Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
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Chapter 15, Problem 15.2P
a)
To determine
To determine profit maximising
b
To determine
Nash
c)
To determine
Nash
d)
To determine
Nash equilibrium quantities for
e)
To determine
To show
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Suppose that firms’ marginal and average costs are constant and equal to c and that inverse market demand is given by P = a – bQ, where a, b > 0
(a) Calculate the profit-maximizing quantity-price combination and for a monopolist.
(b) Calculate the Nash equilibrium quantities for Cournot duopolists, which choose quantities and for their identical products simultaneously. Also compute market output and market price.
(c) Calculate the perfectly competitive equilibrium price and market output.
(d) Suppose now that there are n identical firms in a Cournot model (oligopoly). Compute the Nash equilibrium quantities as functions of n. Also compute market output and market price.
(e) Verify (i) that the monopoly outcome from part (a) can be reproduced in part (d) by setting n = 1;
(ii) that the duopoly outcome from part (b) can be reproduced in part (d) by setting n = 2;
(iii) that letting n approach infinity yields the same market price and output as…
A monopolist can produce at a constant average and marginal cost of ATC = MC = $5. It faces a market demand curve given by Q = 53 - P.
Suppose there are N firms in the industry, all with the same constant MC = $5. Find the Cournot equilibrium. How much will each firm produce, what will be the market price, and how much profit will each firm earn? Also show that as N becomes large, the market price approaches the price that would prevail under perfect competition. (Hint: your answers will be functions of N)(BONUS)
Gamma and Zeta are the only two widget manufacturers in the world. Each firm has a cost function given
by: C(q) = 10+20q + q^2, where q is number of widgets produced. The market demand for widgets is
represented by the inverse demand equation: P = 200 - 2Q where Q = q1 + q2 is total output. Suppose that
each firm maximizes its profits taking its rival's output as given (i.e. the firms behave as Cournot oligopolists).
a)
What will be the equilibrium quantity selected by each firm? What is the market price? What is the profit level for each firm?
Equilibrium quantity for each firm__
price__
profit__
b)
It occurs to the managers of Gamma and Zeta that they could do a lot better by colluding. If the two firms were to collude in a symmetric equilibrium, what would be the profit-maximizing choice of output for each firm? What is the industry price? What is the profit for each firm in this case?
Equilibrium quantity for each firm__
price__
profit__
c) What minimum discount factor is required…
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- Consider two firms, i = 1; 2, producing differentiated products and engaged in Cournot a. Given the market demands, what are the best-response functions of the two firms? b. Draw the best-response functions both for complements (d 0). c. Compute the Cournot equilibrium quantities and prices in this market. d. Compare the outcome between substitutes and complements goods. e. What are the profit-maximizing quantities and prices if firm i is a monopolist in this market? Compare with part c.arrow_forwardSuppose that the market demand for mountain spring water is given as follows: P = 1200 - Q Mountain spring water can be produced at no cost. Determine the level of output produced and price charged by each firm in a Cournot duopoly. A monopolist faces a demand with constant elasticity of -2.0.It has a constant marginal cost of R20 per unit and sets a price to maximise its profit. If marginal cost should increase by 25 percent, would the price charged also rise by 25 percent? Provide a brief explanation.arrow_forwardTo examine the effects of a subsidy, consider the large passenger jetliners market with two firms that sell identical products, Firm 1 and Firm 2. Without any subsidy, both firms will have the same cost functions of C(q) = 40q and MC = 40. The market demand is P = 100 – Q. NEED CALCULATION HELP PLEASE!!! Solve for the Cournot equilibrium price, quantities, and profits for each firm given the same MC= 40. Compare the deadweight loss in a monopoly, a Cournot duopoly, and a Bertrand duopoly if both firms have the same marginal cost of 40. How would this market change if Firm 2 receives a subsidy lowering the marginal cost to 25 and Firm 1's marginal cost remains at 40. Calculate new market equilibrium quantity, price, and profits for each firm. Calculate the change in welfare after the subsidy. In this case welfare is defined as the Firm 2’s profit minus the subsidy. Who gains from the subsidy? Explainarrow_forward
