Consider a residual claimant entrepreneur that has an expected utility function of

where Y is residual claimant entrepreneur's incomeand is a term that measures residual claimant's lowering utility due to i) effort ii) rising future risks due to higher incomes. and are positive constant parameters.

a)At which level of Y, the entrepreneur's utility will be maximized? What will be the maximum utility that the residual claimant gets?

b)Under which conditions, the residual claimant is risk-averse? Under which conditions the residual claimant is risk-seeker?

c)Now consider the utility of a partner entrepreneur that shares (1-s) of her income with the other partner. The utility of the partner entrepreneur is

b \

where and Y is the total income earned.

Find the level of Y that would maximize the partner entrepreneur's utility? Will the partner entrepreneur earn higher or lower income compared to the residual claimant? Explain the intuition behind your result.