If 21% of unemployed find jobs and 0.9% of the employed lose their jobs, the natural rate of unemployment will be:Group of answer choices4.1%3.1%3.5%4.8%

Break Down the Problem

1. Identify the variables:
   • $u$: Unemployment rate
   • $f$: Fraction of unemployed finding jobs $= 0.21$
   • $s$: Fraction of employed losing jobs $= 0.009$
2. Set up the equation for the natural rate of unemployment $u^*$: $u^* = \frac{s}{s + f}$

Relevant Concepts

• The natural rate of unemployment can be calculated using the job finding and job separation rates, wherein:
  • $s$: Job separation rate
  • $f$: Job finding rate

Analysis and Detail

1. Using the values:
   • $s = 0.009$
   • $f = 0.21$
2. Plugging into the formula: $u^* = \frac{0.009}{0.009 + 0.21}$
3. Simplifying the denominator: $0.009 + 0.21 = 0.219$
4. Now calculate: $u^* = \frac{0.009}{0.219} \approx 0.041$

Verify and Summarize

1. The calculation gives $u^* \approx 0.041$, which corresponds to $4.1\%$.
2. Thus, verifying all calculations confirm the natural rate of unemployment.

Final Answer

The natural rate of unemployment is 4.1%.