. A risk neutral manager has utility function (, ) = 20 ( ^2/ 2 )+ , where is the amount of leisure consumed and is labour income. The manager is endowed with = 24 of and zero units of . The manager's best alternative opportunity provides a level of utility of 0 = 192. If the manager supplies units of effort then the firm profit will be 10 + , where is a random variable with expected value zero. is profit before deducting the managers pay.

Suppose that the owner of the firm offers the manager the compensation contract = + , where 0 1 and is a constant.

Derive the managers effort supply function.

Show that effort increases when increases.

Derive the managers effort supply function.

Derive the optimal contract that maximises the owners expected profit by employing the managers effort supply function

What is the owners expected profit, the managers expected utility and the effort supplied by the manager under the contract that maximises the owners expected profit?