Advanced Micro II
Practice Final Exam Winter 2019
Advanced Micro Welcome! Please only write on the pages in this packet. Before you begin, write your name below. You will have 120 minutes ···
Welcome! Please only write on the pages in this packet. Before you begin, write your name below. You will have 120 minutes to complete this test. The test is also worth 120 points, so plan your time so that you spend one minute per point. You will get partial credit so it is very costly to leave a question completely blank. The points per question are listed in parentheses.
True, False, or Uncertain Advanced Micro
Are the following statements True, False, or Uncertain? Whatever your answer, to get credit you must provide a justification.
- (5points) A risk-averse person with decreasing relative risk aversion (DRRA) necessarily has decreasing absolute risk aversion (DARA)
- (5 points) If Jack has expected utility preferences over lotteries, then a monotonic transformation of his expected utility function still has the expected utility form and preserves the same
- (5 points) If only one person in a group of 10 risk-averse people faces a large risk, spreading this risk over all 10 people is a Pareto
- (5 points) Home insurance companies occasionally send employees to client homes in order to make sure that everything seems to be in order and that the home is occupied. This is an example of the full disclosure
- (5points) The marketplace eliminates statistical discrimination in the long
2 Problems Advanced Micro
- (20points total) Suppose Johnny is risk
- (10 points) Johnny is offered a choice between a gamble that pays $1000 with a probability of 25% and $100 with a probability of 75%, or a payment of $325. Which would hechoose?
- (10points) What if the payment was $320?
- (25points total) Consider the Rothschild and Stiglitz model of insurance discussed in In partic- ular, assume that people in the economy have the same wealth W and each face a potential loss of size
- However, individuals vary in their probability of experiencing this loss: A fraction λ are high risk and have a probability pHof a loss, while a fraction 1 λ are lower risk and have a probability pL < pH of a loss. Assume that the probabilities are private information to the agent. Agents maximize their expected Suppose that there exists a competitive insurance market that consists of insurance companies attempting to maximize expected profit by providing insurance contracts. Recall that in equilibrium, no offered contract makes negative expected profits and no un-offered contract could make a positive expected profits.
- (15 points) Graphically depict the only type of contracts offered in equilibrium. Be sure to at minimumlabel 1) the uninsured endowment of wealth across states 2) the 2 agent’s indifference curves 3) the break-even line(s) 4) the 45 degree line and 5) the separating
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(10 points) **2019 students Advanced Micro
- I wouldn’t really ask you this question on the test, but perhaps you want to think about it for practice. If not, just skip it!** Now, assume that a small fraction of thepopulation s have 100% probability of a loss L. The high-risk are now a fraction (1 − s)λ of
the population and the low risk are a fraction (1 s)(1 λ) of the population. Can the insurance company offer separating contracts?
- (15 points total) In deciding to park in an illegal place, any individual knows that the probability of getting a ticket is p and that the fine for receiving a ticket is f . Suppose that all individuals are risk-aversewith utility U (W ) over wealth W . Suppose that the city wants to raise revenue from
- (3points) Write an expression for the city’s ticket revenue which depends on the probability that an individual is caught (gets a ticket) and the ticket
- (3points) Suppose the city decides to increase revenue by increasing the probability an individual is caught by x%. Write an expression for the change in expected utility of
- (3points) Suppose instead that the city decides to increase revenue by increasing the fine by x%. Write an expression for the change in expected utility of
- (6 points) Suppose that x is small and use the Taylor series approximationU (W f ) U (W ) f U j(W ) + (f 2/2)U jj(W ) to answer the following question: will a small proportional increase in the probability of being caught or a proportional increase in the fine be a more effective deterrent to illegal parking?
Since U jj is negative (individual is risk averse) Advanced Micro
increasing the fine results in a larger change in utility. Therefor it’s a larger deterrent.
- (20 points) Sally is a police officer who gives tickets on the highway in order to reduce the accident rate. She has 2 years until she will definitely retire from the labor force. If Sally shirks, in each year there is a 20% chance that there will be an accident. If Sally does not shirk, she reduces the accident rate so the probability of an accident in each year is 10%. When Sally shirks, she gets to spend time ata If Sally does not shirk, her cost of effort (period disutility) is b. Sally period utility from
wages u(wt) = √wt, and discounts each year in the future at rate β.
- (10 points) Suppose that the police commissioner who sets Sally’s pay has utility U = 1000 if no accident occurs and U = 0 if an accident occurs. What does the first-best contract (in which the commissionercan observe Sally’s effort) look like?
- (10 points) Consider an incentive plan in which Sally will be paid a constant wage w until an accident occurs. If an accident occurs in period t, she is paid w that period but is fired and paid 0 (her outside option) the following period. Write an expression for the lowest wage w that will motivate Sally not to shirk. [Note: you do not have to solve the equation! just write the expression]
- (15points total) Show that any utility function which is DARA (decreasing absolute risk aversion) has a strictly positive third derivative and displays
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