Please help me with this long question. Thank you
Verizon is a monopolist and faces two types of customers, those who rarely use the phone (type ( for low use) and those who use the phone a lot (type h for heavy use). Type / customer's demand (in terms of minutes of cell phone use) is given by: qi(p) = 450 - 10p. Type h customers demand (in terms of minutes of cell phone use) is given by: qu(p) = 650 - 10p. The consumer's outside option is normalized to 0. The marginal cost of providing connection to a cell phone is 5 cents a minute (for convenience, all prices are in cents). That is, C(q) = 5q. For part (a) and (b), suppose that Verizon knows the type of each customer. (a) First, suppose that by law, Verizon must charge by the minute. That is, it must sell any number of minutes a customer wants for a uniform price per minute. To maximize profit, what price would Verizon charge per minute for each type of customer? What is the consumer surplus for a type ? and h customer respectively? What is its profit from a type I and h customer respectively? Show your work and explain briefly. Hint: in general, consumer surplus from any given quantity g is the total area under the demand curve from q = 0 to q, net of the total price paid for the quantity. (b) Suppose instead, Verizon is no longer constrained to charge by the minute. That is, it can offer different types of customer different price and quantity packages. 3 Specifically, it offers a contract (p(h), q(h)) for type h and a contract (p(), q()) for type / since it knows the type. A contract is a package of (p(q), q)). That is, each package describes the total price p(q) a customer must pay for a given number of minutes q. For example, 30 dollars for 70 minutes of cell phone time. Find the optimal price and quantity packages for Verizon. What is its profit from a type / and h customer respectively? Is Verizon better or worse off than in part a)? What is the socially efficient quantity for each type of customer? Show your work and explain intuitively and briefly. From now on, type is private information: each customer knows his/her own type, but Verizon does not. Verizon only knows that a customer is type / and h with equal probabilities. (c) Suppose Verizon offers two packages (p, q:) and (Ph; 9 ) to screen the customers. A consumer chooses the package that gives her a higher consumer surplus. Note that pr is the total price paid for qr minutes; and pr is similar. Write down the conditions that must be satisfied for these packages to be successful screening contracts. Does your solution from part b) satisfy these conditions? Why or why not? Show your work and explain briefly. (d) Which of the conditions you found in part c) must be satisfied with equality? Show your work and explain these conditions briefly and intuitively. Set up the firm's maximization problem. Derive the first order conditions and explain these FOC briefly and intuitively. Note: you do not need to solve the problem. (e) Find the optimal screening contracts. Are both types of customers served by Verizon? Show your work and explain the difference between the optimal screening contracts you find and your answer in part b)
