Question

calculate income price elasticity

1. Suppose Shabana has $200, and her optimal bundle of goods X and Y is (16,12) respectively. The price of good X is $5 and that of good Y is $10. However, she lost $20 while travelling and now only has $180 in her pocket. Given this, she changed her demand for goods X and Y as (14,11) respectively. Can you comment on the nature of goods X and Y?

Answer 1

Answer

both goods are normal as the decrease in income decreased the demand for both goods.

Income elasticity for X

Income elasticity of demand=(change in quantity/average quantity)/(change in income/average income)
Change in quantity=14-16=-2
average quantity=(14+16)/2=15
Change in income=180-200=-20
average income=(180+200)/2=190
Income elasticity of demand=(-2/15)/(-20/190)
=1.26666667
=1.27
the elasticity is positive so the good is normal

Income elastcity of Y
Income elasticity of demand=(change in quantity/average quantity)/(change in income/average income)
Change in quantity=11-12=-1
average quantity=(11+12)/2=11.5
Change in income=180-200=-20
average income=(180+200)/2=190
Income elasticity of demand=(-1/11.5)/(-20/190)
=0.826086957
=0.83
the elastcity is positive so the goods is normal