代做Homework 2 Spring 2025代做Prolog

1. Torts and Harm
Wiley E. Coyote’s utility function is , where w is Wiley’s wealth in $dollars and h is Wiley’s units of health.  To start, Wiley has $25 and 36 units of health, so Wiley’s utility is 30.
Suppose the Roadrunner drops an Acme Anvil on Wiley, decreasing Wiley’s health from 36 to 9.

a. What is Wiley’s level of utility post-anvil?

b. If health units can be bought for $2, how much should the damages be to restore Wiley to his pre-Anvil utility?

c. Now suppose that the Anvil has done irreparable harm to Wiley, and his health is stuck at 9 units.  What should the damages be to restore Wiley to his pre-anvil utility?

2. Damages and Efficiency
Itchy hits Scratchy with a hammer and does $1,000 worth of damages.

a. What are the total payoffs under the different damage amounts: (a) Itchy owes $0; (b) Itchy owes $500; and (c) Itchy owes $1,000?

b. How do your results above help answer the following question: what is more important for efficiency: what happens after an accident or the decisions leading up to an accident?

3. Victim and Injurer Precaution
Runners who run in the dark can reduce the risk of getting hit by a car by wearing reflective vests. Drivers can reduce the risk of hitting a runner by installing HID (High Intensity Discharge) headlights, which are brighter than normal headlights. Imagine there’s only one driver and one runner, and the likelihood of an accident is as follows:

		Injurer Precaution
		Normal Headlights	HID Headlights
Victim Precaution	No Vest	8%	3%
	Vest	5%	1%

Suppose the damage done by an accident is $2,000 with perfect compensation.  Vests cost $30 and HID bulbs cost $60.  There is no insurance for either runners or drivers.

a. Calculate the cost of precaution and expected injury cost for each combination above.  Which combination generates the socially optimal level of precaution by both sides?

b. If runners wear vests, is it efficient for drivers to buy HID headlights?  What about if runners do not wear vests?  If drivers buy HID headlights, is it efficient for runners to wear vests?  What about if drivers do not buy HID headlights?

c. What levels of precaution would both sides take under the following rules: (i) no liability; (ii) strict liability; and (iii) simple negligence.  What about levels of driving and running?

4. Damages and Social Costs.
Suppose that the probability of an accident as a function of the amount of precaution, x, is p(x) = 1/x.  If an accident occurs, its cost will be $1000.  Each unit of precaution costs $10.  What is the optimal amount of x to minimize the total social cost?

5. Consider the brewery industry, which is composed of five major companies: Incendiary, Wise Man, Fiddlin’ Fish, Foothills, and Lesser Known.

a. Suppose the market shares of these companies are:

Incendiary: 30%

Wise Man: 25%

Fiddlin’ Fish: 20%

Foothills: 15%

Lesser Known: 10%

Calculate the Herfindahl-Hirschman Index (HHI) for this industry using these market shares.  Would the government consider this market to be concentrated?

b. Instead, suppose the market shares of these companies are:

Incendiary: 75%

Wise Man: 10%

Fiddlin’ Fish: 7%

Foothills: 5%

Lesser Known: 3%

Calculate the Herfindahl-Hirschman Index (HHI) for this industry using these market shares.  Would the government consider this market to be concentrated?

6. Explain why counterfeiting money is a crime. Who is the victim? Is there a private victim as well as public victims? (from C&U)

7. Relatedly, insider trading (trading on the stock exchange to one's own advantage through having access to confidential information) is also a crime.  Explain why insider trading is a crime. Who is the victim? Is there a private victim as well as public victims?

