Short Question 1: (30 points) A) Consider the bathtub model. Assume a monthly job separation rate equal to 5 = 2.1%, and a monthly job nding rate equal to f = 60%. Assume that the labor force is given by L = 200 million. i Derive the steady-state unemployment rate. How many people are unemployed in the steadystate? How many people lose their jobs every month? How many people nd a job every month? (10 points) ii Lets assume the actual unemployment rate is determined by the bath-tub model stud- ied in the textbook. Equations 7.2 and 7.3 in the textbook are as follows: E1+U1=L Ut+1 U: = 5E: _fUt where E are the number of employed people, U; are the number of unemployed people. s, f and L are given in the question on last page. From the second equation, we know that the number of unemployed people at time t + 1 is given by Ut+1 = Ut + 3E: f0; (1) Let unemployment rate in February 2021 be 7.5%. Using equation (1) and a calcula- tor, show the evolution of the unemployment rate over time. On the x-axis, plot dates (02/ 2021, 03/2021, 04/ 2021, 05/2021, and so on...). On the y-axis, plot the unemploy- ment rate corresponding at each time. Your graph will start at a yintercept of 7.5%. That is, U0 = 0.075. How long before the unemployment rate reaches 3.5%? (6 points) iii If job-separation rate 3 = 2.5%, what is the steady state unemployment rate. Assume job nding rate is same as given above. (4 points)