A) Consider the bathtub model. If a monthly job separation rate equal to s[bar] = 2.1%, and a monthly job finding rate equal to f[bar]= 60%. If that the labor force is given by L = 200 million.

i)Derive the steady-state unemployment rate. How many people are unemployed in the steady-state? How many people lose their jobs every month? How many people find a job every month?

ii)Lets assume the actual unemployment rate is determined by the bath-tub model as follows:

E_t + U_t = L[bar]

U_t+1 - U_t = s[bar]*E_t - f[bar]*U_t

where E_t are the number of employed people, U_t are the number of unemployed people. s[bar], f[bar] and L[bar] are given in the question. From the second equation, we know that the number of unemployed people at time t + 1 is given by

U_t+1 - U_t = s[bar]*E_t - f[bar]*U_t

Let unemployment rate in February 2021 be 7.5%. Using equation (1) and a calculator, 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 unemployment rate corresponding at each time. The graph will start at a y-intercept of 7.5%. That is, U₀ = 0.075. How long before the unemployment rate reaches 3.5%?

iii) If job-separation rate s = 2.5%, what is the steady state unemployment rate. Assume job finding rate is same as given above.

B) Hyperinflations are periods of rapidly increasing inflation caused by a sharp increase in money supply growth. Why are hyperinflations ultimately self- defeating from the standpoint of the government.

C) Briefly provide two reasons why higher levels of inflation might be costly for an economy.