Suppose Two Colas Compete in a Bertrand Market Structure with Differentiated

question 53

Essay

Suppose two colas compete in a Bertrand market structure with differentiated products. Demand for the first cola is given by where p₁ is price for cola 1 and p₂ is the price for cola 2. Demand for the second cola is The costs of providing the colas are C₁ = q₁ and C₂ = q₂ respectively.
a. Identify firm 1's profit function.
b. Identify firm 2's profit function.
c. Identify firm 1's reaction function.
d. Identify firm 2's reaction function.
e. Identify the equilibrium price charged for each cola.

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Definitions:

Standard Error

A statistical measure that describes the accuracy with which a sample distribution represents a population using the standard deviation.

Mean

The mean of a series of numbers, determined by dividing their total sum by the quantity of numbers in the series.

Confidence Interval

A range of values derived from sample statistics that is likely to contain the true population parameter with a given level of confidence.

Standard Error

A measure of the variability or dispersion of a sample statistic from the population parameter it estimates.