Please answer question A all parts(1-5). Please be detailed in your explanation.

A. One-Sided Matching with a Probability of Not Matching In lecture we considered the case where a worker who rejects the wage offer of Wo in period zero will only get a new offer wj ~ U[w, w] with probability p. Assume wo has the same distribution as w1. 1. Is the unemployment rate higher or lower at the end of Period Q relative to the case where the worker always gets an offer in Period 1? Explain, intuitively, why that is the case. Derive a mathematical expression for how much higher it is. (Hint: The case where the worker always gets an offer in Period 1 is just the special case where p=1.) 2. Recall in class that we discussed the results of a paper that measured how the probability of exiting unemployment changes when a worker's unemployment benefits are about to expire. Suppose that the worker earns b if unemployed at the end of Period 0, but earns no benefit in if unemployed at the end of Period 1. How much higher or lower is the probability of being unemployed at the end of Period 0? (Give your answer as the change in probability relative to the case where unemployment benefits last through the end of Period 1.) Is the prediction of the model consistent with the papers we discussed in class? Assume again that unemployed workers earns b in both periods. Suppose a tech company introduces a job search technology that raises p infinitesimally. 3. How much higher or lower would unemployment be at the end of Period 0? Derive a mathematical expression for the change in unemployment. (Hint: you should take a derivative.) Explain, intuitively, why the derivative has the sign that it does (i.e. why the technology raises or lowers unemployment). 4. How much higher or lower would unemployment be at the end of Period 1? Derive a mathematical expression for the change in unemployment. 5. Suppose that b = 3, w = 5, w = 15, / = 1. Draw a diagram of the expression you derived in (4) as a function of p for 0