Utility maximization problem.

Maggie's utility function is !! and her income is $5000. Then her MRS at generic bundle (x1,x2) is 50-0.25x1. Commodity 2 is a composite good, and hence its price is unity. Commodity 1 is the good that is a refered to in problem 1, for which X is the total market demand. We let P denote the price of commodity 1. Consumer welfare calculation, pretend that maggie is the only consumer in the market. Therefore, the market demand function for comodity 1 is X = 200 - 4pP, where X represents x1.

1.Continue to assume that fixed costs are zero. Compute Maggie's utility when the company is competitive, and when the market is served by a monopoly (or a cartel).

2.Now we assume (realistically) that fixed costs is $800. Would commodity 1 be provided at all by a competitive industry? describe your answer. If commodity 1is provided by a competitive industry what would be maggie's resulting utility?

3.Would commodity 1 be provided at all by a monopoly? describe your answer. If commonly 1 is provided by a monopoly, what would be Maggie's resulting utility?