In a particular economy the labor force (the sum of employed and unemployed workers) is fixed at 4 million. In this economy, each month, \(0.3 \%\) of the workers who were employed at the beginning of the month lose their jobs, and 9.7\% of the workers who were unemployed at the beginning of the month find new jobs.

a. The January unemployment rate is 3\%. For the rates of job loss and job finding given, what will the unemployment rate be in February? In March?

b. In April an adverse productivity shock raises the job loss rate to \(0.5 \%\) of those employed. The job loss rate returns to \(0.3 \%\) in May, while the job finding rate remains unchanged at \(9.7 \%\) throughout. Find the unemployment rate for April, May, June, and July.