Bertand Economics

Joseph Louis Francois Bertrand (1822-1900) was a French mathematician who worked on the theory of a duopoly model that uses price as its competing factor. Equilibrium, in this model, turns out to be the most competitive price. This is also typical of perfect competition. Like perfect competition, the following assumptions can be made about Bertrand competition:
  • 2 firms (minimum) produce a homogeneous product
  • the firms do not cooperate
  • Marginal Cost is the same in each firm
  • Marginal Cost is constant
  • Demand is linear
  • Firms compete in price and choose price at the same time
  • Both firms compete strategically in terms of price
  • Consumers will buy the cheaper product where possible
  • If both firms have the same price, consumers will by evenly from both

If one firm has lower average cost, limit pricing will ensue. This is where a firm will charge the highest price that is lower than the average cost of the other one (i.e. a price just below the lowest price the other firm can set) and take all the business in order to become a monopoly.
Limitations to Bertrand's theory include:
  • Capacity constraints–Sometimes firms do not have enough capacity to satisfy all demand
  • Dynamic competition–Repeated interaction or repeated price competition can lead to the price above MC in equilibrium.
  • Oligopoly - If the two companies can agree on a price, it is in their long-term interest to keep the agreement: the revenue from cutting prices is less than twice the revenue from keeping the agreement, and lasts only until the other firm cuts its own prices

Bertrand’s focus is on pushing prices down to a level that matches marginal cost, and the result will be conditions similar to perfect competition. The implication of the model is that non-price issues are not considered, and that price is the dominant perspective when choosing which firm to purchase from. Driving distance, marketing, sales, competition from retailers for shelf space, promotional items, and consumer competition are not taken into account.

The key flaw in the Bertrand model is that it is a static or one show game. Each competitor takes the external/competitive environment as a static and “given” variable. In reality, competitors will react to strategies. The moves of one firm will immediately be met by another, and so no firm will truly gain a better grasp of the market by lowering prices. The idea is to keep everything at monopoly prices and for each to maintain a hold over a stable percentage of the market. Increasing one’s market share would mean that the company now has to cater to more people and therefore put a strain on the MC=P determination.

Producers of commodity products like corn, wheat and oil cannot easily change their prices. Since the parameters that hold true for perfect competition are shared by Bertrand theory, goods and services typical of perfectly competitive environments are also common to Bertrand economics. Additionally, commodities often implement minimal advertising, marketing, promotional budgets, and strategies making the model more applicable to these types of goods and services.

The practical use of Bertrand or Cournot models depends on the type of industry they are used in and how reflective they are of the strategy decision process. If the output and available capacity are more flexible, then Bertrand is more reflective of duopoly competition. If these things are hard to adjust, the Cournot is a better indicator.

Test Questions:

1. If cost is C

4Q and P

1000 - (Q + Q) and there are 2 firms in competition, what price will firms set in a Bertrand equilibrium?
a. 6
b. 996
c. 4
d. 3
Answer: Marginal Cost = 4 and price is equal to marginal cost in the Bertrand model

2. What is the best pricing strategy for firms in Bertrand competition?
a. infinite game setting, firms cooperate and charge the same price
b. one firm charges a lower price than the other firm possibly can (a monopoly price)
c. by colluding,each firm splits the profits evenly
d. all of the above are acceptable strategies
Answer: All of the above are acceptable strategies

3.. All of the following are true for Bertrand competition except:
a. There are at least two firms producing heterogeneous products
b. Marginal cost is constant
c. Demand is linear
d. Firms do not cooperate

3. Answer a). The firms produce homogeneous products. They are often similar but not necessarily identical. Business in the same industry will compete with one another based on whichever price-oriented strategy they choose. Homogeneous products allow for the actions of one firm to be tied more directly to those of another. Competitors’ actions and movements will have a greater impact on the market itself and make the ramifications of each firms decisions more profound.

4. In a Bertrand oligopoly, firms simultaneously choose
0 Prices
0 Quantities

4. Answer Prices. Strategy is based around choosing price first and then the quantity to be sold second. Competing based on n price means that firms can easily change the quantity they supply, but once they have chosen that price, it is very hard to change it. The prices are essentially non-negotiable.

5. In a Cournot duopoly, firms simultaneously choose_
0 Prices
0 Quantities

5. Answer Quantities. This strategy sets optimal output levels and then makes pricing considerations a secondary concern. Focus is on meeting market expectations and doing so in a way that beats the competition for a better share of consumers. Danger is if demand expectations fall below expectations, in which case quantity produced cannot be readjusted except through price changes in an effort to eliminate excess.

6. Bertrand Oligopoly, there are _ economic profits.
0 Positive
0 Zero
0 Negative

6. Answer Zero. No economic profits are gained because the businesses are already setting their prices to margnical cost. This keeps them competitive, yet within a range that allows very little opportunity to use resources elsewhere or in another fashion.

7. Of the following oligopoly models, which one features the same conditions as the competitive model?
a. Cournot
b. Stackelberg
c. Bertrand
d. All of the above

7. Answer c. Bertrand. The answer is Bertrand because the price war that occurs is reminiscent of the competitive framework. Firms compete on price to a point where their marginal cost equals the price, and they seek to establish monopoly prices from the onset. A firm may gain more market share based on their ability to offer a lower price to consumers.

8. When one firm sets its output level, then the second firm determines its output level based on the first, this is most reflective of:
a. Bertrand
b. Monopolistic competition
c. Cournot
d. None of the above

8. Answer d. None of the Above. In Cournot and Bertrand, the moves are made almost simultaneously, without collusion or prior agreement. Their decisions are independent, focusing on price and quantity determinations that reflect their production abilities, but done so with an understanding of little to no economic profits to be earned.