A salesperson working for a car dealership may not choose to work hard all the time. The dealership owner can't observe the salesperson's effort, but can observe the number of cars sold. The salesperson's personal cost of working at the dealership is C(H) = 1000 + H^2, where H is the number of hours of hard work. Without any hard work, the salesperson will, on average, generate a profit of $800. With each hour of hard work, he has a 4% chance of selling a car. Each car sale generates a profit of $1,000.

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5. A salesperson works for a car dealership, but mag.r choose not to work hard all of the time. The dealership owner cannot observe the salesperson's effort, but can observe the number of cars sold. The salesperson's personal cost of working at the dealership is CH!) = 1,000 +H2, where H is the number of hours of hard work. Without an}r hard work, the salesperson will, on average, generate a prot of $300. With each hour of hard work, he has a 4% chance of selling a car. Each car sale generates a prot of $1,000. (a) What is the efcient number of hours of hard work {this is the number of hours of hard work that maximizes prots while include the personal cost of hard work to the agent)? (b) How much surplus does the relationship generate (prot to the owner minus cost to the agent)? (c) Suppose the owner gives the salesperson $1, 200 111 base pa},' plus a bonus of $500 for each car he sells How hard will the salesperson work (what ts the level of H that maximizes "utility" to the agent}? (d) Describe an incentive scheme (a base pay and a bonus per car sold) that leads to the efcient level of hard work (from a)}? _