oligopoly

[dia]

suppose there are 2 profit maximising firms who produce a homogenous good at zero cost.the dd fn is p=30-q1-q2.firms choose their output sequentially firm 1 choosing q1 first then firm 2 follows.Ratio of profits is given by

a. Pi1/Pi2=1
b. Pi1/Pi2=1/3
c. Pi1/Pi2=1/2
d. none of the above

answer is 1/2 but im getting 2.please explain...

[aditi5000]

p=30-q1-q2

MR firm 2 = 30 - 2q2-q1 = 0 so q2= 30-q1/2

profit= 30q1-q1^2-q2q1 = 30q1-q1^2-(30-q1/2)q1
dpi=30-2q1-30/2 + q1=0
q1=15 and q2= 15/2
so ratio of prof = 1/2

[dia]

yeah q1=15, q2=15/2..so q=45/2 and p=15/2...

so profit of firm 1=15*15/2 and profit of firm 2=15*15/2*2 so profit1/profit2=2 how is it 1/2....and even if it is,it means that the leader firms profit is half dat of the follower..shouldnt the leader choose an output such that his market share is bigger?

[aditi5000]

p= 30 - 45/2= 15/2
profit of firm 1=15*15/2 and profit of firm 2=15/2*15/2 so

profit1/profit2=15*15*2*2/15*15*2 = 2.

Yep it seems you are right. And yes, leader should have higher profits. So i guess the answer is none of the above. where is this question from?

[Amit Goyal]

you are right. its 2. don't worry. there is an error in the key.

[Chinni18]

im getting that too aditi