Suppose that an industry consists of two Cournot firms selling a homogenous product. The market demand is given byp(Q)=100Q, whereQ=q1+q2. Each firm has a constant marginal cost of $10 per unit.

a) Find the Cournot Nash equilibrium. What is the equilibrium price?

b) Find the quantities and price that would prevail if the firms acted as if they were a monopolist (i.e., the collusive outcome).

c) Suppose now Firm 1 and Firm 2 sign the following contract where Firm 1 agrees to pay Firm 2 an amount equal toTdollars for every unit of output Firm 1 produces; and symmetrically, Firm 2 agrees to pay Firm 1 some amountTdollars for every unit of output Firm 2 produces. What value ofTshould they choose if they want to realize the collusive outcome?