Question

Alistair spends his weekly income on 2 goods, movie tickets and potatoes. Potatoes are an inferior good. Movie tickets are a normal good. Assuming he purchases amounts of the 2 goods to maximize his utility, how will those amounts change if his income and the prices of both goods all decrease by 43%?

A) his purchases of movie tickets will increase and his purchases of potatoes will decrease

B) his purchases of both goods will increase

C) his purchases of both goods will decrease

D) his purchases of movie tickets will decrease and his purchases of potatoes will increase

E) his purchases of either good will not change

Answer 1

ANswer
E) his purchases of either good will not change

there will be no changes
as the price and income ratio is the same at both times so the maximum affordability of both goods is the same and the budget line looks completely the same.

Suppose,
current income is 100
price of good potato is $1, and the price of the movie ticket is $5

maximum potato Alistair can buy =100/1=100
Movie tickets =100/5=20

after change
income =100*(1-0.43)= 57
price of potato =1*(1-0.43)=0.57
Price of movie ticket =5*(1-0.43)=2.85

the quantities after the change
potato=57/0.57=100
movie tickets =57/2.85
=20

so there is no change in the optimum bundle as the same old indifference curve will touch at the same place and the optimum bundle will not change.