Question

Two firms compete in a market to sell a homogeneous product with inverse demand function P = 400 – 2Q. Each firm produces at a constant marginal cost of $50 and has no fixed costs -- both firms have a cost function C(Q) = 50Q.

If the market is defined as a Bertrand Oligopoly, what is the market price?

Refer to the information above.

What is the total amount of Q produced in this market?

How much does firm 1 produce? (Round to one decimal place)

Answer 1

Here it is given that Marginal Cost(MC) of both firms are 50. So, if Firm 1 charges Price greater than 50 then firm 2 will charge just below firm 1 price(but greater than 50) and will take all the market demand and thus firm 1 will not charge price greater than 50. Also Firm 1 will not charge price < MC(50) as this will result in loss for firm 1. Finally if Firm 1 charges price = 50 then Firm 2 will also charge price = 50 and thus both will divide market equally.

Similarly, if Firm 2 charges Price greater than 50 then firm 1 will charge just below firm 2 price(but greater than 50) and will take all the market demand and thus firm 2 will not charge price greater than 50. Also Firm 2 will not charge price < MC(50) as this will result in loss for firm 2. Finally if Firm 2 charges price = 50 then Firm 1 will also charge price = 50 and thus both will divide market equally.

Thus, In Bertrand Nash equilibrium Both will charge price = 50 and hence Market price in the market(P) = 50.

From demand curve and P = 50 we have P = 400 - 2Q => 50 = 400 - 2Q => Q = 175

Hence, Total amount of Q in this market = 175 units.

As, discussed above that both will divide market equally and thus Firm 1 will produce Q/2 = 175/2 = 87.5 units.

Hence, Firm-1 will produce 87.5 units.