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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 question 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 x_1.

1.Continue to assume that fixed costs are zero. Calculate Maggie's utility when the industry 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? Explain 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? Explain your answer. If commonly 1 is provided by a monopoly, what would be Maggie's resulting utility?

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