Consider an industry in which all firms have constant marginal costs of 50, MC = 50,...

Consider an industry in which all firms have constant marginal costs of 50,
MC = 50, and market demand is Qd = 385 - 0.5P
(a) If there are two firms operating as Cournot duopolists, find the equilibrium price
and total quantity
(b) If there are two firms operating as Stackelberg duopolists, find the equilibrium price,
how much the leader firm produces and how much the follower firm produced?

Solutions

Expert Solution

b. Assume A is sophisticated firm, B is follower firm.

A's profit function=

720Q1-2Q12-2 Q1Q2

Substitute B’s reaction function in in A’s profit function

Profit funtion= 720 Q1-2Q12-2 Q(180-.5 Q1)

=720 Q1- Q12-360 Q1

=360 Q1- Q12

Maximise

First derivative of profit function

360-2 Q1

Q1=180

Q2= 180-.5(180)

=90

P=720-2(180+90)

=180

Rahul Sunny answered 1 year ago

Next > < Previous

Related Solutions

The gadget industry has four firms. All the firms have constant marginal cost, MC = 9...

The gadget industry has four firms. All the firms have constant marginal cost, MC = 9 and their fixed cost is zero. The market demand for gadgets is G = 400 − 40P, where G is the quantity of gadgets and P is the price of the gadgets. a. If P = 8.5, how much would a firm would produce? b. In a short-run equilibrium, it is possible to have an equilibrium price such that P > 9? Why or...

Consider the long run in a competitive industry in which all firms have the same marginal...

Consider the long run in a competitive industry in which all firms have the same marginal cost function: ??(?)=2?, where ? stands for the amount of output produced. Part 1: Suppose the market price for the good equals $15 per unit. If there are currently 38 firms in the industry, they will supply a total of __________ units of output. Part 2: Suppose the price was actually one dollar higher (so $16 instead of $15). The total amount of output produced...

The Toy business has 4 firms. All firms have an identical marginal cost of MC =...

The Toy business has 4 firms. All firms have an identical marginal cost of MC = 9 and a fixed cost of 0. The market demand for Toys is T=200-20P were T is quantity and P is price of Toys. 1. If P=8.5 how much could a firm produce 2. In a short run equili. could the equili. price be P>9? 3. In a SR equili. all firms produce the same amount of toys. What is the equili price, total...

There are two firms in an industry with demand P=130-Q. Both firms have a constant marginal...

There are two firms in an industry with demand P=130-Q. Both firms have a constant marginal cost of production equal to $40. a) If there are no fixed costs what will be the Cournot equilibrium levels of output for each firm? (b) In part a), what is the market price and the profit for each individual firm? (c) If the fixed cost is instead $1300 for each firm and there is entry and exit in the market, how many firms...

Consider an industry with two firms, each having marginal costs and total costs equal to zero....

Consider an industry with two firms, each having marginal costs and total costs equal to zero. The industry demand is P = 100 − Q where Q = Q1 + Q2 is total output. 1. Find the cartel output and cartel profits assuming that the firms share the profit equally. Hint: In cartels, firms behave as if they are a monopoly. Hence, the cartel quantity is at the point where MR = MC. After finding the quantity, use the demand...

Consider a price-setting oligopoly with 4 identical firms, all with constant marginal cost c. The firms...

Consider a price-setting oligopoly with 4 identical firms, all with constant marginal cost c. The firms compete for an infinite number of periods and have the same discount factor. Derive the minimum discount factor such that there exists a collusive equlibirum with monopoly pricing.

4. A monopolist can produce at constant average and marginal costs of AC = MC =...

4. A monopolist can produce at constant average and marginal costs of AC = MC = 10. The firm faces a market demand curve given by P = 100 - Q. (a) Calculate the profit-maximizing level of output and price for the monopolist. Also calculate the monopolist's profit. (b) Assume this industry suddenly becomes perfectly competitive. Calculate the price and industry output if this industry is perfectly competitive. (c) Calculate the deadweight welfare loss that the monopoly in (a) imposes...

(a) [15 marks] Consider two identical firms with no fixed costs and constant marginal cost c...

(a) [15 marks] Consider two identical firms with no fixed costs and constant marginal cost c which compete in quantities in each of an infinite number of periods. The quantities chosen are observed by both firms before the next round of play begins. The inverse demand is given by p = 1 − q1 − q2, where q1 is the quantity produced by firm 1 and q2 is the quantity produced by firm 2. The firms use ‘trigger strategies’ and...

Consider two firms that provide a differentiated product, which they produce at the same constant marginal...

Consider two firms that provide a differentiated product, which they produce at the same constant marginal cost, MC = 3 (no fixed cost). The demand function for Firm 1 is q1 = 10 – p1 + 0.5p2 and for Firm 2 is q2 = 20 – p2 + 0.5p1, where p1 is Firm 1’s price and p2 is Firm 2’s price. a) Write the profit functions for these firms.( 8 marks) b) What are the equilibrium prices and quantities? (...

Consider a monopolist facing a constant marginal cost of MC = $10 per unit and a...

Consider a monopolist facing a constant marginal cost of MC = $10 per unit and a demand curve of P = 200 – 2q for each individual consumer. If the monopolist has zero fixed costs, what are its profit and the resulting deadweight loss? How does your answer change if the monopolist also has a fixed cost of $4000? b. Now the monopolist faces a potential competitor. If the consumer switches to buy the product from the entrant the consumer...

Subjects