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6. If D(p) = 100/p and c(y) = y2, what is the optimal level of output of the monopolist?
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- Is a monopolist allocatively efficient? Why or why not?The monopolist faces the demand curve D(p) = 100 – 2p. Its cost function is c(y) = 2y. What is your optimal level of production and prices? Solve mathematically and graphA monopolist faces the demand curve Q(P ) = 50 − P 2 . The firm can produce output with marginal costs MC(Q) = Q and no fixed costs. Hint for the following questions: if revenue is of the form R(Q) = (a − bQ)Q, then the derivative of revenue is a − 2bQ. (a) What is the profit maximizing price for the monopolist in this market? (b) What is the deadweight loss from monopoly in this market, compared to the efficient output that sets price equal to marginal cost? *Please fully explain out any math
- 3. A monopolist faces a demand curve of P = 120 – 2q and has a production function given by f (L, K) = L'/4K¼. Input prices are w = 1 and r = 4. (a) Calculate the monopolist's (long-run) marginal cost as a function of the quantity it produces. (b) Draw a diagram illustrating the monopolist's problem. Identify each of the following on the diagram and calculate its numeric value: (i) monopolist's profit-maximizing quantity, (ii) price charged, (iii) monopolist's profit, (iv) consumer surplus, (v) producer surplus, and (vi) deadweight loss. Two notes: (1) the area of a triangle is base * height, (2) if you are getting really messy answers here, you may have made a mistake in part (a). (c) The government is concerned about the monopoly and decides to impose a price ceiling. Illustrate the efficient price ceiling on your diagram. i. Illustrate and calculate the price ceiling that will result in an efficient outcome. ii. Compute consumer and producer surplus at the efficient outcome. iii.…Suppose you are a monopolist in the market for a specific Q video game. Your demand curve is given by P = 80- - and 2 your marginal cost curve is MC = Q. Your fixed cost is $400. i) Derive the marginal revenue curve. ii) Calculate the equilibrium price and quantity. iii) What is the profit?1. A monopolist with cost function c(Q) = faces an inverse demand function given by P(Q) = (a) Find the elasticity of demand with respect to price. (b) Assuming that the monopolist uses MR = MC pricing rule, find his profit maximizing price, p", and output level, q™. (c) Find the marginal cost at q" and calculate the Lerner index. (d) Does the monopolist's market power depend on his cost curve? In particu- lar, does it depend on a? Is your answer surprising?
- A monopolist's demand function is given by D(p) = 90 – 2p. This - monopolist is facing a cost function, C(y) = (1/2)y² + 600. (a) Is this a natural monopoly? Explain. (b) How can government regulate this monopolist to produce the efficient amount of products?22A monopolist faces an invepse linear demand function of p(q) = 20 -q and cost function of C(q) = 10 + q². a. How much maximum profit does the monopolist make? b. If the monopolist were to act like a price taker, what would happen to his or her output decision? :
- 14.22. A monopolist has a cost function of c(y) = y so that its marginal costs are constant at $1 per unit. It faces the following demand curve: 0, D(p) = { 100/p if p 20; (a) What is the profit-maximizing choice of output? (b) If the government could set a price ceiling on this monopolist in order to force it to act as a competitor, what price should they set? (c) What output would the monopolist produce if forced to behave as a competitor?could you solve d,e,f Thank youQ)(a) What is the monopolist’s marginal revenue at a production level? (b) What is the monopolist’s profit-maximizing output level? (c) What is the profit that the monopolist can earn in equilibrium?
