PROBLEM (6) A monopolist faces a market demand Q = 180 – 2p and has two plants 1 and 2, producing identical products with total cost functions TC:(q) = q² and TC2(q) = 1/3 q² (hence MC1(q) = 2q and MC2(q) = 2q/3), respectively. (a) Derive the monopolistť's multiplant marginal cost function. (b) What is the optimal quantity produced at each of the plants, and what is the optimal price? (c) Calculate the net profits for the monopoly and the DWL. %3D %3D %3D

PROBLEM (6) A monopolist faces a market demand Q = 180 – 2p and has two plants 1 and 2, producing identical products with total cost functions TC:(q) = q² and TC2(q) = 1/3 q² (hence MC1(q) = 2q and MC2(q) = 2q/3), respectively. (a) Derive the monopolistť's multiplant marginal cost function. (b) What is the optimal quantity produced at each of the plants, and what is the optimal price? (c) Calculate the net profits for the monopoly and the DWL. %3D %3D %3D

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter14: Monopoly

Section: Chapter Questions

Problem 14.9P

See similar textbooks

Similar questions

Consider a monopolist with the cost function C(q) = 6q, facing the market demand function D(p) = 20 − 2p. (a) Find the monopoly quantity and price, the monopolist’s profit and the con- sumer surplus. (b) Now suppose that the government gives to the monopolist a subsidy of $2 per unit sold. Find the monopoly quantity and price, the monopolist’s profit, the consumer surplus, and the cost of the subsidy.
Suppose the inverse demand function is linear: p(q) = a - Bq. The monopolist's cost function is c(q) = 6q2 . Assume the monopolist must charge a uniform price. (a) Find the optimum monopoly price and quantity. Also calculate the deadweight loss. (b) Suppose the government can levy a lump-sum tax T (i.e., a fixed amount independent of production) and an excise tax t per unit of production on the monopolist. These taxes can be negative, in which case they are subsidies. The proceeds of these taxes can be transferred to consumers. The monopolist is always free to quit the market, in which case she does not have to pay any taxes. The government wants to maximize the consumer welfare. Find the optimum values of t and T.
A single firm produces widgets, with a cost function and inverse demand function as follows, C(q) = 150 + 2q P(Qd) = 10 − 0.08Qd (a) Calculate the monopolist’s profit-maximizing price, quantity, and profit if he can charge a single price in the market (single price monopolist). (b) Suppose the firm can sell units after your answer to (a) at a lower price (2nd-degree price discrimination, timed-release). What quantity will be sold for what price in this second-tier market? Calculate the monopolist’s profit. (c) Suppose each new tier of pricing the monopolist introduces increases fixed costs by $2 (quantities can be irrational). What is the profit-maximizing quantity, number of prices, monopolist’s profit, and deadweight loss? (d) Suppose the firm can perfectly price discriminate (1st-degree) with a 40% increase in marginal cost; calculate the profit-maximizing quantity, monopolist’s profit, and deadweight loss? (e) Between (c) and (d), which is socially preferred? Which would the…
(a) A monopolist has discovered that the inverse demand function of a person with income Y for the monopolist’s product is P = 0.002Y-Q where P is the price, Y the income, and Q is the output. The monopolist can observe the incomes of its consumers and hence vary its price accordingly. The monopolist has a total cost function C(Q) = 100Q. Calculate the profit maximising price as a function of the consumer’s income Y carefully explaining all the steps in the derivation of the formula. (b) A monopolist has a constant marginal cost of £2 per unit and no fixed costs. He faces two separate markets in the United States and in the UK. The goods sold in one market are never resold in the other. He sets one price P1 for the US market and another price P2 for the UK market (both measured in £). The demand in the United States is given by Q1=7,000-700P1 and the demand in the UK is given by Q2=1,200-200P1. Calculate the profit maximising output produced and price charged in each country by the…
5) A monopolist sells its product to two countries, labeled 1 and 2. The inverse demand curves in these countries are p1 = 100 – Q, and p2 = 120 – 3Q2. respectively. The monopolist's cost function is C(Q) =02, where Q = Q1 + Q2- a) Find the aggregate demand function and the associated inverse demand function for p < 100. Write down the monopolist's profit function and proceed to find its profit-maximizing output and profit. Calculate the equilibrium price the monopolist would charge in each country. Also calculate the output it would supply to each country. b) c)
A monopolist’s inverse demand function is estimated as P = 450 − 3Q. The company produces outputat two facilities; the marginal cost of producing at Facility 1 is M C1(Q1) = 2Q1, and the marginal costof producing at Facility 2 is M C2(Q2) = 6Q2.(a) Provide the equation for the monopolist’s marginal revenue function.(b) Determine the profit maximizing level of output for each facility.(c) Determine the profit maximizing price.
Consider the case of a monopolist who charges the same price to all consumers. The demand for the good is given by Q=813-7p, where Q denotes the quantity demanded at price p. The firm's total cost of producing Q units is given by the function C(Q) = 7 Q What is the profit maximizing price for this monopolist? (As usual, you must enter a number below, not a ratio, not an expression with symbols..., just a number.)
Consider a market with 190 consumers. Of these, 90 of them have individual (inverse) demands given by: PM(Q)=10−Q, while each of the other 100 has an individual (inverse) demand of PS(Q)=10−10Q. The cost function of the monopolist serving this market is C(Q) = 6Q - Q^2/400 . (a) Find the aggregate demand. Analyze the cost function and find what kind of returns to scale it exhibits. Compute the efficient total output (ignoring break-even constraints).(b) Compute the optimal linear price (and quantity) for this monopolist, and the deadweight loss.
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: D(p) = {100/p if ps 20. 0, if p> 20%3; (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?
A monopolist's inverse demand function is P=150-3Q. the company produces output at two facilities; the marginal cost of producing at facility 1 is MC1(Q1)=6Q1, and the marginal cost of producing at facility 2 is MC2(Q2)=2Q2 A). Provide the equation for the monopolist's marginal revenue function. MR(Q)= ___ -___Q1-____Q2 B). Determine the profit-maximizing level of output for each facility. Output for facility 1: Output for facility 2: C). Determine the profit-maximizing price.
A monopolist with cost function C(q) = ;q? faces 2 consumers with the following demands: p(q1) = 10 - q1 and p(q2) = 20 – 2q2. Determine prices, quantities to be produced and sold and the monopolist's profits in the following cases: (a) The good can be resold at zero cost among consumers and it is technologically impossible to sell it in bundles of more than 1 unit. b) There is resale at zero cost and bundling in packages of arbitrary size. c) Resale is possible at a cost of "t" per unit. d) The good is a personal and non-transferable service. e) Repeat the above analysis, but this time assuming that costs are C(q) = q with q < 8.
A monopolist faces a market demand curve given by: Q= 70−p. a) If the monopolist can produce at constant average and marginal costs of: AC = MC = 6. what output level will the monopolist choose to maximize profits? What is the price at this output level? What are the monopolist’s profits? b)Assume instead that the monopolist has a cost structure where total costs are described by: C(Q) = 0.25Q^2 - 5Q + 300.With the monopolist facing the same market demand and marginal revenue, what price- quantity combination will be chosen now? What will profits be? c)Assume instead that the monopolist has a cost structure where total costs are described by: C(Q) = 0.0133Q^3 -5Q + 250.With the monopolist facing the same market demand and marginal revenue, what price-quantity combination will be chosen now? What will profits be? d) Graph the market demand curve, the MR curve, and the three marginal cost curves from (a), (b), and (c).