On the planet Hyperion, every consumer who has ever lived has a utility function U(x, y)= min{x, 2y}.The currency of Hyperion is the doggerel.In 1850 the price of x was 1 doggerel per unit and the price of y was 2 doggerels per unit.In 2000 the price of x was 11 doggerels per unit and the price of y was 4 doggerels per unit.The Paasche price index of prices in 2000 relative to prices in 1850 is
A)6.50.
B)5.
C)2.75
D)3.75.
E)It is not possible to determine the Paasche price index without further information.

Question

Quizplus · Accepted Answer

The Paasche price index uses current year quantities as weights, so we find the total current year expenditure and divide by the total base year expenditure. The current year expenditure is U(11,4) = 44 for every consumer, and there are F1F1F1S1F1F1F110minF1F1F1S1F1F1F10x, 2yF1F1F1S1F1F1F1 consumers, so the total current year expenditure is F1F1F1S1F1F1F110minF1F1F1S1F1F1F10x, 2yF1F1F1S1F1F1F1* U(11,4) = F1F1F1S1F1F1F110minF1F1F1S1F1F1F10x, 2yF1F1F1S1F1F1F1* 44. The base year expenditure is U(1,2) = 2 for every consumer, and there are F1F1F1S1F1F1F110minF1F1F1S1F1F1F10x, 2yF1F1F1S1F1F1F1 consumers, so the total base year expenditure is F1F1F1S1F1F1F110minF1F1F1S1F1F1F10x, 2yF1F1F1S1F1F1F1* 2. Dividing, we get an index of F1F1F1S1F1F1F110minF1F1F1S1F1F1F10x, 2yF1F1F1S1F1F1F1* 44/F1F1F1S1F1F1F110minF1F1F1S1F1F1F10x, 2yF1F1F1S1F1F1F1* 2 = 6.5, so the answer is (A).

On the Planet Hyperion, Every Consumer Who Has Ever Lived