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一个关于员工犯罪的题，望大家帮忙解决。
Employees in a farm can commit a crime against the firm; yield them a gain of G (which is also the cost to the firm). All employees can seek to commit the crime, but we assume that only one of them actually does so. Each employee expends effort e on committing crime and this leads to a probability of given by φ(e) where φ’(e) >0 , φ’’(e)<0. The marginal cost of this effort is e. The employer spends effort µ on monitoring/detecting crime and, as a result, the probability of detection is p(e,m), where pe<0, pm>0 and pem =pme >0. The marginal cost of monitoring is m. Each employee receive a wage of w, the firm employs a fixed amount of labor L and its revenues is R(L). If an employee is caught committing a crime he does not gain alternative employment. Finally, assume that firms and employees are risk neutral. Their expected payoff functions are as follows:
UE =[1-φ(e)]w +φ(e)[1- p(e,m)]( w +G)-e
UF=(1-φ)[R(L)- w L]+ φ{(1-p)[R(L)- w L-G]+p[R(L)- w (L-1)]}-mL
Here ‘E’ stands for ‘employee’ and ‘F’ stands for ‘firm’.
1. Explain the above payoff functions.
2. Given that employees solve maxe UE and firm solve maxm UF find the two first-order conditions.
3. Suppose that the firms does not monitor employee behavior (i.e. p(e,0)=pe(e,0). What does the employee’s first-order condition now look like? Show whether the employee puts more effort into committing crime than if the firm did monitor behavior. Explain your answer.
4. Now suppose that the firm and the employee are engaged in a simultaneous Cournot-Nash game in which each choose its crime/monitoring effort taking account of what the other’s choice will be. Describe what the term ‘Nash equilibrium’ means in the current model. Using comparative static’s analysis, find expression for de/dG and de/dw, indicate whether these can be given unambiguous signs and explain why, or why not. (You may assume that the sufficient second-order conditions for the employees’ and the firm’s problems hold.) Under what circumstances do larger gains from crime and higher wages lead to higher probabilities of crime? Does your result necessarily mean that crime official crime statistics would indicate an increase in employee crime under these circumstances?
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