Extra Practice 11

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Feb 20, 2024

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Econ 351x Extra Practice Chapter 11 1 1. How many of the following options are best described as examples of adverse selection? I – Lemons problem in the market for used cars II – Risk Averse individuals in the market for extra health care coverage III – Risk Averse drivers purchasing extra auto insurance IV – The fact that managers cannot directly observe the actions of workers a. All four options b. Zero options c. One option only d. Two options only e. Three options only 2. Consider the following two examples: I – Unhealthy people are more likely to want health insurance; II – A consumer with complete medical insurance may visit the doctor more often than he would if his coverage were limited. The two examples best describe: a. Both are examples of Adverse Selection b. Both are examples of Moral Hazard c. Example I is Moral Hazard; Example II is Adverse Selection d. Example I is Adverse Selection; Example II is Moral Hazard. e. Both are examples of the Lemons Problem 3. Consumers have utility 𝑢(𝐼) = √𝐼 and income $200. The cost of going to the doctor is $120, and the cost of going to the gym is $6. If the consumer goes to the gym, the probability of getting sick is 10%; if he/she does not go to the gym, the probability of getting sick is 90%. When sick, the consumer must go to the doctor. An insurance company is offering an insurance plan with an insurance premium of $12 and a co-pay of $15 (that is, the consumer must pay the $15 if he/she goes to the doctor). The consumer’s expected utility from going to the gym and buying this insurance plan is approximately a. 12.9 b. 13.2 c. 12.7 d. 12.5 e. 13.4 4. The $15 co-pay from the previous question a. Fixes the adverse selection problem b. Fixes the moral hazard problem c. Should be lower otherwise the consumer will not buy it d. Should be higher to fix the moral hazard problem e. Should be higher to fix the adverse selection problem

Econ 351x Extra Practice Chapter 11 2 5. Consumers have utility 𝑢(𝐼) = √𝐼 and income $200. The cost of going to the doctor is $120, and the cost of going to the gym is $20. If the consumer goes to the gym, the probability of getting sick is 10%; if he/she does not go to the gym, the probability of getting sick is 90%. When sick, the consumer must go to the doctor. An insurance company is offering an insurance plan with an insurance premium of $12 and a co-pay of $15 (that is, the consumer must pay the $15 if he/she goes to the doctor). The consumer’s expected utility from going to the gym and buying this insurance plan is approximately a. 12.9 b. 13.2 c. 12.7 d. 12.5 e. 12.3 6. The $15 co-pay from the previous question a. Fixes the adverse selection problem b. Fixes the moral hazard problem c. Should be lower otherwise the consumer will not buy it d. Should be higher to fix the moral hazard problem e. Should be higher to fix the adverse selection problem 7. Elmo has a factory which is worth $40,000. The probability of a fire in the factory without a fire prevention program is 90%. The probability of a fire in a factory with a fire protection program is 40%. If a fire occurred, the value of the loss would be $30,000 (that is, the value of the factory would go down to $10,000). A fire prevention pro gram would cost $10 to run. Elmo’s utility from wealth is 𝑢(𝐼) = √𝐼 An insurance company would like to fully insure Elmo’s factory, but the insurance company cannot observe whether the factory is implementing the fire prevention program or not. To circumvent this problem, the insurance company is offering the following policy: the company will fully insure the factory for an insurance premium P=$12,000, but if a fire occurs, then Elmo must pay a $2,000 co-pay to the insurance company. If Elmo buys this insurance policy and implements the fire prevention program, his expected utility is ___________. If Elmo buys this insurance policy and does not implement the fire prevention program, his expected utility is _____________. [Keep as many decimals as possible during all your computations. At the very end, mark the option with the numbers closest to your answer.] a. 171.9; 161.9 b. 164.9; 171.9 c. 164.9; 161.9 d. 161.9; 164.9 e. 161.9; 171.9