- Assume that the market demand and the costs of the duopolists are: P=120-0.4(QA + QB) TCA=5QA TCB= 0.2Q2B Also assume that firm B is the sophisticated leader, Determine: a. The reaction curve of A ,the reaction curve of B and the profit function of A b. Stackelberg equilibrium output level for firm A and Stackelberg equilibrium output level for firm B c. The market pricearrow_forwardAlbert and Johny are the only sellers of Motorbikes in Ireland. The inverse market demand function for motorbikes is P(Y)= 200- 2Y . Both firms have the same total cost function: T(C)= 12Y and the same marginal cost: M(C)=12. Suppose now that the two firms decide to act like a single monopolist. What will the total quantity of Motorbikes sold in the market be and what will the equilibrium price be? Represent the profit maximisation problem on a graph and indicate the price and quantity at the equilibrium. Calculate the total profit made by the two firms when they act like a monopoly. Compare it with the total profit they were making in the Stackelberg oligopoly. For the two firms to be willing to agree to act as a monopoly, how should they split the quantity to produce between them? We assume that if they do not agree to act like a monopoly, then the market structure is the Stackelberg oligopoly studied above. We further assume that no money transfer is possible between the two…arrow_forward3. In a market with demand Q = 780 - p, there are 3 identical firms, A, B and C; each with a total cost function TC(Q) = 3Q^2. Calculating the market price under each of the 5 scenarios below, rank/order the Consumer Surplus in each scenario (don’t calculate each CS; just rank them); (i)They compete in quantities with each other (Cournot-Nash equilibrium) (ii)They collude as though they are all plants of the same single multi-plant monopoly. (iii) B and C act as two plants of a single multi-plant monopoly “B+C”, which competes in quantities (Cournot competition) against A. (iv) B and C jointly form the fringe supply and A is the dominant firm in the dominant firm model (v)They act as perfectly competitive firms -as if trying to maximize total surplus and minimize DWL- that is, their joint MC serves as the “market supply” for the competitive market.arrow_forward
- Answer the following questions, which relate to measures of concentration: a. What is the meaning of a four-firm concentration ratio of 60 percent? 90 percent? What are the shortcomings of concentration ratios as measures of monopoly power?b. Suppose that the five firms in industry A have annual sales of 30, 30, 20, 10, and 10 percent of total industry sales. For the five firms in industry B, the figures are 60, 25, 5, 5, and 5 percent. Calculate the Herfindahl index for each industry and compare their likely competitiveness.arrow_forwardMarket demand for widgets is p = 160 - 2Q. Whether there is just one firm selling widgets or many firms selling widgets, the marginal cost and average cost is 100.Assume there are two firms selling widgets acting as Stackelberg duopolists, with Firm 1 moving first and Firm 2 following. Further assume that Firm 1's marginal profit function at its maximum is Mπ(q1) = 75 - q1, where q1 is the amount of widgets sold by Firm 1. What is the quantity sold for each firm?Options are:Firm 1 sells 0 Firms 2 sells 80Firm 1 sells 25 firm 2 sells 64.5Firm 1 sells 15, Firm 2 sells 30Firm 1 sells 7.5 Firm 2 sells 15From question 12 (Stackelberg duopolists), what is the price of widgets?Options are:1501158565arrow_forwardIn a market with a Duopoly, if Market Demand is P=300-Q find the Cournot reaction curves and the Cournot Quantity solutions then deduce the Price in the case where Marginal Costs curves for either of the Duopoly firms is MC1=q1+30 and MC2=q2+30. Compare your results to the case where a Monopolist that has a MC=Q+30 replaces the Duopoly. What are the Monopoly Quantity and Price? Which quantities are bigger, Cournot or Monopoly? What is the Consumer Surplus in both cases? Set-up the Oligopoly model in a game theoretical prisoner’s dilemma framework. Explain briefly the strategies and how you reach the Nash Equilibrium.arrow_forward
- The market for dark chocolate us characterized by Cournot duopolists - Honeydukes and Wonka industries. The market demand for dark chocolate is: P = 8 - 0.005Qd where P is the price per bar in dollars and Qd is dark chocolate's daily quantity demanded in bars (use qh to represent the quantity of dark chocolate sold by Honeydukes and qw to represent the quantity of dark chocolate sold by Wonka Industries). Honeydukes has a constant marginal cost of $2.50 per bar, while Wonka Industries has a constant marginal cost of $3.00 per bar. The firms move simultaneously in choosing their profit-maximizing quantity of output. a. Given the firms move simultaneously, what is the equation for Honeydukes' reaction function with qh expressed as a function of qw? b. Given the firms move simultaneously, what is the equation for Wonka's reaction function with qw expressed as a function of qh? c. What quantity of dark chocolate will each firm produce in equilibrium and what price will be established for a…arrow_forwardConstruct a numerical example based on a linear demand function and two firms with identical, constant marginal costs. a) Use your model to show that, a Cournot duopolist can "do better" by producing the monopoly output, under the assumption that its competitor reacts and adjusts its output optimally. b) How does this result compare to what the Stackelberg model predicted?arrow_forwardCompare total profits and the total output in the Cournot equilibrium to a monopolist’s profit-maximising choices (assuming the same demand, zero fixed costs and the same constant marginal costs). In Cournot equilibrium, total output is [higher , lower , stay the same] total profits are [higher, lower, stay the same]arrow_forward
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