Consider that there are four firms in a market who compete in quantities with each other. The products are imperfect substitutes (=1/2 to each other. The marginal cost of each firm is Zero.

The inverse demand function faced by each firm is:

Pi=1-Qi-( Qj)

Say for firm 1, inverse demand function would be:

P1=1-Q1-0.5(Q2+Q3+Q4)

1. Calculate the Cournot outcome for each firm (Quantity and Profit) when all the firms compete with each other.

2.Calculate the monopoly outcome for each firm (Quantity and Profit) if all the firms collude and decide the price and quantity jointly.

3.Calculate if there is any possibility of stable partial/full cartel/cartels to exist in this market. Please calculate the all possible partial and full cartels. Also calculate the internal and external stability conditions for the same.