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Let e denote the level of education. There are three types of potential workers: those (type L) with productivity, those (type M) with productivity and those (type H) with productivity , with >>>0. For each type i e{L, M, H} the fraction of type i in the population is Each potential worker knows her own type, while the potential employer cannot tell the type of any potential worker, although he knows the distribution of types in the population. The employer observes the education level of each potential worker (but not her type) and offers a wage which depends on the applicant's level of education. For every type i= {L.M. H) the cost of acquiring e units of education is Each worker's utility is given by the difference between the wage she is paid and the cost of education (a) [Note for this part do not assume that each worker must be paid a wage equal to her productivity ] Is there an incentive-compatible situation where (1) the employer offers two wages, depending on the education level wage w to those whose education level is e' and wage ww to those whose education level is eye and refuses to hire anybody with education ee (e.e), (2) both types 8 and 8 choose education level e, while type , choose education e? [Note that you should make no assumptions about whether e ey and similarly for w, and w ] If there is such an incentive-compatible situation, please describe it in detail. If your claim is that it does not exist, please prove it. For parts (b) and (c) assume that the employer pays each worker a wage equal to the worker's expected productivity (as computed by the employer who is nisk neutral). (b) Define and describe in detail a pooling equilibrium, that is a signaling equilibrium where all three types make the same choice of education level, call it [Assume that the employer believes that anybody who shows up with education level e must be of type L] (c) Find all the pooling equilibria when 81. 82.0 =6.

Now let us change the situation as follows. There are only two types of potential workers: those with productivity, and those with productivity , with 0 >0 >0. The fraction of type 8, in the population is equal to the fraction of type , Assume that the cost of education is the same for both types and is given by c(e) = e. Suppose that the utility of worker of type 0= {0,0H} who is paid wage w and chooses education level e is U(w, e, 0) - Ow-e. Assume also that ee[a,b] with 0

6. Go back to the same example from question 5, just above. Consumers in the economy like two goods: pizza and beer. Prices and quantities consumed are the same as before: Year Price of Pizza Quantity of Pizza Price of Beer Quantity of Beer 2009 $2 $1 2010 $2 ANN 2011 $4 $2 As a first step in computing the consumer price index (CPI), the Bureau of Labor Statistics surveys consumers to determine the "basket of goods" purchased by a typical consumer. Suppose that the BLS chooses 2009 as its base year and, consistent with the data shown in the table, decides that the basket of goods in this economy should consist of one pizza and two beers. a. What is the cost of the basket in each year: 2009, 2010, and 2011? b. Still using 2009 as the base year, what is the CPI in each year: 2009, 2010, and 2011? c. What is the inflation rate in 2010 and 20117 7. In the mid-1920s, the American author F. Scott Fitzgerald wrote a somewhat comical article for the Saturday Evening Post magazine titled, "How to Live on $36,000 a Year," in which he explained how he and his wife managed to spend their entire annual income of $36,000 without saving anything. a. In the mid-19205, the consumer price index was around 18; in 2010, the CPI was around 225. Using these figures, calculate how much Fitzgerald's income would be worth in 2010's dollars. b. More recently, Forbes magazine published a list of the highest paid authors, showing that J.K. Rowling, author of the Harry Potter books, earned $10 million in 2010. After adjusting for the effects of inflation, who earned more: Fitzgerald or Rowling? 8. In each case, please indicate whether the statement is true of false (you don't need to explain why).YUHOLLUIV '1' A new startup rm, IStart, wants to hire 51'.) workers- There are two types of workers that would have the required skills: Hand L. A worker oftype Hwould generate a monthly revenue of$- for the rm and a type L worker would generate a monthly revenue of S. for the rm. All workers are currently employed at a monily salary of EB. . We assume throughout that RL 1:: Sb 1:: RH - Every worker who decides to quit her current job and go to work for IStart will always be able to immediately return to her current job (at 1e current monthly salary of $30) if laid o' by IStart. The proportion of H types is and the proportion of L types is (lqH) with t) {:33