A risk neutral manager has utility function (, ) = 50 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 = 624. If the manager supplies units of efforts then the firm profit will be 30 + , where is a random variable with expected value zero. is profit before deducting the manager's pay.

Suppose that the owner of the firm offers the manager the compensation contract = + , where 0 1 and is a constant. Derive the manager's effort supply function. Show that effort increases when increases.

Derive the optimal contract that maximizes the owner's expected profit by employing the manager's effort supply function

What is the owner's expected profit, the manager's expected utility and the effort supplied by the manager under the contract that maximises the owner's expected profit?