Just have 40 minutes for this. I would very much appreciate if i see the whole solutions. Thank You in advance

Consider a market X that, in the current period (t = 1), is populated by two firms that compete on prices (and set them simultaneously) and produce a perfectly homogeneous good. These two firms, firm A and firm B, are symmetric, as they are characterized by the same cost function C(qi) = cqi for i = A, B, with c = 0. The market demand is: P - 1 -Q 1. What are the assumptions that need to be satisfied for the unique Nash equilibrium of the one-shot price game to be PA = PB = 0? 2. Compute the associated quantities and profits. 3. Under the above assumptions, compute the monopoly quantity, price and profits. Assume now that the two firms have capacity KA - KB 3 4. Indicate the unique Nash equilibrium of the one-shot price game under capacity constrain- ts, and show that it is a Nash Equilibrium. 5. Do firms exert market power? Why? Suppose now that the one-shot game is repeated an infinite number of periods. 6. Absent capacity constraints, write the Incentive Compatibility Constraint for the enforce- ment of a collusive agreement in which at t - 1 each firm sets the monopoly price pm. In each of the following periods t > 1, firms choose p" if all the firms chose the monopoly price in the previous period. If not, they choose the Nash-Equilibrium prices of the one-shot game forever. 7. Compute the critical discount factor for the above strategy to be a Nash Equilibrium of the repeated game. 8. Assume now that firms have capacity KA = KB = 3. Write the Incentive Compatibility Constraint for the enforcement of a collusive agreement in which at t = 1 each firm sets the monopoly price. In each of the following periods t > 1, firms choose p" if all the firms chose the monopoly price in the previous period. If not, they choose the Nash-Equilibrium prices of the one-shot game forever. 9. Compute the critical discount factor for the above strategy to be a Nash Equilibrium of the repeated game. 10. In this case in which firms are capacity constrained is it easier or more difficult to enforce