Gene manages a Cinnabon store owned by Gus. Genes utility function is given by: U=w-1,000e^2

where w is his wage and e represents his effort of running the store. The stores revenue depends on his effort and on random factors. There is a probability p=0.5+e of making a 1000 daily profit an a probability 1-p=0.5-e of making a zero profit.

1. If Gus pays Gene a fixed daily wage w=500, how much effort will Gene put in?

2. If Gus offers Gene 50% of profits, how much effort will gene put in? Show work.