Suppose that two firms both have AVC 50 Market demand is gi

Suppose that two firms both have AVC = $50. Market demand is given by Q = 100 - P. Find the Bertrand Equilibrium. Would your answer be different if there were three firms?

Solution

If there are two firms

Individual demand = 50-0.5P

Q = 50-0.5P

-0.5P = Q-50

P = 100-2Q

Equilibrium is established where demand = AVC

100-2Q = 50

2Q = 50

Q = 25

P = 100-2Q = 100-2(25) = 50

If there are three firms then individual demand curve will be (100-P)/3

Q= 100/3-P/3

3Q = 100-P

P = 100-3Q

Equilibrium will be established where

100-3Q = 50

3Q = 50

Q = 16.66

P = 100-3(50/3) = 100-50 = 50