Cournot Oligopoly Questions!!!!

[Sumit]

Guys, use this page to post you doubt related to Oligopoly, So that it become easy for all to catch all the query relating to oligopoly on one single page....

[Sumit]

Here is Q1.
A cournot oligopoly consists of three firms producing a homogeneous product.The firms have identical constant average costs of Rs.2 per unit.Market demand is given by P=10-Q, Where Q is the combined output of three firms what is the equilibrium Price?

[Sumit]

Q2.Consider two firms. The demand faced by the two firms is Q1 = a – 2P1 + P2 and Q2 = a + P1 - 2P2. Assume zero marginal cost. Find the cournot equilibrium price, quantity and profit for both firms. What is the relationship between the commodities produced by two firms?

[Devika]

Combined quantity=6
Price =4

[Mauli]

getting the same ans for ques1
max  p(q1,q2,q3)*q1-2q1
q1
since the question is symetric , q2 ,q3 can be found in the same way.
q1=q2=q3.
three eq three unknowns.

[Mauli]

for q2
from 1st eqn in the ques

p1= a+p2-q1
p2=a+p1-q2
put p2 in p1
p1 we get as a function of q1 ,q2
then same max
               q1     p(q1,q2)*q1
an similarly for q2.
here also the quest is symetric. so q1=q2.
final ans i m gtng is
q1*=q2*=3a/5.
p*=2a/5. and the profit follows.
pl cnfrm my ans to this ques.

[Sumit]

correct devika...

[Sumit]

Hey Mauli,
Correct answer...

[madhur1987]

consider 2 firms facing dd curve P=50-5q where q =q1+q2. the firm cost fns are C1=20+10q1 and C2=10+12q2
a)suppose that both firms have entered the industry what is the join profit maximizing level of output?how much will each firm produce?how would your ans change if the firms have not yet entered the industry?
b)how much should firm1 be willing to pay to purchase firm 2 if collusion is illegal but a takeover is not?
in a part how will we decide that which firm will produce how much?

[madhur1987]

also dse 2004 que 10 have no idea how the ans is 1\2 pls someone help

[madhur1987]

a competetive industry faces a demand x=865-5p where x is industry o|p. there are n firms having identical cost conditions C1=144+5x1+4X1^2 WHERE Xi is the output of firm i. there is free entry.find out the euillibrium output and price for this industry how much firms will enter this industry?

[Sumit]

Q1 by Madhur1987.
a)Joint profit Max level of output(q)=5.2 where q1=2.8 & q2=2.4.

N I didn't get its last part where question is asking for how would your ans change if the firms have not yet entered the industry?..Possible argument 1)If there is only two firm in a industry n both of them not entered yet which only means no one is producing... or 2) either it has to be one of the firm has not entered the industry...

B)I think firm1 willing to pay a atleast of profit that firm2 is earning in case where two firms are competing to each other...n it's coming out to be 18.8.

n Plz someone help me in this I was wondering how much firm1 will produce in each plant after acquiring firm2.....n what will be profit of the firm in this case...


Q2 by Madhur1987
Ans. Equilibrium output=600.
Equilibrium price=53.
Also 100 firms will enter in the industry.

Note: I'm sure of my answer for Q2. but it takes me hell lot of time to get on this answer the reason for this
I first differentiate Cost function of the single firm n then putting MC=p by doing this I get the firm supply curve n then multiplied it by N(where N= number of firm which will enter in industry) to get the industry supply curve then I equated Industry supply =Industry demand curve(given in the question)....n in the end putting different value of N to get the equilibrium price level n then putting the price in industry demand function to get industry total demand...I keep trying this untill I get the value on N where the total profit earn by industry is equal to zero...n the values which I get are givien above you can also verify total profit of the industry is zero at N=100....If anyone of you found any simple way then this hit n try method plz do share.....

[madhur1987]

thanx sumit:)
but in que 1 q1=2.8 and q2=2.4 are cournot eqillibrium qty's(when they are competing). and profit of firm 1 is 19.2 and that of 2nd firm is 18.8. but in que we are asked joint profit maximizing level of output which is coming out Q=2.8 only. now joint will be max when firm 2 produce nothing out of 2.8. but my doubt is is it possible when 2 firms collude 1 will produce nothing. if not how will we decide which firm will produce how much share of 2.8.
and same doubt if one firm takeover other in which plant production takes place??
and for 2nd que hnx a ton bro
pls if u could also help me for dse 2004 que 10

[duck]

Hey Sumit.. :)
In such strange looking cost functions,just minimise the average cost. You'll get what each firm would like to supply. Multiply it with "N" to get the Market supply. And as we need to find long run competitive equilibirum, we need to make sure that each firm gets exactly zero profit.
So, equate profit of  firm to zero. You'll get number of firms.

[avi]

hey i am getting combined quantity 4 and price 6 ..

[avi]

same ans for q2 but someone just explain q1 again pls my ans isnt matching..