Question

Twenty years ago, Dmitri consumed bread which cost him 10 kopeks a loaf and potatoes which cost him 18 kopeks a sack. With his income of 230 kopeks, he bought 5 loaves of bread and 10 sacks of potatoes. Today he has an income of 400 kopeks. Bread now costs him 20 kopeks a loaf and potatoes cost him 25 kopeks a sack. Assuming his preferences haven’t changed (and the sizes of loaves and sacks haven’t changed), when was he better off?

a. He was equally well off in the two periods.

b. He is better off today.

c. He was better off 20 years ago.

d. From the information given here, we are unable to tell.

e. None of the above.

PLEASE SHOW ALL WORK

Answer 1

The correct answer is (b) He is better off today

Dmitri with his old income of 230 kopeks and old prices of potatoes and bread he consumed 5 loaves of bread and 10 sacks of potatoes.

Lets see that with his new income and new prices can he buy his previous bundle of potatoes and bread.

His New Income = 400 , price of bread = 20 and price of potatoes = 25

His older bundle is (B,P) = (5,10)

Income required to buy this bundle with new income and prices are(Currently):

20*5 + 25*10 = 350 which is less than her current income and hence she can buy more of Potatoes or breads than before with her new income(i.e after buying old bundle she has income remaining = 400 - 350 = $50).

Hence, She can buy currently more of Potatoes and breads than before.

Hence, she must definitely be better off.

Hence, the correct answer is (b) He is better off today