What happens with the levels of law enforcement and crime

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(Crime and Police), Here is a version of a model presented by a Nobel Price winner Gary Becker, to analyze crime enforcement. The game has two players. Criminal (player 1) and Police (Player 2). Criminal chooses a level of crime y 0 and Police chooses a level of law enforcement, x 0. The Police's payoff is -xc4 - y2/x, where c represents cost of law enforcement, and the second term is the negative effect of crime of society. Criminal's payoff is , where stands for the benefit of comitting crime, whereas 1/1 + xy is, roughly, the probability of evading capture. Write down the first order conditions that define the best response functions and write down the best response functions (Best response function for player 1 specifies what is his best response as a function of action chosen by player 2. and vice versa). Graph the best response functions. Find the Nash Equilibrium of this game. What happens with the levels of law enforcement and crime (in Nash Equilibrium) when the cost of law enforcement c goes up?

Reference no: EM13154914

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