How do Coca-Cola

and Pepsi determine

prices?

Explaining the Bertrand Model of CompetitionBy: Brian Camp, Justin Winston, Kiy Webb, Brice Ndayisenga and Breon Weathersby and Robin McKinnie

Joseph Louis Francois Bertrand

•Born March 11, 1822 and died in Paris on April 5 1900

•Mathematician who worked in the fields of number theory, differential geometry, probability theory, economics and thermodynamics

•Professor at Ecole Polytechnique

Joseph Louis Francois Bertrand Cont.

Contributions to economics was his reviewed work on oligopoly theory

•Identified key error in the Cournot Competition Model of French mathematician Antoine Augustin Cournot

•Used prices rather than quantities as the strategic variables, thus showing that the equilibrium price was simply the competitive price

What is an Oligopoly?

Market in which:● Few firms compete● Barriers to entry● Products may be differentiated (automobiles)

or homogeneous (steel)

Examples

1. Coca Cola vs. Pepsi - In the market of soda products

1. Visa vs. Mastercard- In the market of electronic payment processing

1. Airbus vs. Boeing- In the market of large commercial airplanes

π = Revenue(R) - Cost(C)

Homogeneous Products-MC = PDifferentiated Products-Within the Bertrand Competition Model, we will assume that marginal cost equals zero.

π = R - C-Thus, making revenue the main focus for this model.

R=Price X Quantity

Bertrand Model Environment

● Treats the price of competitors as fixed, and all firms decide simultaneously what price to charge

● Few firms that sell to many consumers● Firms produce differentiated but highly substitutable products

at constant marginal cost● Each firm independently sets its price in order to maximize

profits (Price is each firm’s control variable)● Barriers to entry exist.● Consumers enjoy perfect information● Firms price at marginal cost and make no profit

Bertrand Model Critical Analysis

● Assumes firms compete purely on price, ignoring non-price

competition such as quantity, promotion, place

● Assumes that sales are divided equally among the competing firm

and that the firm,in undercutting its competitor, is able to meet the

full demand of the market.

● Assumes that the pricing game is a one shot game, however, in a

dynamic competition, repeated price competition can lead to an

equilibrium price above MC.

● Assumes products are identical, whereas in reality, most firms

produce products that at least, their consumers perceive as

different from a rival's.

Practice: Assumptions

PC ≠ PS

π = R - Cπ = P * q

qC= 90 - 2PC + 1PS

qS = 240 + 1PC - 2PS

𝝅C = TRC = (PC * qC)=PC (90 - 2PC + 1PS)

= 90PC- 2PC2 + PSPC

(ԀTRC/ԀPC)= 90 - 4PC + PS = 090 +PS = 4PC

PC = 22.5 + (¼)PS

𝝅S= (PS * qS)=PS(240 + 1PC-2PS)= 240PS + 1PCPS-2PS

2

(ԀTRS/ԀPS)= (240 + 1PC - 4PS) = 0240 + PC = 4PS

PS = 60 + (¼)PC

PC = 22.5 + (¼)(60 + (¼)PC )PC = 22.5+ 15 + (¼)2 PC

(15/16)PC = 37.5 PC = $40

PS = 60 + (¼)(PC)PS = 60 +(¼)(40)

PS = 60 + 10PS = $70

What Does This All Mean?

22.5

PS= 60+(1/4)PC

PC= 22.5+(1/4)PS

40

60 70

Price for

Coke

Price for

Pepsi