Question

One commonly used measure of inflation is the annual rate of change of the Consumer Price Index (CPI). A TV news story says that the annual rate of change of the CPI is increasing. What does this say about the shape of the graph of the CPI?

Name: Problem 83, Chapter 4: Calculus for Business, Economics, Life Sciences, and Social Sciences
Uploaded: 2021-05-21T07:37:10-08:00
Duration: 1 min 13 s
Channel: Aman Gupta
Description: One commonly used measure of inflation is the annual rate of change of the Consumer Price Index (CPI). A TV news story says that the annual rate of change of the CPI is increasing. What does this say about the shape of the graph of the CPI?

   One commonly used measure of inflation is the annual rate of change of the Consumer Price Index (CPI). A TV news story says that the annual rate of change of the CPI is increasing. What does this say about the shape of the graph of the CPI?

Calculus for Business, Economics, Life Sciences, and Social Sciences

Raymond A. Barnett,… 13th Edition

Chapter 4, Problem 83

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Solved by Expert Aman Gupta

05/21/2021

Step 1

The annual rate of change of the CPI can be represented as $F'(t)$, which is the derivative of $F(t)$ with respect to time. Show more…

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One commonly used measure of inflation is the annual rate of change of the Consumer Price Index (CPI). A TV news story says that the annual rate of change of the CPI is increasing. What does this say about the shape of the graph of the CPI?

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Key Concepts

Rate of Change

This concept refers to how much a quantity, represented by a function, changes over a given interval of time. In economic data like inflation, the rate of change (often calculated as the first derivative) indicates the speed at which prices are rising or falling.

Increasing Rate of Change

An increasing rate of change implies that the first derivative of a function is growing over time. In other words, not only are the prices rising, but the speed at which they rise is also accelerating.

Graph Concavity

Graph concavity describes the curvature of a graph and is determined by the second derivative. If the curve is bending upward (convex), it indicates that the rate of change itself is increasing, which is consistent with a positive second derivative.

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