenue went down. Should he have lowered the tax on gasoline?
If demand for Nike sneakers is inelastic, should Nike raise or lower price?
If demand for Nike sneakers is elastic, should Nike raise or lower price?