Consider a duopoly market for a homogeneous product in which firms set quantity. Inverse demand is P (q) = 1- q with q = q₁ + q₂. Firm 1 has marginal costs equal to 0.7. Firm 2 has marginal cost 0.65 with probability 1 / 2 and 1 with probability 1 / 2.

1. Suppose that the cost type is publicly observed by both firms prior to the quantity setting. Characterize the equilibrium outcome of this game.

2. Suppose from now on that firm 2 privately observes its cost type before setting its quantity. Determine the equilibrium of this game. What is the appropriate equilibrium concept? In particular, determine equilibrium quantities and profits.

3. Would firm 2 have an incentive to reveal its cost type to firm 1 if it could do so at zero cost?

4. Would firm 1 have an incentive to find out about firm 2’s costs? Would it like to do so privately (assuming that firm 2 does not know the cost of firm 1 has when investigating) or publicly?

5. Are consumers better off if firm 2’s cost type remains private information? Discuss.