Suppose that you spend half of your income on necessities and half on luxury goods. If...

Suppose that you spend half of your income on necessities and half on luxury goods.

If the income elasticity of necessities is 0.5, what must the income elasticity of luxury goods be? SHOW HOW YOU KNOW. (10)
If your income FALLS by 20%, what will happen to the amount of each type of good you purchase, and how will your budget shares change? (You do not have to calculate the new budget shares or exact quantity of goods.) (12)

Expert Solution

sol

a

Formula s_l e_l + s_ne_n = 1 where s is share and e is income elasticity, l is for luxury and n for necessity

given s_l = s_n = .5 and e_n = .5

.5e_l + .5*.5 = 1

e_l = [1- .25]/.5

e_l = .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%

Rahul Sunny answered 2 years ago

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