Discouraged workers and involuntary part$-$time workers

Simply counting the number of unemployed workers will not necessarily give the Bureau of Labor Statistics $($BLS$)$ the most accurate indication of the extent of underemployment in the economy. Some part$-$time workers will be counted as employed even if they'd like to work full$-$time. Furthermore, some jobless workers will not qualify as unemployed because they have given up on their job search, frustrated with their inability to find work. Fortunately, the BLS can use the information provided in the household survey to classify workers in ways that account for these types of underemployment.

The BLS classifies those who work part$-$time because they cannot find full$-$time employment as involuntary part$-$time workers. The BLS classifies as discouraged workers those who want and are available for work but have not searched for employment during the previous four weeks because they believe their job search is currently futile. By keeping track of discouraged and involuntary part$-$time workers, the BLS gets a clearer picture of underemployment than if it looked only at the number of unemployed workers.

Which of the following statements correctly describe discouraged workers? Check all that apply.

They are part$-$time workers who want to work full$-$time.

They are available for work.

They are full$-$time workers who would like to work only part$-$time.

They would like to have a job.

Consider a hypothetical economy in which the labor force consists of $250$ people. Of those, $225$ people are employed full$-$time and $25$ people are unemployed. The economy follows the same conventions as the U$.$S$.$ Bureau of Labor Statistics $($BLS$)$ in computing its employment figures. Therefore, initially the unemployment rate is calculated as follows:

Unemployment Rate $=\frac{\text{N}\text{u}\text{m}\text{b}\text{e}\text{r}of\text{U}\text{n}\text{e}\text{m}\text{p}\text{l}\text{o}\text{y}\text{e}\text{d}\text{P}\text{e}\text{o}\text{p}\text{l}\text{e}}{\text{N}\text{u}\text{m}\text{b}\text{e}\text{r}of\text{f}\text{o}\text{o}\text{p}\text{l}\text{e}in\text{t}\text{h}\text{e}\text{L}\text{o}\text{b}\text{a}\text{r}\text{F}\text{o}\text{r}\text{c}\text{e}}100$

$=\frac{25}{250}100$

$=10\%$

Suppose a reduction in foreign demand for this economy's products causes an economic recession$-$a prolonged period of declining output. The