Please solve these questions

A monopolist operates in a market of demand q = 10−p with a total cost of C(Q, e) = (3/2)e^2 +(5−e)Q, where e represents effort.

a. Calculate the price, effort, quantity, and welfare that results from an unregulated monopoly.

b. A regulator establishes that price must equal marginal cost. The monopolist is free to select the level of effort. Calculate price, effort, quantity, and welfare in this situation.

c. A regulator decides to force price equal to marginal cost and mandates that monopolist must choose the level of effort that minimizes costs for a given level of quantity. Calculate price, effort, quantity, and welfare in this new situation.

d. Based on your answer to the previous parts, should a regulator focus on allocative efficiency and ignore productive efficiency?

Consider a monopolist that produces the drug Daraprim. The monopolist has a demand of Q(p) and a total cost curve of cQ. The monopolist expects some consumer backlash from its pricing. Let μ(p) represent the cost of the consumer backlash, which is increasing in price so that dμ > 0.

a. Derive an expression for the price cost margin (p−MC)/p at the profit maximizing price in terms of the elasticity of demand and the cost of consumer backlash.

b. Does the monopolist set a lower or higher price when it faces a public backlash compared to the case where it does not?

Suppose that we have an industry in which the total demand is q(p) = 20 − 2p. The market is served by a dominant firm and four firms that behave in a competitive manner. The dominant firm faces a total cost function equal to C = q^2. The competitive firms have identical cost functions given by Ci = C(q) = q^2/2.

a. Find the quantity produced by the dominant firm and the quantity produced by the competitive fringe.

b. Find the consumer surplus at the market price.

c. Find the aggregate producer surplus at the market price.