Econ 351x Extra Practice Chapter 11 3 8. For workers in Group A (high skill workers) the cost of attaining an educational level y is C A (y)=$10y; for workers in Group B (low skill workers) the cost of attaining an educational level y is C B (y)=$20y. Employees will be offered $40 if they have y ≥ y*, where y* is an educational threshold determined by the employer. They will be offered $20 if they have y < y*. In equilibrium, education can be used as a signal of the worker’s true type if a. 2 ≥ y* ≥ 1 b. 4 ≥ y* ≥ 2 c. 4 ≥ y* ≥ 1.33 d. 2 ≥ y* ≥ 1.33 e. 4 ≥ y* ≥ 1 9. For workers in Group A (high skill workers) the cost of attaining an educational level y is C A (y)=$10y; for workers in Group B (low skill workers) the cost of attaining an educational level y is C B (y)=$20y. Employees will be offered $40 if they have 5 or more years of education. They will be offered $20 if they have less than 5 years of education. In this case, can education be used as a market signal of the worker’s skill? 10. For workers in Group A (high skill workers) the cost of attaining an educational level y is C A (y)=$10y; for workers in Group B (low skill workers) the cost of attaining an educational level y is C B (y)=$15 y. Employees will be offered $40 if they have y ≥ y*, where y* is an educational threshold determined by the employer. They will be offered $20 if they have y < y*. On top of this amount, firms also pay $5 for every year of education (y is the number of years of education). In equilibrium, education can be used as a signal of the worker’s true type if a. 2 ≥ y* ≥ 1 b. 4 ≥ y* ≥ 2 c. 4 ≥ y* ≥ 1.33 d. 2 ≥ y* ≥ 1.33 e. 4 ≥ y* ≥ 1 11. It takes y* years to graduate from college. For workers in Group A (high skill workers) the cost of going to college is $6 per year (Cost A =6y*). For workers in Group B (low skill workers) the cost of going to college is $12 per year (Cost B =12y*). In addition to this cost, when accepted by the college, each worker also has to pay a one-time enrollment fee of $8, independently of skill and independently of y* (it is a fixed cost, not a per year cost). Employers cannot observe the skill of job candidates, but they can observe whether or not they graduated from college. Employees will be offered $70 if they graduate from college, and they will be offered $20 if they don’t have a college degree. In equilibrium, a college degree can be used as a signal of the worker’s true type if a. 5 ≥ y* ≥ 2.5 b. 7 ≥ y* ≥ 2.5 c. 5 ≥ y* ≥ 3.5 d. 7 ≥ y* ≥ 3.5 e. Because of the fixed cost, workers optimally choose not to go to college independent of y*

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Econ 351x Extra Practice Chapter 11 4 12. Firm 1 produces high-quality cars. Its marginal cost is $3,000. Firm 1 can also offer y years of warranty. The expected cost of the warranty for Firm 1 is $2,000 per year. Firm 2 produces low-quality cars. Its marginal cost is $2,000. Firm 2 can also offer y years of warranty. The expected cost of the warranty for Firm 2 is $3,000 per year. Consumers cannot observe the quality of the car (only the firm knows the quality of its car). Consumers are willing to pay $8,000 for high-quality cars, and $5,000 for low-quality cars. Moreover, consumers are also willing to pay an addition $1,000 for each year of warranty offered. In this market, consumers believe that only high-quality cars have y* years of warranty. Find the minimum and the maximum values of the threshold y* such that the consumers’ beliefs will be consistent with the optimal behavior of the firms. a. 5 ≥ y* ≥ 2 b. 3 ≥ y* ≥ 2 c. 3 ≥ y* ≥ 1.5 d. 2 ≥ y* ≥ 1.5 e. 5 ≥ y* ≥ 3 13. When firms participate in group health insurance for all employees, it might reduce health insurance premiums because it reduces the_______ problem a. free rider b. moral hazard c. principal-agent d. adverse selection e. winner’s curse

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