# Bertrand

Bertrand Oliogopoly
The Bertrand Oligopoly model was devised by Joseph Louis Francois Bertrand in 1883 after he read a book by Augustin Cournot called, “Recherches sur les Principes Mathematiques de la Theorie des Richesses”1. Cournot argued in his book that in an oligopoly, each firm examines the reactions based on their output decisions, concluding that if one firm altered its output the other firm would also change its output by the same quantity2. Bertrand went on to devise a model which argued against Cournot’s theory.

 Joseph Bertrand
The main concept behind Bertrand’s Oligopoly is that price is set at the perfect competition price, which is equal to marginal costs (mc). There are some assumptions which need to be met to be able to accept this model.

These assumptions are:
• There are at least two firms producing homogenous products;
• Firms do not cooperate;
• Firms have the same marginal cost (MC);
• Marginal cost is constant;
• Demand is linear;
• Firms compete in price, and choose their respective prices simultaneously;
• There is strategic behavior by both firms;
• Both firms compete solely on price and then supply the quantity demanded;
• Consumers buy everything from the cheaper firm or half at each, if the price is equal3.

Based on these assumptions, when two firms compete in the market, the price they charge will equal the marginal cost. The reason that the price equals the marginal cost is because if the product is homogenous, then the consumers will purchase the product at the lowest cost available. Because of this, one company can not afford to have the price of their good to be higher then the competition. If this does occur, the company pricing their product above marginal cost wouldn’t sell one unit of its product and the other company in the market will have 100% market share. Therefore, both companies will choose to sell their product at the lowest price possible, which equals the marginal cost.

Real World Example:
· There are only two companies, Ball Inc. and Cardinal & Co., in the city of Muncie that produce widgets. Consumers believe these widgets are identical and have no preference on who produces these widgets. The consumers behave rationally and decide to purchase the widgets at the lowest available cost. Since Ball Inc. and Cardinal & Co. do not engage in collusion, they both sell their widgets at the lowest possible price (\$ 2.00 each) to retain a portion of the widget market. The lowest price which both companies are willing to sell their widgets for is the marginal cost. At the marginal cost, both companies do not make an economic profit. Ball Inc. decides to raise the price of their widgets to \$ 2.50 and try to make an economic profit. Since consumers view the widgets produced by each company as identical, they choose to continue to buy the widgets for \$ 2.00 each. Cardinal & Co. gains 100% of the widget market in Muncie, and Ball Inc. does not sell any widgets in Muncie for the price of \$ 2.50.

The Bertrand Oligopoly model shows that oligopoly power does not always involve positive economic profits. This model implies that both companies behave as if they are competing in a perfect competition in the long run.

The theory is commonly called Bertrand Oligopoly, but is also called by the name of Bertrand Duopoly. Duopoly is defined as “an oligopoly limited to two sellers”4. There is also some controversy on who devised this model. Some people believe the model may instead be due to Francis Ysidro Edgeworth, and is sometimes called the "Bertrand-Edgeworth Oligopoly" model5.

Questions:

1. The Bertrand Oligopoly model assume that firms behave in Collusion.
a. True
b. False

2. McDonalds and Burger King will earn zero economic profits if they are the only competing in an oligopoly situation.
a. True
b. False

3. The Bertrand Oligopoly model states that firms will set their output levels based on changes their competitors do with their output level.
a. True
b. False

4. When meeting all of the assumptions for Bertrand Oligopoly model, if one firm decides to lower their cost they will gain the entire market share.
a. True
b. False

5. The price of a product will be calculated by finding the intersection where Marginal Revenue intersects Marginal Costs
a. True
b. False

1. False. Collision means that the firms are working together. The Bertrand Oligopoly model assumes that firms do not cooperate with one another.
2. False. McDonalds and Burger King do not compete in a oligopoly situation as they do not have homogenous products.
3. False. The Bertrand Oligopoly model does not refer to firms setting output levels, that is the Cournot Oligopoly model.
4. True. Since the product is homogenous, consumers will purchase the lowest price available to them.
5. False. The price of the product is set at the Marginal Cost, which is constant.

Works Cited

1 Morrison, Clarence. “Cournot, Bertrand, and modern game theory”. Atlantic Economic Journal 1 June 1998.

2 Joseph Louis Francois Bertrand Economy Professor. viewed 20 Oct 2007 http://www.economyprofessor.com/theorists/josephbertrand.php

3 Bertrand Competition Wikipedia. viewed 20 Oct 2007 http://en.wikipedia.org/wiki/Bertrand_competition

4 Duopoly Merriam Webster. viewed 20 Oct 2007 http://www.m-w.com/dictionary/duopoly

5 Bertrand Oligopoly Everything2. viewed 20 Oct 2007 http://www.everything2.com/index.pl?node_id=1047523