Homework ACCT $780-001$

Problem $1$

Carl is negotiating with Sharon as a possible manager. He wants Sharon to

work hard. Based on his experience $80\%$ of the time hard work generates net

income $($before any manager compensation$)$ of $$2,500,$ while $20\%$ of the time

it generates $$850.$ Carl's recent experience, when he has not worked hard, is

that the $$2,500$ net income is generated only $20\%$ of the time; otherwise, net

income is $$850.$

Sharon is both risk and effort$-$adverse with utility equal to the square root of

the amount of money received. Her disutility of effort is $8,$ if she works hard

and $2$ if she shirks. Her reservation utility is equal to $10.$

Carl decides that Sharon is the right person for the job and offers her an

annual compensation of $$121$ plus $10\%$ of the net income $($before any

manager$$s compensation$).$ Sharon accepts the contract.

Required

$($Take calculations to two decimal places$).$

a$.$ Show calculations to demonstrate that Sharon accepts the position. Will

she work hard or shirk?

b$.$ After a few years, Carl notices that the net income is always $$850.$ He

decides to offer Sharon a salary of $$30$ plus a profit share of $9\%$ before

any manager$$s compensation. Will Sharon accept the contract?

Assuming Sharon accepts the contract, will she work hard or shirk?

c$.$ Carl is risk neutral, with utility equal to the amount of profit received

after any manager$$s compensation. Is Carl expected utility higher $($or

lower$)$ under the contract offered in b compared to the original

contract? Show calculations.