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Over the past few years, one of the most closely monitored economic variables has been the inflation rate, which measures the change in the price level. Measuring it is complicated because different prices change by different amounts and sometimes in different directions (for example, the price of college tuition has been steadily rising for decades, whereas the price of TV sets has been decreasing). We can use the expenditure function to aggregate the change in the price level, by asking how much more it costs to achieve the same utility level under the new prices. That is, if the prices change from (P₁, P₂) to (P₁, P₂), where p₁ > p₁ and pź > P₂, we can define the inflation rate as:

Over the past few years, one of the most closely monitored economic variables has been the inflation rate, which measures the change in the price level. Measuring it is complicated because different prices change by different amounts and sometimes in different directions (for example, the price of college tuition has been steadily rising for decades, whereas the price of TV sets has been decreasing). We can use the expenditure function to aggregate the change in the price level, by asking how much more it costs to achieve the same utility level under the new prices. That is, if the prices change from (P₁, P₂) to (P₁, P₂), where p₁ > p₁ and pź > P₂, we can define the inflation rate as:

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
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2. Over the past few years, one of the most closely monitored economic variables has been the inflation rate, which measures the change in the price level. Measuring it is complicated because different prices change by different amounts and sometimes in different directions (for example, the price of college tuition has been steadily rising for decades, whereas the price of TV sets has been decreasing). We can use the expenditure function to aggregate the change in the price level, by asking how much more it costs to achieve the same utility level under the new prices. That is, if the prices change from (P₁, P₂) to (P₁, P₂), where p₁ > p₁ and pź > P₂, we can define the inflation rate as: b. i 1 1 Suppose Bebel has a Cobb-Douglas utility, U = 9₁²9₂², and an income level of Y = 1600. Suppose p₁ = 100 and p = 100 so the price of good 1 doesn't change, but the price of good 2 increases from p₂ = 16 to p2 = 25. a. Calculate Bebel's optimal consumption bundle and utility level at the initial prices p₁ E(P₁, P2, U) - E(P₁, P2, U) E (P₁, P2, U) = = 100 and P2 16. Solve for the income level Bebel would need to achieve the same utility level under the new prices p₁ 100 and p2 = 25.
Transcribed Image Text:2. Over the past few years, one of the most closely monitored economic variables has been the inflation rate, which measures the change in the price level. Measuring it is complicated because different prices change by different amounts and sometimes in different directions (for example, the price of college tuition has been steadily rising for decades, whereas the price of TV sets has been decreasing). We can use the expenditure function to aggregate the change in the price level, by asking how much more it costs to achieve the same utility level under the new prices. That is, if the prices change from (P₁, P₂) to (P₁, P₂), where p₁ > p₁ and pź > P₂, we can define the inflation rate as: b. i 1 1 Suppose Bebel has a Cobb-Douglas utility, U = 9₁²9₂², and an income level of Y = 1600. Suppose p₁ = 100 and p = 100 so the price of good 1 doesn't change, but the price of good 2 increases from p₂ = 16 to p2 = 25. a. Calculate Bebel's optimal consumption bundle and utility level at the initial prices p₁ E(P₁, P2, U) - E(P₁, P2, U) E (P₁, P2, U) = = 100 and P2 16. Solve for the income level Bebel would need to achieve the same utility level under the new prices p₁ 100 and p2 = 25.
C. Given your answer to part (b) what is the inflation rate for Bebel given the price change? How much more money would Bebel need to maintain her initial standard of living after the price of good two increases from $16 to $25? d. In practice, economists can't observe utility functions but only the consumption levels chosen. For this reason, it is necessary to try to approximate the inflation rate using consumption levels. One approach is the Laspeyeres price index which calculates how much more money would be needed to afford the initial consumption bundle, q₁ (P₁, P2) and qž (P₁, P2), at the new prices: e. LI = P₁qi (P₁, P₂) + P2qž (P₁, P2) – P₁q† (P₁, P2) – P292 (P₁, P₂) P₁9† (P₁, P2) + P29₂ (P₁, P2) Calculate the Laspeyere's price index for Bebel when the price of good 2 increases from 16 to 25. f. Does the Laspeyres price index over or under estimate the inflation rate? Illustrate on a graph, using roughly drawn indifference curves and budget constraints, and briefly provide an economic intuition (no more than 3 sentences) for your answer in terms of the substitution effect.
Transcribed Image Text:C. Given your answer to part (b) what is the inflation rate for Bebel given the price change? How much more money would Bebel need to maintain her initial standard of living after the price of good two increases from $16 to $25? d. In practice, economists can't observe utility functions but only the consumption levels chosen. For this reason, it is necessary to try to approximate the inflation rate using consumption levels. One approach is the Laspeyeres price index which calculates how much more money would be needed to afford the initial consumption bundle, q₁ (P₁, P2) and qž (P₁, P2), at the new prices: e. LI = P₁qi (P₁, P₂) + P2qž (P₁, P2) – P₁q† (P₁, P2) – P292 (P₁, P₂) P₁9† (P₁, P2) + P29₂ (P₁, P2) Calculate the Laspeyere's price index for Bebel when the price of good 2 increases from 16 to 25. f. Does the Laspeyres price index over or under estimate the inflation rate? Illustrate on a graph, using roughly drawn indifference curves and budget constraints, and briefly provide an economic intuition (no more than 3 sentences) for your answer in terms of the substitution effect.
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