dse 2004 10

[s]

consider a cournot duopoly with inverse dd p=1-q1-q2. c1=cq1 and c2=q2/2...suppose prior to choice of quantities by 2 firms firm 1 can choose c by investing (9c^2-13c)/18. assuming that the firm chooses c anticipating cournot competition thereaftr the optimal choice of c is?
a.1/2
b.2/3
c.3/4
d.0

 Ref:dse 2004 10

im not being able to understand the deal with the 'investing'..

thanks in advance

[deepak]

Firm 1 knows it's going to produce quantity q1 and q2. If you had solved for Cournot nash equilibrium, you would obtain q1 and q2 as functions of c, from which you can calculate price as a function of c.
Now, Firm one needs to find the optimal value of 'c'. The 'invest' part here just means he needs to put some amount to buy say a new factory or something, to produce goods at a marginal cost of c. This fixed cost is given by (9c2 - 13c)/18.
So to find the optimal value of c, find that c which maximizes profit
ie Max : P(c) * q1(c) - c * q1(c) - [(9c2 - 13c)/18] . FOC will give you c = 1/2

[Abhyudaya]

Thanks Deepak ...ur reply also helped me.... :)

[Gayyam]

Thank you Deepak! :)