Consider an economy with 5000 people in the labour force. At the beginning of every month, 50 people lose their jobs and remained unemployed for exactly one month; one month later, they find new jobs and become employed. On January 1 of each year, 200 people lose their jobs and remained unemployed for 6 months before finding new jobs. Finally, on July 1 of each year, 200 people lose their jobs and remain unemployed for six months before finding new jobs. a) What is the unemployment rate in this economy in a typical month? (3 points) Now, a study shows that in the long run the job finding rate and the job separation are 18% and 2% respectively. b) What is the natural rate of unemployment? If the unemployment rate in part (a) were the current unemployment rate, what would you expect to happen in the unemployment rate over the long run? Briefly explain. (5 points) c) Suppose, in order to help those who suffer from the unemployment spell, the government of this economy decides to provide unemployment insurance to the unemployed. How does the provision of unemployment insurance affect the natural rate of unemployment in this economy? Explain and you should relate your answer to the job finding and job separation rates. (7 points)