3. Water Works is a single-price monopolist in a Heaven, MI (ok, I don't know if there is a Heaven MI, but there is a Hell, MI for sure!). They own and operate the water productions facilities for all businesses and residents in Heaven and the surrounding county. The inverse demand for water is P=20Q, where P is the price of 1 gallon of water and Q is the quantity of gallon. Water Works faces the average total cost shown in the graph below (ATC=10+20/Q) and the marginal cost of production is constant at MC=$10. a. In words, what is the profit maximizing condition for Water Works? b. Write and graph an equation for the marginal revenue of Water Works: MR= c. If this monopolist is a single price monopolist, graphically show the profit-maximizing level of output (Q), price (P), profit (), and inefficiency (dead weight loss). (Note: ATC=10+20/Q ). Show your work. Q=P==Inefficiency= d. In this case, what is the most likely reason this firm exists as a monopolist? e. Suppose that the town residents argue that the price is too high and the quantity of water is too low. If the mayor regulates Water Work's so that P=MC. Recall that P comes from the demand curve, so you have an equation for both P and MC. Calculate short run output, price, profit, and inefficiency. Show your work. Q=P==Inefficiency= Is this sustainable in the short run? Long run? f. Water Work' complains to the mayor that P=MC is too low. They say they will leave the market in the long run. The mayor decides to compromise and sets a new price, P= ATC. The precise \#s for P and Q are messy, but what is Q(approximately)=P(approximately)== How does the inefficiency compare to MC pricing