Cross-price Elasticity
The cross-price elasticity of demand measures the rate of response of quantity demanded of one good, due to a price change of another good. For example, if the price of Pepsi goes down, then we would expect the demand for Coke to decrease. Cross-price elasticity of demand would measure the magnitude of Coke consumer's responsiveness to a change in Pepsi's price.

The sign for cross-price elasticity of demand depends on whether the goods are complements or substitutes of each other. If they are complements of each other, like peanut butter and jelly, then a decrease in the price of one will produce an increase in demand for the other. On the otherhand, when the items are substitutes for each other (like the Pepsi and Coke example) then a decrease in price would decrease the demand for the other. So the cross-price elasticity of demand will tend to be positive for substitutes and negative for complements. If the cross-price elasticity of demand is equal to zero, then the demand for the product is independent of the price of the other product.

To determine cross-price elasticity, the formula is:

external image b107341360804aecc3531c8b3e4ad2dc.png

Another way to look at this formula is as follows:

external image e3fd351e4577bfc664eff753d8d3e777.png

To display the use of the first version of the formula, imagine that in response to a 5% increase in the price of peanut butter, quantity of jelly demanded decreased by 15%.
So the cross-price elasticity of demand would be =
-15%/5% =
-3

To display the use of the second version of the formula, imagine that a hospital's patients are buying a total of 350 meals a day in the hotel, and that they are paying $200 a day for the room. The hospital realizes that when they lower their room's to a $175 a day for the room, the number of meals purchased goes up to 400.
So the cross-price elasticity is =
( 50 / -$25) x ( $187.50 / 375 ) =
( -2 ) x ( .50 ) =
-1.


Sample Questions:
1) If the price of one of two complement products goes up, what should
happen to the other complement product?

A) The demand for the other complement should go down.
B) The price of the other complement will automatically change by the same
amount as the initial complement product.
C) The demand for the other complement should go up.
D) Both A & B
2) If the cross-price elasticity of demand is equal to zero for two products, then:
A) the demand for one must have gone up, and the demand for the other must have gone down.
B) the demand for the product is independent of the price of the other product.
C) the products are neither complements nor substitutes of one another.
D) Both B & C.
3) What would be the cross-price elasticity if, in response to a 10% increase in the price of fuel, the quantity of new cars that are fuel inefficient demanded decreased by 20%?
A) .5
B) 2
C) -2
D) -.5
4) What would be the cross-price elasticity if hospital patients initially purchase 450 meals a day and patients pay a daily room fee of $105, and then realize that lowering the room fee to $95 a day raises meals bought a day to 550?
A) 0
B) -2
C) -1
D) 1


Answers:
1) A) The demand for the other complement should go down.
2) D) Both B & C.
3) C)- (-2).
4) B)- (-2).
Sources
[1]economics.about.com/cs/micfrohelp/ a/cross_price_d.htm
[2]en.wikipedia.org/wiki/ Cross_elasticity_of_demand
[3]Santerre, Rexford E. and Neun, Stephen P. "Health Economics - Theories, Insights, and Industry Studies- 4th Ed."

Page made by Logan Pilcher and Susan Richardson.