Question

Below are some data on price, income and demand for four different time periods.



Year


Income


Price of X


Quantity


Price of Y


Quantity











Demanded





Demanded











of X





of Y


1


$40 000


$140


50


$40


200


2


40 000


150


40


40


160


3


40 000


150


30


70


140


4


50 000


150


40


70


160



a) What is the price elasticity of demand for product X between years 1 and 2? Is the demand elastic or inelastic?



b) What is the price elasticity of demand for product Y between years 2 and 3? Is the demand elastic or inelastic?



c) What is the income elasticity for product X between years 3 and 4? Is it a normal product or inferior? Is it a necessary product or a luxury?



d) What is the cross price elasticity of demand of product X for Y between years 2 and 3? Are the products X and Y substitute or complementary?

Answer 1

a) price elasticity of demand for x between years 1 and 2.

$P_{\epsilon D} =\frac {\Delta Q_D(x)} {\Delta P(x)} *\frac {P(x)} {Q_D(x) }$

=$\frac {40-50}{150-40}*\frac {140}{50}$

=2.8

The demand is Elastic because Elasticity is greater than one. The consumer is sensitive to changes in price.

b) price elasticity of product y between years 2 and 3.

$P_{\epsilon D} =\frac {\Delta Q_D(y)} {\Delta P(y)} *\frac {P(y)} {Q_D(x) }$

=$\frac {140-160}{70-40}*\frac{40}{60}$

=0.1667

The demand is inelastic since the value is less than 1. The consumer is less sensitive to price changes.

c) Income elasticity for product x between years 3 and 4

$I_{\epsilon D} =\frac {\Delta Q_D(x)} {\Delta I} *\frac{I} {Q_D(x)}$

$=\frac {40-30}{50000-40000}*\frac {40000}{30}$

=1.333

Since the value obtained is positive, x is a normal good. If the change in income is pisitive then the quantity demanded is positive and vice versa.

d) cross elasticity of demand for x and y between years 2 and 3

$X_{\epsilon D} =\frac {\Delta Q_D(x)} {\Delta P(y)} *\frac {P(y)} {Q_D(x) }$

$=\frac {30-40}{70-40}*\frac{40}{40}$

=-0.333

The cross price elasticity is negative hence x and y are complimentary. If there is a percentage increase in price then the change in quantity demanded is negative. If price of a compliment increases then the demand falls.