pcecon.com Class Notes

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Elasticity is a measure of buyer responsiveness; it measures relatively how much the quantity demanded will change when the price is changed, ceteris paribus.

In addition to being sort of interesting (OK, not really), elasticity tells us how changes in price will affect the revenue sellers get when they sell a good (or the amount buyers spend altogether on the good). This revenue (or spending) is PxQ.

For example, the following is a demand table, and the revenue that results.

Price | Quantity Demanded | Revenue =PxQ |

$100 | 0 | 0 |

$90 | 100 | 9000 |

$80 | 200 | 16000 |

$70 | 300 | 21000 |

$60 | 400 | 24000 |

$50 | 500 | 25000 |

$40 | 600 | 24000 |

$30 | 700 | 21000 |

$20 | 800 | 16000 |

$10 | 900 | 9000 |

0 | 1000 | 0 |

Notice that lowering price increases quantity demanded, but the revenue rises, and then falls.

Graphing the demand curve and the revenue (using quantity demanded as the horizontal axis for both graphs) gives the following diagrams:

Why does the revenue have this strange behavior?

Because at high prices, any change in price is small compared to the initial price, while a change in quantity demanded is large in comparison to the small initial quantities being purchased. It is the relative changes in price and quantity that matter.

If there is a change in price and buyers respond dramatically (relatively speaking) in terms of Q_{d}, we say that the buyers’ demand is "relatively elastic." As a result, the revenue increases when price decreases, since the relatively large increase in quantity demanded is enough to offset the decrease in price when PxQ is calculated. What this means that revenue is controlled by what is happening to quantity demanded, and does the opposite of what is happening to price. This is what is happening on the top half of the demand curve.

If there is a change in price and buyers do not respond much in terms of Q_{d}, we say that the buyers’ demand is "relatively inelastic." As a result, the revenue increases when price increases, since the slight decrease in quantity demanded is not enough to offset the increase in price when PxQ is calculated. What this means that revenue is controlled by what is happening to price. This is occuring on the bottom half of the demand curve.

A one-number way to summarize this result is with the price elasticity of demand.

(price) elasticity (of demand)=__
% change in quantity demanded
__% change in price

If buyers are responsive to price changes, the formula will give us a value of elasticity that is greater than one, in absolute value (again, it’s always negative)

|E|>1, demand is elastic (relatively)

If buyers are not responsive to price changes, this formula gives a value for elasticity that is less than one, in absolute value (it’s always negative):

|E|<1, demand is inelastic (relatively)

In calculating a percentage change in a price, which we must do to get elasticity, we generally would use the formula

old price

This is generally how percentage changes are calculated.

For example, if price is raised from $10 to $11, the percentage change would be

$10

However percentage changes are odd little buggers, in that they depend on which number we start with. If we lowered price from $11 to $10 (just going back to the previous price) we would find the percentage change to be

$11

since $11 dollars is the price we started with when we cut the price by a dollar. This goes against our intuition, since cutting a price from $11 to $10 seems like it should result in the same size change as raising price from $10 to $11 does. To get around this inconvenience, we can use something called an arc, in which we take the $1 change in price (either up or down) and divide it by the average of the two prices. This entails a bit more math, but at least we would get the same percentage change whether we raised or lowered the price.

arc percent change:

We can do the same kind of calculation for the percentage change in quantity demanded. For example, if changing the price from $11 to $10 changed quantity demanded from 500 units to 550 units, the percentage change in Q would be

To now find the elasticity, we would take the percentage change in Q (quantity demanded) and divide it by the percentage change in price, to get what we call the “arc elasticity” (since we used arcs to calculate it).

% change in P

This is just an example; they don’t always end up being -1. When the elasticity is -1, we say the demand is “unitary elastic.” The special significance of this is that revenue is maximized when elasticity is -1.

Even without having numbers, we can get some idea of elasticity by considering the characteristics of the good or its buyers.

Other things the same, demand for a good is MORE elastic...

*the MORE substitutes the good has

*the MORE of buyers’ income the good takes up

*the MORE time buyers have to adjust

*the MORE the price of the good is to start with

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