ECON 302 Simeon Alder
Intermediate Macroeconomics Fall 2025
Midterm Exam #3
Sample Answers for Short-Essay Questions
Short-Essay Question (Bathtub Model)
At the start of the COVID-19 pandemic, many older workers decided to leave the
labor force rather than become unemployed. They went into early retirement.
In this question, you are tasked with analyzing this wave of early retirements
using the bathtub model of unemployment.
Let sMarch 2020 be separation rate in the first month of the pandemic. To capture
early retirement, you can assume that a fraction αof these separated workers
become unemployed. The remaining fraction 1−αleaves the labor force perma-
nently.
1. How does this labor force exit affect the number of unemployed workers in
April 2020 assuming that the job-finding rate remains steady (denoted ¯
f)?
[1.5 points]
Sample Answer:
The number of unemployed workers in April 2020 is given by UApril 2020 =
sMarch 2020αEt−¯
fUt. Note that the number of unemployed workers is in-
creasing in α. The drop in αdue to early retirements implies that, all else
equal, the number of unemployed workers drops.
2. Considering that the labor force shrinks between March and April of 2020,
how does the exit affect the unemployment rate in April 2020? Keep in
mind that the unemployment rate is given by ut=Ut
Ltand take into account
that between March and April both the number of unemployed workers
and the size of labor force can change. If the effect is ambiguous, you should
emphasize that and explain why. [1.5 points]
Sample Answer:
From the previous question we know that the numerator in Ut
Ltis falling be-
tween March and April of 2020. Due to early retirements, the denominator
1