8. Let x denote the seriousness of a crime, where x = 0 indicates no crime, and as x increases, the seriousness of the crime increases.  Let y denote the criminal’s payoff, where y = y(x) and y(x) increases as x increases.
Let f denote the severity of the punishment, where f = 0 indicates no punishment. More severe punishments attach to more serious crimes, so f = f(x), and f(x) increases in x.
Efforts to detect, prosecute, and convict criminals normally increase with the crime’s seriousness. Thus, the probability p of a sanction is a function of the crime’s seriousness, p = p(x), and p(x) increases in x.  Thus, the total expected punishment for a crime is p(x)f(x).

a. Combine this information together in a graph to illustrate how y(x) and p(x)f(x) evolve as x increases.  How would you find the optimal level of crime (x*)?  Describe either in words or using calculus.

b. On your graph, show what is likely to happen to crime if (i) the payoff to the crime decreases or (ii) the probability of being captured decreases.

c. (tricky) Suppose that the payoff to the crime increases by a constant, k, so y = y(x) + k.  What happens to x*?  What happens to the overall net benefit of crime?

9. I Fought the War on Drugs and Lost

Suppose the inverse demand curve for drugs is p(q) = 200 - 4q and the inverse supply curve is p(q) = q.

a. Draw the supply and demand curves on the graph below.  Label the current price and quantity, label and calculate the current producer and consumer surplus, and calculate and label the total revenue accumulating to suppliers in this market.

Suppose the Forsyth County Bureau of Investigation (FBI) wants to decrease the amount of drug-related crime.  Since every trade in drug market is illegal, the drug-related crime in this market is equal to the total revenue from this market (a bit of a simplifying assumption, but probably not too bad).

b. First, suppose the FBI considers a tough-on-crime policy where the FBI arrests more drug dealers and increases jail sentences.  This is like an increase in the cost of doing business, so it shifts the supply curve in to p(q) = 50 + q.
Draw the (new) supply and demand curves on the graph below.  Label the current price and quantity, label and calculate the new producer and consumer surplus, and calculate and label the total revenue accumulating to suppliers in this market.

c. Instead, suppose the FBI considers a drug-treatment policy where the FBI funds drug treatment centers.  This is like a shift in the demand curve for drugs curve in to p(q) = 150 - 4q.
Draw the (new) supply and demand curves on the graph below.  Label the current price and quantity, label and calculate the current producer and consumer surplus in this market, and calculate and label the total revenue accumulating to suppliers in this market.

d. Given your answers to (i) and (ii) above, which policy is likely to reduce drug crime more?  Did this surprise you?  What is the intuition behind this result?  What if we measured the incentives to participate in drug crime by the total surplus generated by the market?  Which policy would be more effective then?

10. Fighting Crime (adapted from Dan Quint at UW Madison)
Suppose a particular crime is always inefficient: it harms the rest of society $10,000 more than it benefits the criminal. Every time an offender is caught, he or she is tried, convicted, and imprisoned; the total (social) cost of trials and punishment is $100,000 per criminal caught. A city is considering hiring additional police officers dedicated to detecting this particular crime. This change would increase the fraction of offenders who get caught from 15% to 20%.
The aim of criminal law is to minimize the sum of three things: (1) the social cost of the crimes that are committed, (2) the cost of detection, and (3) the cost of trying and punishing the offenders who get caught.

a. Suppose this increase in detection would result in a decrease in the number of crimes committed from 1,000 a year to 700 a year.

i. Calculate the effect that hiring the new police officers would have on the social cost of crimes committed.

ii. Calculate the effect it would have on the cost of trying and punishing offenders.

iii. From an efficiency point of view, what is the most that the city should be willing to pay for the new police officers?

b. Now suppose instead that the increase in detection would decrease the number of crimes committed from 1,000 a year to 900 a year.

iv. Calculate the effect that hiring the new policemen would have on the social cost of crimes committed.

v. Calculate the effect it would have on the cost of trying and punishing offenders.

vi. From an efficiency point of view, is there any positive amount that the city should be willing to pay for the new police officers?

c. Continuing on with the decrease in (b), suppose that each crime harms the rest of society $50,000 more than it benefits the criminal.  Recalculate your numbers from (b).