Question

Two identical firms compete in a Bertrand duopoly. The firms produce identical products at the same constant marginal cost of MC = $10. There are 2000 identical consumers, each with the same reservation price of $30 for a single unit of the product (and $0 for any additional units). Under all of the standard assumptions made for the Bertrand model, the equilibrium prices would be Group of answer choices $10 for both firms $30 for both firms $50 for both firms $10 for one firm, $30 for the other firm

Answer 1

Setup:

Two identical firms A and B:

Marginal Cost = MC = $10

2000 identical consumers with $30 as reservation price for sigle unit and $0 for any additional unit

This means that each consumer buys exactly one unit of good

Firm A and B compete in a Bertarnd Duopoly: Both firms compete in Price competition simultaneously

Solution:

No firm will charge a price greater than $30 as they'll get 0 demand

No firm will charge less than $10 as it will occur them losses

Since both the firms has same Marginal Cost = 10

Market price will be set to $10 as at any other price the competitor firm has an incetive to undercut the other firm and grab the whole market demand

Hence Price will be set equal to Marginal cost of $10 for both the firms and both will earn 0 profit

P = MC is always the solution of a Bertran Price competition problem.

You see here the result is same as if there was perfect competition.