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 10 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.
B)4.67.
C)2.50.
D)3.50.
E)not possible to determine without further information.

Question

Quizplus · Accepted Answer

The Paasche price index is calculated using the formula: (Σ (P1 * Q1) / Σ (P0 * Q1)), where P1 and P0 are the prices in the current and base periods, respectively, and Q1 is the quantity in the current period. Assuming the consumer buys in the ratio of their utility function, Q1 can be taken as 1 unit of x and 0.5 units of y. Thus, the index is ((10*1 + 4*0.5) / (1*1 + 2*0.5)) = (10 + 2) / (1 + 1) = 12 / 2 = 6.

On the Planet Hyperion Every Consumer Who Has Ever Lived