Question

include correctly labeled diagrams, if useful or required, in explaining your answers. a correctly labeled diagram must have all axes and curves clearly labeled and must show directional changes. if the question prompts you to \calculate,\ you must show how you arrived at your final answer. the table below shows unemployment and labor force statistics for an economy. actual rate of unemployment 3% natural rate of unemployment 4% civilian, noninstitutional population age 16 and over 125 million number of people employed full time 92 million number of people employed part time 5 million number of people unemployed 3 million number of discouraged workers 2 million (a) calculate the size of the labor force. show your work. (b) calculate the labor force participation rate. show your work (c) given the state of the economy described in the table, is actual real output less than, greater than, or equal to potential real output? explain. (d) calculate what the cyclical unemployment rate would be if the actual rate of unemployment increased to 5 percent. show your work. (e) suppose discouraged workers reenter the labor force and find employment. will the actual rate of unemployment increase, decrease, or stay the same?

Explanation:

Step1: Calculate labor - force size

The labor - force is the sum of the employed and the unemployed. The number of employed is the sum of full - time and part - time employed. So, the number of employed is $92 + 5=97$ million, and the number of unemployed is 3 million. The labor - force size $L$ is $L=(92 + 5)+3=100$ million.

Step2: Calculate labor - force participation rate

The labor - force participation rate $LFPR$ is calculated as $\frac{\text{Labor Force}}{\text{Civilian non - institutional population age 16 and over}}\times100\%$. We know that the labor force $L = 100$ million and the civilian non - institutional population age 16 and over $P=125$ million. So, $LFPR=\frac{100}{125}\times100\% = 80\%$.

Step3: Determine relationship between actual and potential output

The natural rate of unemployment is 4% and the actual rate of unemployment is 3%. When the actual rate of unemployment is less than the natural rate of unemployment, the actual real output is greater than the potential real output. This is because when unemployment is below the natural rate, the economy is operating above its long - run capacity, with workers working overtime and firms running their plants at a high utilization rate.

Step4: Calculate cyclical unemployment rate

The natural rate of unemployment $u_n = 4\%$. If the actual rate of unemployment $u_a=5\%$, the cyclical unemployment rate $u_c$ is calculated as $u_c=u_a - u_n$. So, $u_c=5\%−4\% = 1\%$.

Step5: Analyze effect on unemployment rate

Discouraged workers are not counted in the labor force. When they reenter the labor force and find employment, the number of unemployed does not change (since they move directly from non - labor force to employed) and the labor force increases. However, since they find employment, the actual rate of unemployment will decrease.

Answer:

(a) 100 million. Work: $(92 + 5)+3=100$ million.
(b) 80%. Work: $\frac{100}{125}\times100\% = 80\%$.
(c) Actual real output is greater than potential real output. Explanation: Actual unemployment (3%) is less than natural unemployment (4%), so the economy is operating above its long - run capacity.
(d) 1%. Work: $5\%−4\% = 1\%$.
(e) Decrease. Explanation: Discouraged workers enter the labor force and find employment, so the number of unemployed does not increase while the labor force increases, leading to a decrease in the unemployment rate.