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Respond to the question: cournot nash equilibrium problem wit?

04/23/2009 11:18 PM by name withheld; cournot - nash equilibrium - problem with exercise

i have an question about how i should do this:
there are 2 countries with 1 firm in each country. the countries can choose to export subsidise the companies (subsidy from country 1 is s1 and s2 for country two).
There are also a third country, which is the country the 2 companies sell their goods to.
the inverse demand in country 3 is:
P(Q) = 70 - Q, Q= q1+q2

the marginal cost of the companies is 10.

i've begun by finding the best response for the 2 companies by using this formula:

q1 = 0,5(a-c1-q2)
Which then is: q1=0,5(70-10-s1-q2)
and q2=0,5(70-10-s2-q1)

And when i combine these two i get the best responses for the companies.

My problem is now that i need to find the best response for the countries, when they maximise social welfare equal to: the sum of their firm's profit and trace tax revenue. But what should i do here to make the best response functions? [Manage messages]