
A Bertrand Game Question
Firstly, sorry if this is in the wrong section.
I have an exam tomorrow, and going over the practice paper I am having problems with the following question.
5. Two competitor, firm 1 and firm 2, who produce differentiated products face demand functions in the form
D1 (p1 p2) = 10  2 p1 + p2
D2 (p1 p2) = 10  2 p2 + p1
where pi is the price of good i = 1, 2
Both firms face constant marginal costs c1 = 1, and c2 = 2 respectively.
(i) Suppose that the two firms set their quantities simultaneously. Find the equilibrium prices and quantitites in this market.
(ii) Suppose that firm 1 moves first by setting its price, followed by firm 2 which sets its quantity after observing the price set by firm 1. Find the equilibrium prices and quantities in this market.
I know how to get the equilibrium prices for part (i), using a 2 firm Bertrand Game.
My question is, how would I get the quantities? And then secondly, how would I go about answering part (ii)
An explanation of what I need to do would be great if you don't actually want to do all the actual calculations. Thanks.
*P1 and p2's should have the 1's and 2's sub scripted, but I couldn't find a button to do it.)