Over the past few years, one of the most closely monitored economic variables has been the inflatio 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 inflatio 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:
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
![**Text for Educational Website:**
c. Given your answer to part (b), what is the inflation rate for Bebel given the price change?
d. 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?
e. 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 Laspeyres price index, which calculates how much more money would be needed to afford the initial consumption bundle, \( q_1^*(p_1, p_2) \) and \( q_2^*(p_1, p_2) \), at the new prices:
\[
LI = \frac{p_1' q_1^*(p_1, p_2) + p_2' q_2^*(p_1, p_2) - p_1 q_1^*(p_1, p_2) - p_2 q_2^*(p_1, p_2)}{p_1 q_1^*(p_1, p_2) + p_2 q_2^*(p_1, p_2)}
\]
Calculate the Laspeyres price index for Bebel when the price of good 2 increases from 16 to 25.
f. Does the Laspeyres price index over or underestimate 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad5f8718-b822-43a6-888a-6d9b997f8030%2Fd7208d92-4350-4eff-8d3e-0f21017ac10f%2Fxkd0fbo_processed.png&w=3840&q=75)
Transcribed Image Text:**Text for Educational Website:**
c. Given your answer to part (b), what is the inflation rate for Bebel given the price change?
d. 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?
e. 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 Laspeyres price index, which calculates how much more money would be needed to afford the initial consumption bundle, \( q_1^*(p_1, p_2) \) and \( q_2^*(p_1, p_2) \), at the new prices:
\[
LI = \frac{p_1' q_1^*(p_1, p_2) + p_2' q_2^*(p_1, p_2) - p_1 q_1^*(p_1, p_2) - p_2 q_2^*(p_1, p_2)}{p_1 q_1^*(p_1, p_2) + p_2 q_2^*(p_1, p_2)}
\]
Calculate the Laspeyres price index for Bebel when the price of good 2 increases from 16 to 25.
f. Does the Laspeyres price index over or underestimate 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.
![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 \((p_1, p_2)\) to \((p'_1, p'_2)\), where \(p'_1 > p_1\) and \(p'_2 > p_2\), we can define the inflation rate as:
\[
i = \frac{E(p'_1, p'_2, U) - E(p_1, p_2, U)}{E(p_1, p_2, U)}
\]
Suppose Bebel has a Cobb-Douglas utility, \(U = q_1^{\frac{1}{2}} q_2^{\frac{1}{2}}\), and an income level of \(Y = 1600\). Suppose \(p_1 = 100\) and \(p'_1 = 100\) so the price of good 1 doesn't change, but the price of good 2 increases from \(p_2 = 16\) to \(p'_2 = 25\).
a. Calculate Bebel’s optimal consumption bundle and utility level at the initial prices \(p_1 = 100\) and \(p_2 = 16\).
b. Solve for the income level Bebel would need to achieve the same utility level under the new prices \(p'_1 = 100\) and \(p'_2 = 25\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad5f8718-b822-43a6-888a-6d9b997f8030%2Fd7208d92-4350-4eff-8d3e-0f21017ac10f%2F1agq2r9_processed.png&w=3840&q=75)
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 \((p_1, p_2)\) to \((p'_1, p'_2)\), where \(p'_1 > p_1\) and \(p'_2 > p_2\), we can define the inflation rate as:
\[
i = \frac{E(p'_1, p'_2, U) - E(p_1, p_2, U)}{E(p_1, p_2, U)}
\]
Suppose Bebel has a Cobb-Douglas utility, \(U = q_1^{\frac{1}{2}} q_2^{\frac{1}{2}}\), and an income level of \(Y = 1600\). Suppose \(p_1 = 100\) and \(p'_1 = 100\) so the price of good 1 doesn't change, but the price of good 2 increases from \(p_2 = 16\) to \(p'_2 = 25\).
a. Calculate Bebel’s optimal consumption bundle and utility level at the initial prices \(p_1 = 100\) and \(p_2 = 16\).
b. Solve for the income level Bebel would need to achieve the same utility level under the new prices \(p'_1 = 100\) and \(p'_2 = 25\).
Expert Solution
Step 1: Describe the problem
Utility function : U = q10.5 q20.5
Income : Y = 1600
Price of good 1 : P1 = 100
Price of Good 2 : P2 = 16
Original Budget Constraint : P1q1 + P2q2 = 1600
100q1 + 16q2 = 1600
*Hi there , as per our guidelines we solving first three sub parts of the question . Kindly repost the remaining parts to get them solved*
Step by step
Solved in 5 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.Recommended textbooks for you
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education