B.I.2 Cars come in many di?erent qualities. The quality of a car is given by ?. (Assume that ? has auniform distribution on the interval 1 ? 5.) The seller of each car knows its value and getsutility...

B.I.2 Cars come in many di?erent qualities. The quality of a car is given by ?. (Assume that ? has auniform distribution on the interval 1 ? 5.) The seller of each car knows its value and getsutility ln(1 + ?) from owning the car. If they sell their car at price p they get utility p.There are ? <> e, this market has excess demand when p = 1.(f) Use calculus to show that at every price p the average quality of cars o?ered for sale isgreater than p.(g) Hence, or otherwise, show that at the equilibrium price 4? + 2 = ep , if 2 + 4? > e.B.I.3 A worker can either exert e?ort or shirk. It costs the worker c > 0 to provide e?ort and shirkingpcosts nothing. The utility of earning wage w and providing e?ort is w c. The utility ofpearning wage w and not providing e?ort is w. When the worker provides e?ort there is aprobability p of an innovation, when the worker shirks there is zero probability of an innovation.The manager of the firm decides to o?er a basic wage 1 for every worker and a bonus b toworkers who generate an innovation. If workers leave the company, they can obtain the wage delsewhere.(a) Write down the conditions b must satisfy to get the worker to be willing to work for thecompany.(b) Write down the conditions that b must satisfy it is to be e?ective at getting the workers togenerate innovations.(c) Suppose that d 1 and an innovation is worth 3 to the manager. When is it worthproviding these incentives for innovations?(d) How does your answer to part (3c) change if d > 1? ECON2001 9