03 Jun Question Problem 1: A Model of Crime and Police Here is a game that illustrates how the government
Question
Problem 1: A Model of Crime and Police
Here is a game that illustrates how the government balances the social cost of crime with law-enforcement costs and how criminals balance the value of illegal activity with the probability of arrest. The game has two players: a criminal (C) and the government (G). The government selects a level of law enforcement, which is a number x ? 0. The criminal selects a level of crime y ? 0. These choice are made simultaneously and independently. The government’s payoff is given by uG= – xc4 – y2/x with the interpretation that – y2/x is the negative effect of crime on society (moderated by law enforcement) and c4 is the cost of law enforcement, per unit of enforcement. The number c is a positive constant. The criminal’s payoff is given by uC= y0.5/(1+xy), with the interpretation that y0.5 is the value of criminal activity when the criminal is not caught, whereas 1/(1+xy) is the probability that the criminal evades capture.
1. Write the first order conditions that define the players’ best response functions and solve them to find the best response functions.
2. Compute the Nash Equilibrium of this game.
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