Question

Suppose the United States economy is represented by the following equations:

Z = C + I + G            C = 100 +0.5Y_D                     T = 200                     I = 30

Y_D = Y - T                 G = 100

Suppose the Okun's law is given by:

u_t - u_t-1 = -0.4(g_yt - 3%)

a-) What is the output growth needed to result in reducing unemployment by 1% in a year.

b-) What is the output growth needed to reduce unemployment by 2% over the next 4 years.

c-) What is your interpretation of the 3% in Okun's law above?

Answer 1

Ans : Okun's Law gives the relationship between thye unemployment rate and the Gross National Product (GNP)

(a) If the unemployment needs to be reduced by 1% in a year, then u_t - u_t-1 = -1%

Substuting in the equation given in the question we get:

-1% = -0.4 (g_yt - 3%)

2.5% = g_yt - 3%

g_yt = 5.5 %

Output growth needed to reduce the unemployment by 1% in a year is 5.5%. 5.5 % growth in output is needed to reduce the unemployment 1% in one year.

(b) In we want to reduce the unemployment by 2% over the next 4 years, then it means that 0.5% unemployment is required in one year.

u_t - u_t-1 = -0.5 %

-0.5% = -0.4( g_yt - 3%)

1.25 = g_yt - 3

g_yt = 4.25%

If we want to reduce the unemployment by 0.5% in one year and 2% over the next 4 years, then growt in output that is required is 4.25% over the next 4 years, that is 4.25% ouput growth is needed.

(c) 3% is natural growth rate of output. It is output that is required to maintain the full employment. If the g_yt = 3% then the u_t - u_t-1 = 0 that is u_t = u_t-1 which means that unemployment rate remains same, If the natural rate of growth rate is 3% it means that the unemployment level remains same which implies that there is no change in unemployment.