Consider a duopoly where the inverse demand function (as a function of
total output), Y = (y1 + y2) is
p(Y ) = 10 - Y;
and firms have cost functions
c1(y1) = y1; c2(y2) = 2(y2):
1. Find the Cartel solution (total output and price) and compute the firms profits assuming equal split (each rm producing half of total output).
2. Find and draw on a graph the firms reaction functions.
3. Find the Cournot Equilibrium, i.e., the outputs produced by each firm, the market price and the firms profits.