Question

Duopolists share a market in which the market demand is P = 10 – Q, where Q = q1 + q2. The firms’ cost functions are C1 = 4 + 2q1 and C2 = 3 + 3q2.

d) If firms compete over price in Bertrand competition, compute total output and profit.

Answer 1

MC1 = 2, MC2= 3

Then in Bertrand eqm, P1= P2= 3,

For Firm 2, it can't charge P <3, as it leads to loss

If P > 3, then price war will start , both try to undercut each other

But firm 1, it has advantage of lower MC, can charge more than 2, so maximum it can charge , P1= 3

So both share profits equally

Thus , market P = 3,

From demand function, Q = 10-3= 7 : total output

both share output equally, Q1=Q2= 7/2= 3.5

π1= (P-MC)*q1 -4

= (3-2)*3.5 -4

= -.5

π2= -3

answered by: anonymous