Hi, I've solved #4 according to the given question, but I'm not sure how rebate on consumers would effect the monopoly structure. May I have explanations on #5 and #6? Thank you!

4. The government is concerned about high prices and underproduction in this industry and wishes to restore the competitive output level, but it is impractical to break up the monopoly. Instead they subsidize the industry at a rate of $5 per unit sold, payable to the rm on proof of sale. The rm's revenues now include those from consumers and the government's subsidy. What is marginal revenue, in terms of s and q? What is the new prot-maximizing quantity, in terms of 5? What price is charged to consumers, in terms of 3? What value of 3 results in zero deadweight loss? How much does the government then pay out in subsidies? (In real life, such a subsidy might take the form of a "tax break", which sounds better to voters.) 5. Suppose the subsidy of $s per unit were instead payable as a rebate to consumers on proof of purchase. Answer again the questions in the previous problem. 6. Another strategy the government might use to restore efficiency is a price ceiling. What price ceiling would make the market efficient? Sup- pose that, by court ruling, the government must compensate the mo- nopolist for any loss in profits compared to profits without the ceiling (as calculated in #3). How much will the compensation be? How does this compare to the amount paid in subsidies, in problem 4?The industry we studied on the last assignment has become a monopoly. Sup- ply and demand are unchanged, with inverse functions M C = S'1(q) = q+3 and D'1(q) = 11 q/3. The rm is an ordinary monopolist, i.e. they charge all consumers the same price. We have left their xed costs unspecied, and for simplicity, we will ignore them throughout the assignment