Answer Happy

Problem IV (Collusion) In Long Island there are 3 suppliers of distilled water, labeled firm 1, firm 2 and firm 3. Distilled water is considered to be a homogenous good. Long Island's inverse demand function for distilled water is given by P = 10 ·Q Where Q = 91 +92 +93 denotes the aggregate industry supply of distilled water in Long Island. All of the firms bear the same production marginal cost of C₁ = C2 = C3 = 4 per one gallon of water. Lastly, the game among these firms is repeated indefinitely in each period t = 1, 2, 3, ... . Let 8 € (0, 1) denote the firms' common time discount factor. (a) Find the static (joint) monopolist's quantity, price and profit when they collude. (b) Solve the static Cournot game. That is, find q₁, 9₂, 93, p², 1₁, 1₂, 13. (c) Now find the static profit of firm 1 when he solely deviates from collusion. (d) Compute the minimum threshold value of 8 that would make collusion sustainable.