monopolist-economy-question

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Consider firm M, a monopolist for an effective herbicide. M’s fixed costs are 7. The marginal cost for producing a unit of the herbicide is MC(Q) = 2. After doing market research, M learns that the aggregate demand curve for units of herbicide is D(p) = 10 − p. 

What are the profit maximizing price pMon and quantity QMon for firm M? 

 Mark and label QMon, pMon, producer surplus (PS), consumer surplus (CS) and dead weight loss (DWL) in the figure from 

What are M’s profits? 

How big is the deadweight loss in this market? 

what would be the market price p∗ and quantity Q∗ (in the short run) if firm M would be forced to act as a price taker? In this case, would firm M make a loss? If yes, how much of a loss? 

What price ceiling should the government impose if it wants to minimize the deadweight loss under the constraint that it wants firm M at least to break even?