Question

On the planet Homogenia every consumer who has ever lived consumes only two goods, x and y, and has the utility function U(x, y) = xy. The currency in Homogenia is the fragel. In this country in 1900, the price of good 1 was 1 fragel and the price of good 2 was 2 fragels. Per capita income was 60 fragels. In 2000, the price of good 1 was 5 fragels and the price of good 2 was 3 fragels. The Laspeyres price index for the price level in 2000 relative to the price level in 1900 is

2.67.

5.75.

4.

3.25.

not possible to determine from this information.

Answer 1

Demand for x = (share of x in total utility) * income / price of x

Demand for y = (share of y in total utility) * income / price of y

For 1900, demand for x = (1/2)*60/1 = 30 and demand for y = (1/2)*60/2 = 15

For 2000, demand for x = (1/2)*60/5 = 12 and demand for y = (1/2)*60/3 = 10

Laspeyres price index = Cost of basket in current year (base year quantity) / Cost of basket in base year (base year quantity)

= (5*30 + 3*15)/(30*1 + 2*15)

= 3.25

Select 3.25.