Question 2: (Bertrand competition with identical products) Two firms that produc

Question

Question 2: (Bertrand competition with identical products) Two firms that produce identical products compete by choosing prices. Market demand for this product is P 6- Firm1 has marginal cost MC1-1, while firm 2 has marginal cost MC2 2. All consumers purchase from the firm with the lonwest price. If prices are the same, firns split the demand equally. Assume that firms can only set integer prices. (a) Write out cach firm's best response function. (b) Is (Pi.Pa) (3,:3) a Bertrand ib Why? (c) Is (p,P2) (2,2) a Bertrand equilibrium? Why? (d) Find all Bertrand equilibria of this game

Explanation / Answer

Answer

a)

Assume Firms can set only integer prices

Best Response for Firm 1

Best Response for Firm 2

Best Response for Firm 1

Best Response for Firm 2

b)

(p1,p2) = (3,3) is not a Bertrand Equilibrium Becaue If p2 = 3, Then Firm 1 will charge 2 instead of 3.

Because If firm 1 charge 2 their profit will be 4 and If it charges 3 then there profit will be 2*1.5 = 3

Hence this is not a Bertrand Equilibrium

c)

(p1,p2) = (2,2) is a Bertrand Equilibrium. Because If p2 = 2 then p1 will also be 2 beacuse if price charge by firm 1 is lesser than 2 i.e. 1, there profit will be 0 and If p1>2 there demand will be zero and If firm 1 charges price = 2 then its profit will be 2. Hence If firm 2 charges 2 then best option for firm 1 will be 2 as well.

Similarly If firm 1 charges 2 Then firm 2 charge 2 or more. If it charges lesser than 2 it will incurr a loss and If it charges more than 2 there demand will be zero. Hence it also charge 2 as well.

Hence Both Best response are same i.e.,

p1(p2) = p2(p1), when they charges 2

d)

As we can see from part (a) that p1(p2) = p2(p1), only when they charges 2 i.e. (2,2)

hence it is a Bertrand equilibrium.

there can also be one more equilibrium (2,3). As Choosing 3 is firm 2 dominant strategy and for that firm 2 will chage leser than 3 namely 2

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