1. Suppose that Anthony has monopoly power over babysitting in his neighborhood. Parents have no other choice if they want to hire a babysitter. Anthony estimates that each hour of babysitting comes with an opportunity cost of $15 per hour (e.g., he could be studying instead, and the value of each hour is $15). There are no other tangible costs associated with providing an hour of babysitting services. By varying the rate he charges over time, Anthony learns a lot about the demand for babysitting in the neighborhood. When he only wants to babysit for one or two hours, he decides to charge a very high price. A few desperate parents still hire him! When he seeks more hours of babysitting, however, he has to offer a lower rate that is acceptable for a larger number of parents. In particular, if he charges $35 an hour or higher, no one is willing to pay for babysitting. At a price of $34, his favorite customer is willing to pay for 2 hours of babysitting. In fact, every time he lowers the price by $1 after that, he gets a request for 2 more hours of babysitting.

Finally, he notices that revenue changes at a different rate depending on how much he babysits. He estimates that marginal revenue (MR) can be expressed as a function of hours of babysitting (Q): MR = 35 4Q

a)(2 points) In order to maximize profits, what price should Anthony charge for an hour of babysitting?

(b)(2 points) In order to maximize profits, what quantity of hours of babysitting does Anthony provide?

(c)(2 points) What are Anthony's profits?

(d)(2 points) Suppose a neighborhood association decides to subsidize babysitting. They offer Anthony $4 for every hour of babysitting he provides. How many hours of babysitting does Anthony provided now?

(e)(2 points) Who benefits from the subsidy: Anthony, the parents, or both? Provide your answer in one or two sentences, but also justify your reasoning with either math or graphs.