Question

Vera is an impoverished graduate student who has only $100 a month to spend on food. She has read in a government publication that she can assure an adequate diet by eating only peanut butter and carrots in the Öxed ratio of 2 pounds of peanut butter to 1 pound of carrots, so she decides to limit her diet to that regime.

a) If peanut butter costs $4 per pound and carrots cost $2 per pound, how much can she eat during the month?

b) Suppose peanut butter costs rise to $5 because of peanut subsidies introduced by a politically sensitive government. By how much will Vera have to reduce her food purchases?

c) How much in food stamp aid would the government have to give Vera to compensate for the e§ects of peanut subsidy?

d) Explain why Veraís preferences are of a very special type here. How would you graph them?

Answer 1

As Vera spends on peanut butter and carrots in a proportion of 2:1

So,X=2B=C (1)

a) When the price of butter is $4 and price of carrot is $2,Budget constraint would be

4B+2C=100,substitute in(1)

Or, 8X+2X=100

X=10

so,Vera eats 20 pounds of peanut butter and 10 ponds of carrot during the month.

b) When the price of butter rise to $5

New budget constraint = 5B+2C=100 substitute in (1)

or, 10X+2X=100

X=100/12=8.33

Vera would eat 16.67 pound of peanut butter and 8.33 pound of carrot so the reduction in food purchase is 20-16.67 = 3.33 pounds of peanut butter and 10-8.33=1.67 pounds of carrots.

c) Let the food stamp be denoted by F

Vera's original consumption =20 butter+10 carrots

so,5(20)+2(10)=100+F

F=120-100 = 20

d) As Vera's consumption of two goods is in a fixed proportion so the two goods are perfect complements to each other and her graph would be L-shaped as follows: