Consider the "bathtub" model of unemployment we discussed in Chapter 7. Consider an economy with a labor force of 1 million people. a. Take the initial parameter values: job separation rate 5 = 0.02, and job finding rate f = 0.38. Suppose the eocnomy begins the experiment in its steady state. What is the unemployment rate in this economy? How many people are employed? How many people are unemployed? How many people lose and find jobs every month? b. Suppose a recession hits, leading to the job separation rate increasing to 5 = 0.03, and the job finding rate decreasing to f= 0.17. Use these values to calculate the movements in employment, and unemployment over the next 12 months. What is the unemployment rate after 3, 6, and 12 months? 3 months after the shock, what was the number of job separations and what was the number of job finds? If these parameter values were to remain at this level, what would be the unemployment rate in the new steady state? c. Suppose that after 12 month the economy recover. As a result, the job separation rate comes back to 8 = 0.02. However, the job finding rate doesn't return to the original level, but only increases to f= 0.23. Calculate the unemployment rate for the next 12 months. What is the new steady state unemployment rate? Over the period of 12 months, how close does the economy get to its new steady state? d. Plot the unemployment rate over time, from periods 0 (initial steady state), to t = 24 (12 months after it begins to recover). Does this model replicate the experience of European countries in the 1980s shown on slide 24 of Chapter 7 slides? Briefly discuss