2. The distribution of wages among the job vacancies in the economy is as follows: Table 1: Distribution of Wages Hourly Wage (35) l Fraction of vacancies 10 15% 15 25% 20 30% 25 25% (a) Consider a worker who is willing to accept any job offer. What is her expected wage. conditional on receiving a job offer? (b) Now suppose that the worker has a reservation wage of $18 and receives a random job offer with 100% probability. i. Write a table with the possible outcomes for the worker and their associated proba- bilities. ii. What is the probability that the worker will become employed? iii. What is the worker's expected wage. conditional on becoming employed? (c) Now suppose that the probability that the worker receives a random job offer falls to 80%. i. Assuming that the worker's reservation wage is still $18, write a new table with the possible outcomes for this worker and their associated probabilities. ii. How does this change in the arrival rate of job offers affect the worker's unemploy- ment probability, holding the reservation wage constant? (d) We showed that in the job search model, the reservation wage must satisfy the following: A r+q x=z+ [mun szHtw) In the case with a discrete number of possible jobs. this would correspond to: )1 +oa = + P :r: z r + q Em: :3} (in) where Phil] is the probability that the wage is equal to 11!. i. Write out the equation above for the specic case where the reservation wage is $18 and the distribution of wages is as given in Table 1 above. Keep z. )t, r and q as parameters. ii. Suppose that z = 10, the discount rate is 0.05 and the job destruction rate is 0.02. What value of /\\ is consistent with the equation above? iii. Now suppose that the reservation wage increases to $21. Find the new value of A that satises the reservation wage equation. given 2: = 10. 1' = 0.05 and q = 0.02. iv. What do your answers above imply about the relationship between the arrival rate of job offers and the reservation wage? What is the intuition for this result