Any one know how to do this ECON Question?

Question

Three silver mines near Goldenstate, are part of a national triopoly that consist of three main firms a, b and c.
P = 1000 – 1000x, the demand function,
p = price per ounce of gold
x = number of ounces of gold produced per day.
Marginal costs, although constant, vary at each firm.

Firm A is $100 per ounce
Firm B is $ 350 per ounce
Firm C is $ 400 per ounce

Determine the Cournot triopoly equilibrium, including

(i) The number of ounces of gold produced per day?
(ii) The price of gold?
(iii) The social surplus?
(iv) The M – Firm concentration ratio of this gold triopoly?
(v) The Herfindahl – Hirschman Index applicable

I have no idea how to do it. please help.

Answer 1

let a,b,c be the amount of gold produced by each firm then
x=a+b+c
and profit for firm A is A = a (1000 – 1000 (a+b+c))- 100 a
and the max profit is when dA/da=0
do the same for b and c and you will have 3 equations with 3 unknowns which you can solve for a,b,c