A store manager must hire a clerk to work in her store. The sales of the store are uncertain and also a function of how hard the clerk works. If the clerk works hard (high effort) then there is a 75% chance that sales will be $500 per day and a 25% chance that they will be $100 per day. If the clerk does not work hard (low effort) then there is only a 25% chance that sales will be $500 and a 75% chance that they will be $100. The store manager is risk neutral and her utility is the expected profits of the store i.e.U^Manager = Expected (Sales – Wages). The clerk is risk averse. In addition, the clerk does not like to work hard so exerting high effort lowers her utility. Her utility function is given by U^clerk(w,e)=w^0.5-e where e is either 0 (low effort) or 4 (high effort). Finally, assume that the clerk could work somewhere else where her total utility would be 10. Thus, she will only work in this store if the total utility of working here is at least 10. Below, assume that if the clerk is indifferent between working here and somewhere else then she will work here and that if she is indifferent between high effort and low then she will choose high. 1) Given that the store manager would like to offer the lowest wages that elicit high effort, use Incentive Compatibility (IC) and Participation Condition (PC) to find the values of w_500 and w_100. 2) Show that if the store manager offers the wages these wages then her expected profits are lower than $104 but higher than $100. Note: this is an example of using sales commissions to ameliorate a moral hazard problem.
A store manager must hire a clerk to work in her store. The sales of the store are uncertain and also a function of how hard the clerk works. If the clerk works hard (high effort) then there is a 75% chance that sales will be $500 per day and a 25% chance that they will be $100 per day. If the clerk does not work hard (low effort) then there is only a 25% chance that sales will be $500 and a 75% chance that they will be $100. The store manager is risk neutral and her utility is the expected profits of the store i.e.U^Manager = Expected (Sales – Wages). The clerk is risk averse. In addition, the clerk does not like to work hard so exerting high effort lowers her utility. Her utility function is given by U^clerk(w,e)=w^0.5-e where e is either 0 (low effort) or 4 (high effort). Finally, assume that the clerk could work somewhere else where her total utility would be 10. Thus, she will only work in this store if the total utility of working here is at least 10. Below, assume that if the clerk is indifferent between working here and somewhere else then she will work here and that if she is indifferent between high effort and low then she will choose high.
1) Given that the store manager would like to offer the lowest wages that elicit high effort, use Incentive Compatibility (IC) and Participation Condition (PC) to find the values of w_500 and w_100.
2) Show that if the store manager offers the wages these wages then her expected profits are lower than $104 but higher than $100. Note: this is an example of using sales commissions to ameliorate a moral hazard problem.
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