Question

1. The restaurant hamburger market in a small town has two firms. The product is undifferentiated (in other words, homogeneous) and the demand curve is Q = 200 – 2P. Firm 1 has constant average total cost of $4 per unit, and firm 2 has constant average total cost of $7. If the two firms simultaneously choose prices, what is the Bertrand equilibrium? How much will each firm sell, and what will each firm’s profit be?

Answer 1

We have the following information

Market demand: Q = 200 – 2P

Q = Output

P = Price

Average total cost (ATC) = Total Cost ÷ Total Output

Average total cost of Firm 1 (ATC₁) = $4

So, Total Cost of Firm 1 (TC₁) = 4Q₁

Q₁ = Output of Firm 1

Average total cost of Firm 2 (ATC₂) = $7

So, Total Cost of Firm 2 (TC₂) = 7Q₂

Q₂ = Output of Firm 2

Marginal cost of Firm 1 (MC₁) = ΔTC₁/ΔQ₁ = 4

Marginal cost of Firm 2 (MC₂) = ΔTC₂/ΔQ₂ = 7

Now, it is given that the product is undifferentiated (homogenous) and the two firms are choosing the price simultaneously. So, in such a situation the consumer will purchase from the lowest price seller only. As a result, if the two firms charge different prices than the one with the lowest price will supply all the quantity of the product demanded. In such a situation, since both the firms have the incentive to cut price so, the equilibrium will be perfectly competitive outcome in which each firm will equate the price to the marginal cost.

However, in the present case the marginal cost of Firm 1 is lower as compared to the marginal cost of Firm 2. So, Firm 1 will supply the entire market and Firm 2 will sell nothing.

So, Firm 1 will charge $4 as the price

Q = 200 – 2P

Q = 200 – (2 × 4)

Q = 200 – 8

Firm 1 will supply 192 units.

Since, the price is equal to the marginal cost so, Firm 1 will earn zero profit.