Limit pricing game tree question P = 100 – Q • fixed costs are equal to £850 • m

Question

Limit pricing game tree question

P = 100 – Q • fixed costs are equal to £850 • marginal cost is equal to £10 • limit price is equal to £34 Draw a game tree and show that limit pricing is not sub-game perfect when the entrant is certain about post-entry competition and price.

I understand where monopoly and Cournot equilibrium quantity and price come from and how to derive them. However, I don't understand where the quantity for entry and no entry comes from in the limit pricing scenario. Below are the answers in the limit pricing scenario for entry and no entry. I don't understand where the 66 and 33 come from.

limit pricing scenario of PL = 34. If no entry occurs, quantity is equal to 66 and profits

= PQ – (850 + 10Q)

= 34(66) – (850 + 10(66))

= 2244 – 1510

= 734

and if entry occurs, each firm produces 33 units and the profit per firm is

= PQ – (850 + 10Q)

= 34(33) – (850 + 10(33))

= 1122 – 1180

= -58

Explanation / Answer

It is obtained from the demand function

Q = 100 - P

Since In case of limit price , there will be onlyplayer and P =34

Q = 100 - 34 = 66

In case of entry , by symmetry q1 = q2 , S0 Q = q1 + q2 = 2q1

2q1 = 100 - 34 = 66

q1 = 33

If you don't understand anything then comment , I'ill rever back on the same .

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