Clare manages a piano store. Her utility function is given by Utility = w − 100 where w is the total of all moentary payments to her and 100 represents the cost to her of the effort of running the sotre. Clare’s next best alternative to managize the store provides her with zero utility. The store’s gross profit depends on random factors. There is a 50% chance it earns $1,000 (where by earnings, I mean gross profits, not including payments to the manager) and a 50% chance it earns only $400.
a. If shareholders offered to share half of the store’s gross profit, what would Clare’s expected utility be? Would she accept such a contract?
b. What would be the lowest share she would accept to manage the firm?
c. Suppose that Clare has the added option of managing the store without exerting any effort. If she does not exert effort, the cost to her of running the store is zero so her utility is just the wage w; the shop’s return would be $400 for certain. If shareholders offered to share half of the store’s gross profit, what effort would Clare choose?
a. Expected utility from exerting effort = 250 (EU = 0.5*(1000/2-100) + 0.5*(400/2-100) b. Now we need to solve:
0.5*(1000*share-100) + 0.5*(400*share-100) > 0
share > 1/7