Question

Suppose that 2 percent of the employed lose their jobs each month (s = 0.02) and 38 percent of the unemployed find a job each month (f = 0.38). Then, the steady-state rate of unemployment is:

A) 2%
B) 36%
C) 38%
D) 40%

Answer 1

The steady-state rate of unemployment can be found using an equation using the given information. The solution to the equation is approximately 3.125% (Option D).

Step-by-step explanation:

To find the steady-state rate of unemployment, we can set up an equation using the given information. Let x be the steady-state rate of unemployment. Each month, 2% of the employed lose their jobs, so the decrease in the number of employees is 0.02 times the number of employed. Similarly, 38% of the unemployed find a job each month, so the increase in the number of employed is 0.38 times the number of unemployed. This can be represented as:

x = 0.02(1 - x) + 0.38x

Simplifying the equation, we get:

x = 0.02 - 0.02x + 0.38x

Combining like terms:

x = 0.02 + 0.36x

Subtracting 0.36x from both sides:

0.64x = 0.02

Dividing both sides by 0.64:

x ≈ 0.03125

Therefore, the steady-state rate of unemployment is approximately 3.125% (Option D).