很難的問題 - 經濟

Suppose that there are two identical countries.Each country produces and
consumes one good: widgets. There are three identical widget-producers in each
country: each producer's production technology is characterized by the cost
function c(q) = 0.3. That is, there is a fixed cost, 0.3, while mc= 0.
Suppose that each country's inverse demand for widgets is p = 1-1/8q
and the firms compete in the Cournot fashion.
(i) In autarky, how much profit does each firm make under a (symmetric)
Cournot equilibrium.
(ii) What is the average cost of producing a widget in this equilibrium?
(iii) Now suppose that with free trade, these two countries are integrated so
that the single world price of widgets is a function of the total supply of
both countries. Again,all the firms compete in the Cournot fashion. In a
(symmetric) Cournot equilibrium,How much profit does each firm make?
(iv) In the long run, how many firms will there be in the market? (Find the
maximum integer of firms that each firm makes a positive profit.)
我不知道要如何算3家廠商的Cournot均衡,只知道2家的
是不是有公式可以套N家廠商的情況,直接算應該很複雜吧?
卡在這裡 後面都算不下去 也沒有什麼概念
這題超難 根本不是我的程度能算的 唉~
有人能提供一些想法或公式嗎?
謝謝

--