2. Consider a game between a government and a crime syndicate where the gov ernment chooses...
2. Consider a game between a government and a crime syndicate where the gov ernment chooses the level of law enforcement activity, e, and the criminal syn- dicate chooses the level of criminal activity, c. Given c level of crime and e level of law enforcement, the probability that the syndicate will not be caught is and the value to the syndicate from the crimes, if it is not caught, is el Therefore, the payoff function of the syndicate is given by Uslc,e) 14 ce The government dislikes crime. The disutility to the government from the crim inal activity is given by -. However, law enforcement is costly to the govern ment and is given by ek, where the constant k> is the marginal cost of the enforcement activity. To summarize, the government's payoff function is Uale,e)=-S et (a) Find the syndicate's best response function. (b) Find the government's best response function. (c) Find the Nash equilibrium level of crime and law enforcement. (d) What happens to the equilibrium level of law enforcement as the cost of enforcement, k, increases? What happens to the equilibrium level of crim- inal activity?