## Advanced Micro II

### Homework 5 自然科学

1. Suppose100 cars will be offered on the used-car  Let 50 of them be good cars, each worth \$10,000 to the buyer. And let 50 of the be lemons, each worth only \$2,000 to the buyer.
• Compute a buyer’s maximum willingness to pay or a car if he or she cannot observe the car’s
• Suppose that there are enough buyers relative to sellers that. Competition among them leadscards to be sold a their maximum willingness to What would the market equilibrium be if sellers value good cars at \$8000? At \$6000?
1. Consider the principal-agent relationship between a patient and a doctor. Suppose that the patient’s utility function is given by U (m, c) where m denotes medical care (whose quantity is determined by the doctor) and c denotes other consumption goods.  The patient faces budget constraint W  = pmm + c  where pmis the price of medical care relative to other consumption. The doctor’s utility function is Ud(cd) + Up where cd is the doctor’s consumption and satisfies cd  pmm.  The doctor then derives  utility from the patient’s well-being, but also would like a higher
• Write down the patient’s maximization
• Writedown the doctor’s maximization problem and show that the doctor will generally choose a level of m that is higher than what a fully informed patient would choose.

#### 3.Consider a simpler version of the market for insurance than what we discussed in class 自然科学

Which allowedfor insurance companies to decide what type of contracts they offered. Suppose that insurance companies cannot decide what       types of contracts to offer. And instead decide what price  people  must pay for  a  fixed contract.  The nature of insurance is that the more risk you face, the more you would be willing to pay for insurance.   This means that in the market for insurance. Tthere is a connection between the expected cost to an insurance company of insuring an individual. And that person’s demand for insurance (usually, we think that demand and cost are unrelated). This is depicted in the figure below:

• Why is average cost above marginalcost?
• Whatwill be the level of insurance (ie, what fraction of the population will purchase the insurance contract) in this market? There is a hint in the graph, please explain your answer for full
• What is the efficient level ofinsurance?
• What does the shaded area represent? Now consider the graphbelow:

• ### What forces might cause the cost curve to be upward sloping? What does this mean for the equilibrium? 自然科学

1. After finishing your Master’s at Harris. You go on to a prestigious consulting job at McKinsey.  Who is assisting a client accused of discriminating based on race. Your job is to get at the bottom of how the client is calculating wages. You have access to four variables: two that you know the company had access to when it was hiring and determining wages.  Race and gender, and two that you know the company did not ever have access to. Nor did employees ever report them to anyone: old employee SAT scores and their parent’s

Your assistant provides you with the following table of summary statistics. For each of the five years an employee is employed. He has run a regression of wages that year on the four covariates: black, female, SAT, and parental education. Coming into your office scratching his head. He noticed that some coefficients declined in importance over time. While some increased in importance, but can’t make heads or tails of his results, displayed in Table 1 below.

Your  assignment:  in one or two  paragraphs,  come up with a coherent explanation of what’s going    on with these regression coefficients. Clearly explain why some fall in importance and some rise in importance, assuming that the client did know employee’s race and gender at the time of hiring them, but did not know their SAT score or their parent’s level of education.

Hint: You don’t have to do any math on this problem: you should think about it instead!