In: Economics
Suppose that you spend half of your income on necessities and half on luxury goods.
sol
a
Formula sl el + snen = 1 where s is share and e is income elasticity, l is for luxury and n for necessity
given sl = sn = .5 and en = .5
.5el + .5*.5 = 1
el = [1- .25]/.5
el = .75/.5 = 1.5
b
Given 20% fall in income
percentage fall in demand of necessities = .2*.5 = .10
quantity demanded of necessities fall by 10%
% fall in luxury = .2*1.5 = .30
demand for luxury falls by 30%
income elasticity = %change in share of income spent / % change in income
change in %share of necessities = .2*.5 = .10
share of necessities falls by 10%
change in%share of luxury = .2*1.5 = .30
share of luxury falls by 30%