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 84 fragels.In 2000, the price of good 1 was 3 fragels and the price of good 2 was 4 fragels.The Laspeyres price index for the price level in 2000 relative to the price level in 1900 is
A)2.50
B)3.50.
C)2.33.
D)4.
E)not possible to determine from this information.

Question

Quizplus · Accepted Answer

The Laspeyres price index is calculated using the formula: (Σ(P1Q0) / Σ(P0Q0)) * 100, where P1 is the price in the current period, P0 is the price in the base period, and Q0 is the quantity in the base period. Given the information, we first need to determine the quantities consumed in 1900 (Q0) using the budget constraint and utility maximization. With a budget of 84 fragels, and prices of 1 fragel for good 1 and 2 fragels for good 2 in 1900, consumers would allocate their budget to maximize utility, which is not directly provided but can be inferred to be equal quantities due to the nature of the utility function and the given prices. However, for the Laspeyres price index, we only need the prices and the base quantities, which are implied to be the same due to the utility function's symmetry and the budget allocation. Without explicit quantities, we focus on the price change: (3*1 + 4*2) / (1*1 + 2*2) = (3 + 8) / (1 + 4) = 11 / 5 = 2.2. However, without explicit quantities or a clear method to determine them from the utility function provided, the correct calculation of the Laspeyres price index cannot be completed as described, suggesting a misunderstanding in the explanation process. The correct approach involves using the given prices and a method to determine base quantities, which isn't directly provided, leading to an error in the initial explanation. The correct answer relies on understanding how to apply the Laspeyres price index formula to the given scenario, considering the prices in 1900 and 2000 and the implied or assumed quantities consumed based on the budget and prices.

On the Planet Homogenia Every Consumer Who Has Ever Lived