Suppose the economy has a natural rate of unemployment of 6%.
a. Suppose short-run output over the next 4 years is +1%, 0%, -1%, and -2%, According to Okun's law, what unemployment rates would we expect to see in this economy?
b. Consider another economy in which the unemployment rate over the next 3 years is 6%, 7%, and then 4%. According to Okun's law, what are the levels of short-run output(Y~) in this economy?
Okun's Law -- u - u- = -1/2 x Y~
u -- current rate of unemployment
u- -- natural rate of unemployment
Y~ -- short run output.

Explanation:

a)  Okun's law suggests a GDP gap of -2% for every 1% that the unemployment rate exceeds its natural rate, thus according to it unemployment rates that we expect to see in this economy at the levels of +2%, +1%, 0%, and -1% are calculated as below:-

1) If output rate fall at the rate of 2%, it means that unemployment rate might have been rise by 1%, thus unemployment rate will be: - 6% natural rate +1% = 7%

2) If output rate fall at the rate of 1%, it means that unemployment rate might have been rise by 0.5%, thus unemployment rate will be: - 6% natural rate +0.5% = 6.5%

3) If output rate fall at the rate of 0%, it means that unemployment rate might have been rise by 0%, thus unemployment rate will be: - 6% natural rate +0% = 6%

4) If output rate fall at the rate of -1%, it means that unemployment rate might have been fall by 0.5%, thus unemployment rate will be: - 6% natural rate - 0.5% = 5.5%

b) Calculations of level of output is as follows:

If the unemployment rate is 6%, then considering natural rate of unemployment at 6%, there would be no change in output.

If the unemployment rate is 7% that is 1% rise, then a country's GDP/output will fall by 3% as compared to its potential GDP

If the unemployment rate is 4% that is 2% fall than the natural rate of unemployment of 6%, then a country's GDP/output will rise by additional 4% than its potential GDP

answer(b); ; ; the quantitative or qualitative variable for which the experimenter wishes to determine how its value is affected by the explanatory variable;