Imagine firms A and B produce a differentiated product and behave as Bertrand co
ID: 1206592 • Letter: I
Question
Imagine firms A and B produce a differentiated product and behave as Bertrand competitors, simultaneously determining prices (i.e., PA and PB) according to the following reaction functions:
Firm A’s reaction function: P A= 200+ P B
Firm B’s reaction function: P B=100 + 1/2 P A
At the Nash equilibrium, firm A sets a price equal to ____ while firm B sets a price equal to ____.
A.300; 100
B.300; 250
C.400; 200
D. None of the above
Suppose two firms, a and a, produce a homogeneous product, with each firm having a marginal and average total cost equal to a constant, c. Behaving a Bertrand competitors, at the Nash equilibrium each firm will set price equal to c.
True OR False
Explanation / Answer
PA = 200 + PB
PB = 100 + 1/2*PA
Now putting PA = 200 + PB
So PB = 100 + 1/2*(200 + PB)
PB = 100 + 100 + 0.5PB
0.5PB = 200
PB = 400
And PA = 200 + PB = 600
This option is not mentioned so the answer would be D-None of the above.
2)True.
As per Bartrand Model both the firms will set the price at its marginal cost c.