This question requires the use of calculus. Consider the model of the monopoly telecommunication service provider described in Section 5.2, but suppose that consumer types are indexed by x on the interval [0, 2] (instead of [0, 1]). In order to simplify the calculation, suppose that the density of consumers is η = 1, meaning that there is only one consumer per type (instead of η consumers per type). Assume that the utility function of eachconsumer x, x ∈ [0, 2] is given by Ux =  (1 − x)qe − p if she subscribes 0 if she does not subscribe. Answer the following questions.

(a) Formulate the inverse demand function facing the monopoly telecommunication service provider.

(b) Formulate monopoly’s profit maximization problem. Calculate the first- and second-order condition for profit maximization.

(c) Solve for the monopoly’s price, size of the served market and profit level.