sample ques 2010 eco

[priyanka p]

hi all, lets discuss the questions 1st ques is direct and doesnt need much explanation.  2nd ques abt cournot eqb i solved , i got answers (a) (a-m)/(s+2)  for both firms    (b)   direct dd fns i got q1=p2-p1 +(a-m)/(s+2)    and q2= p1-p2+ (a-m)/(s+2)   and for (c)   bertrand eq prices p1=p2= {(a-m)/(s+2)} -m

[Rahul Agarwal]

Hi Priyanka,

Which questions are you talking about :)

[priyanka p]

i am talking abt msqe 2010 sample questions eco part

On Sat, Apr 24, 2010 at 6:57 PM, Rahul Agarwal [via Discussion forum] <[hidden email]> wrote:

Hi Priyanka,

Which questions are you talking about :)

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[priyanka p]

question ----      Consider a market with 2 firms. cost fn of each firm is c(q)= mq where q> or=0  let the inverse dd fns of firm 1 and firm 2 be p1=a-q1-sq2 and p2=a-q2-sq1 respectively (a) find the cournot equilibrium quantities of 2 firms.     (b) using the inverse dd fns p1 and p2, derive direct dd fns D1(p1,p2) and D2(p1,p2) of firms 1 and 2.    (c) using the inverse dd fns D1(p1,p2) and D2(p1,p2), find the bertrand equilibrium prices.                                                                                                                                                                                                                                                       i have solved and i get the answers as follows, pls check !!                                     (a)   q1=q2=(a-m)/(s+2)        (b) D1=p2-p1+ (a-m)/(s+2)     and D2= p1-p2+(a-m)/(s+2) (c)  p1=p2= {(a-m)/(s+2)} -m

[Benhur]

i got d same ans in part a

but how did u get 'm' in part b?
i did part b) by simultaneously solving inverse demands curve..i got d following equations..

D1=a/(1+s) - {1/(1-s^2)}p1 + {s/(1-s^2)}p2

D2=a/(1+s) + {s/(1-s^2)}p1 - {1/(1-s^2}p2

then part c)
p1=p2={(a+m)(1-s)(2+s)}/{2(2-s)}

[Benhur]

plz check n say if its rite

[sonal]

your ans to ques 2 b) is correct.i'm getting another ans for p1,p2 in c) i'l check if yours is correct or not

[Shweta Singhal]

I got the part c) ans as :-
 
p1=p2= {a(1-s)+m}/(2-s)

[Bhaskar]

I do not get the answer for 2(c).

in the bertrand model, the prices are equal to the marginal cost as i found out from the book "Satyaranjan Chakravarty"...

so, p1=p2=m...where m= marginal cost of the firms...

what do you think???

[duck]

the correct answer for 2c is

p1=p2= (a+m) (1-s) / (2-s)