In this question, we extend the model with search friction discussed in class by adding non-pecuniary preferences over jobs. There are two periods and workers search for a job every period. Workers have linear utility and no saving. If unemployed, workers draw a job offer from a job offer distribution. Each job offer has two components - a wage w and a disutility v. Assume that w and v are independently distributed. The distribution of wages is 9w and the distribution of disutilities is gv. If the agent accepts the job offer, her utility at that period is given by: u(w, v) = w-v If the worker accepts a job at period 1, she remains employed for the next period on the same job. If the worker rejects the job offer from period 1, she receives unemployment insurance bat that period and searches for a new job in the next period. The worker has to accept the job offer received in the second period. Utility in the second period is discounted by rate . 1. Suppose the worker receive job offer (w, v) on the first period. Write down the value of accepting this job offer in period 1, Vaccept (w, v). 2. Calculate the expected utility of being unemployed on the next period as function of E(w) and E(v). Hint: Use that the utility is linear, u(w, v) = w-v, and that w and v are independently distributed. 3. Calculate the disutility of rejecting job offer (w, v) on the first period, Vreject (w, v). 4. Calculate the utility of receiving job offer (w, v) on the first period, V(w, v), using your answer to questions 1 to 3. 5. Conditional on a disutility of working v, plot the utility of rejecting a job and the utility of accepting a job on a graph with wages on the x-axis and the utility value on the y-axis. Mark the reservation wage (v) on this figure. 6. Calculate the reservation wage as a function of the disutility, w(v). Is the worker willing to accept a lower wage if she finds the job more meaningful? 7. Conditional on a wage w, plot the utility of rejecting a job and the utility of accepting a job on a graph with disutility on the x-axis and the utility value on the y-axis. Mark the reservation disutility (w) on this figure. Suppose there are two types of used cars: peaches and lemons. A peach is worth $3000 to a buyer and $1900 to a seller. A lemon, on the other hand, is worth $1000 to a buyer and $500 to a seller. The fraction of used cars that are peaches is 4 and the fraction that are lemons is 4. All parties are risk neutral, and when buyers and sellers bargain, the agreed sale price is always the maximum that buyers willing to pay. Assume that buyers cannot tell if a car is a peach or a lemon. Sellers know which type of car they own. (1) What kind of cars will be sold in this market? (ii) Now assume that the fraction of lemons is now 2. What kind of cars will be sold in this market? 14-21. Regina Hitechia, the CIO of Aurora Glass Fibers, Inc., is considering whether to lease or buy some new computers in the company's manufacturing plant. The new computers can be purchased for $800,000 with the proceeds from a 4-year, 10 percent interest rate loan, or leased for $250,000 a year, payable at the beginning of each year for the next four years. The computers fall into MACRS depreciation three-year asset class and have an expected useful life of four years. The salvage value of the computers at the end of the fourth year is $100,000. If the computers are leased, they will be returned to the leasing company at the end of the fourth year. Aurora's marginal tax rate is 40 percent. a. What is the present value of the cash flows associated with buying the computers? b. What is the present value of the cash flows associated with leasing the computers? c. Should Ms. Hitechia purchase or lease the new computers? 6e S