A model of crime and policy (Taken from Watson). The game has two players: a criminal (C) and the government (G). The government selects a level of law enforcement x 22 0, and the criminal selects a level of crime y 2 0. These choices are made simultaneously. 3,2 2 The government's payoff is given by uc = xc4 :with the interpretation that - y? is the negative effect of crime on society (moderated by law enforcement) and c\" is the cost of law enforcement, per unit of enforcement. The number r: is a positive constant. The criminal's payoff is given by ac = 153? with the interpretation that J; is the value of criminal activity when the criminal is not caught, whereas; is the probability that 1+xy the criminal evades capture. a. Compute the Nash equilibrium of this game. b. How does the equilibrium values of (y, 7:) change with parameter c? Show how the total effect of c on x is moderated by the change in y