Answer
a) 1
b) 1
c) Since she is spending less on clothes, then her demand curve for clothing shifts to the left. The price elasticity and income elasticity are still 1 and 1.
Work Step by Step
a) There is no change in her income. If her income increased by 3%, then she would be spending only 1% of that increase. (The change in her income would be the same as the change in how much she spends on clothing.)
b)
price elasticity of demand = percent change in quantity demanded/percent change in income
$Elasticity = \frac{(Q_{2}-Q_{1})/[(Q_{2}+Q_{1})/2}{(I_{2}-I_{1})/[(I_{2}+I_{1})/2}$
Let's assume she starts with an income of 30 and now has an income of 60. She consumed 10 pieces of clothing and now consumes 20 pieces of clothing.
$Elasticity = \frac{(20-10)/[(20+10)/2]}{(60-30)/[(60+30)/2]}$
$Elasticity = \frac{10/15}{30/45}$
$Elasticity = \frac{10/15}{30/45}$
$Elasticity = \frac{2/3}{2/3}$
$Elasticity = 1$
c) Since she would still spend a flat amount (25%) on clothing, the elasticities are still 1.
Let's assume she starts with an income of 20 and now has an income of 60. She consumed 5 pieces of clothing and now consumes 15 pieces of clothing.
$Elasticity = \frac{(15-5)/[(15+5)/2]}{(60-20)/[(60+20)/2]}$
$Elasticity = \frac{10/10}{40/40}$
$Elasticity = \frac{1}{1}$
$Elasticity = 1$
