Unemployment and inflation are inversely related, with one rising as the other falls, and an equation giving the relation is called a Phillips curve after the economist A. W. Phillips (1914-1975). Phillips used data from 1861 to 1957 to establish that in the United Kingdom the unemployment rate x and the wage inflation rate y were related by y = 9.638x-1.394 - 0.900 where x and y are both in percents. Find the derivative of this function at each x-value. (Round your answers to two decimal places.) (a) 2 percent % (b) 5 percent. % Interpret your answers. Near full employment, inflation greatly ✔ ---Select--- h small ---Select--- in unemployment but with higher unemployment, inflation hardly ---Select--with--Select--- in unemployment. increases decreases Need Help? Read It
Unemployment and inflation are inversely related, with one rising as the other falls, and an equation giving the relation is called a Phillips curve after the economist A. W. Phillips (1914-1975). Phillips used data from 1861 to 1957 to establish that in the United Kingdom the unemployment rate x and the wage inflation rate y were related by y = 9.638x-1.394 - 0.900 where x and y are both in percents. Find the derivative of this function at each x-value. (Round your answers to two decimal places.) (a) 2 percent % (b) 5 percent. % Interpret your answers. Near full employment, inflation greatly ✔ ---Select--- h small ---Select--- in unemployment but with higher unemployment, inflation hardly ---Select--with--Select--- in unemployment. increases decreases Need Help? Read It
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Understanding the Phillips Curve and Its Derivative
**Unemployment and inflation are inversely related**, with one rising as the other falls. The equation giving this relation is called a **Phillips curve** after the economist **A. W. Phillips (1914–1975)**.
Phillips used data from 1861 to 1957 to establish that in the United Kingdom, the unemployment rate \( x \) and the wage inflation rate \( y \) were related by:
\[ y = 9.638x^{-1.394} - 0.900 \]
where \( x \) and \( y \) are both in percent.
### Derivative Calculation
Find the derivative of this function at each \( x \)-value. (Round your answers to two decimal places.)
- **(a) 2 percent**
Place your calculated value in the box below:
\[
\boxed{\ \ \ \ \ }
\]
%
- **(b) 5 percent**
Place your calculated value in the box below:
\[
\boxed{\ \ \ \ \ }
\]
%
### Interpretation of Results
Interpret your answers based on the calculated derivative.
Near full employment, inflation greatly---Select--- **decreases or increases** ---Select--- with small---Select--- **decreases or increases** ---Select--- in unemployment, but with higher unemployment, inflation hardly---Select--- **decreases or increases** ---Select--- with---Select--- **decreases or increases** ---Select--- in unemployment.
---
For further assistance, click the button below:
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Transcribed Image Text:### Understanding the Phillips Curve and Its Derivative
**Unemployment and inflation are inversely related**, with one rising as the other falls. The equation giving this relation is called a **Phillips curve** after the economist **A. W. Phillips (1914–1975)**.
Phillips used data from 1861 to 1957 to establish that in the United Kingdom, the unemployment rate \( x \) and the wage inflation rate \( y \) were related by:
\[ y = 9.638x^{-1.394} - 0.900 \]
where \( x \) and \( y \) are both in percent.
### Derivative Calculation
Find the derivative of this function at each \( x \)-value. (Round your answers to two decimal places.)
- **(a) 2 percent**
Place your calculated value in the box below:
\[
\boxed{\ \ \ \ \ }
\]
%
- **(b) 5 percent**
Place your calculated value in the box below:
\[
\boxed{\ \ \ \ \ }
\]
%
### Interpretation of Results
Interpret your answers based on the calculated derivative.
Near full employment, inflation greatly---Select--- **decreases or increases** ---Select--- with small---Select--- **decreases or increases** ---Select--- in unemployment, but with higher unemployment, inflation hardly---Select--- **decreases or increases** ---Select--- with---Select--- **decreases or increases** ---Select--- in unemployment.
---
For further assistance, click the button below:
**Need Help?**
\[ \boxed{\text{Read It}} \]
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