1. Janet Yellen, the Chair of the Federal Reserve, is to testify before Congress again. She hired you as a consultant (because she thinks your previous work was simply outstanding). But this time, she wants you to collect the data from 1995-2014 and plot the following figures (x-axis time, y-axis the variable of interest). To get full credit for your work (and you want to be cited before the Congress), add on each graph your last name (example, YourLastName, 2015).

Here are the links to the data:

- Unemployment Rate: http://data.bls.gov/timeseries/LNS14000000
- Unemployment Rate- High School Graduates : http://data.bls.gov/timeseries/LNU04027660
- Unemployment Rate - Some College: http://data.bls.gov/timeseries/LNU04027689
- Unemployment Rate- Bachelor's degree and higher: http://data.bls.gov/timeseries/LNU04027662

(a) Plot the unemployment rate (x-axis years, y-axis the unemployment rate). Is it true that the unemployment rate was the highest during the Great Recession (the recession that occurred during 2007-2008)?

(b) Plot the unemployment rate by education level on the same graph. Is the statement that the level of unemployment is higher for workers with lower levels of education true?

2. Consider an environment where an agent could be either employed E or unemployed U. Let's normalize E + U = 1, so that E and U are interpreted as the fraction of people employed and unemployed at any given point in time, respectively. Conditional on being employed today, the probability of being fired is δ; and conditional on being unemployed today, the probability of finding a job is ω.

(a) What is the probability of staying employed?

(b) What is the probability of not finding a job?

(c) Suppose that we know that today (Monday) the fraction of people who are employed is 0.95, what is the fraction of people employed tomorrow (Tuesday)?

(d) What is the fraction of people employed the day after tomorrow (Wednesday)?

(e) What is the fraction of people employed on Thursday?

(f) What is the steady state level of employment?

3. A simple model of search. Consider an agent who lives two periods. He is unemployed at the beginning of the first period and has a wage offer of w. If he accepts the wage offer w, he will work forever at that wage. If he rejects the offer, he receives an unemployment benefit of 4 dollars this period and he gets to draw a new offer next period. There are only two possible offers with equal probability next period one wage offer of 8 dollars, and another offer of 24 dollars. The worker's objective is to maximize the sum of expected discounted earnings. The discount factor β is 0.5.

(a) How much would the agent value today a dollar tomorrow? (Hint: use the concept of discount factor).

(b) What is the expected value of the potential offers?

(c) What is the value for the worker if he accepts the current offer w?

(d) What is the value for the worker if he rejects the current w?

(e) What is his reservation wage?

(f) Suppose he gets an offer of 16 dollars, would he accept or reject the offer?

(g) Suppose he gets an offer of 6 dollars, would he accept or reject the offer?

(h) Suppose that the government increases the unemployment benefit to 6 dollars. What would happen to this agent's reservation wage? Prove your claim.