EX-8

Cournot vs Stackelberg. $P = 120 - Q$ with $Q = q_1 + q_2$. Each firm has constant MC = 70.

Find the Cournot–Nash equilibrium quantities, total quantity, price, and profits.

Same setup as 1a. Firm 1 is now the Stackelberg leader (chooses $q_1$ first; Firm 2 observes and best-responds). Find $q_1$, $q_2$, $Q$, $P$, and profits.

Compare the Cournot (1a) and Stackelberg (1b) outcomes and explain the differences.

Cournot vs monopoly (acquisition). Identical firms with $TC(q) = 80 q$ ($MC = 80$). Inverse demand $P = 200 - Q$.

Find the Cournot equilibrium quantities, total quantity, price, and per-firm profits.

Same setup as 2a. How much would Firm 1 be willing to pay to acquire Firm 2 (turning the duopoly into a monopoly)? What is the minimum Firm 2 would accept?

Cournot with asymmetric, increasing MC. $P = 550 - Q$. $TC(q_1) = 0.5 q_1^2$ (so $MC_1 = q_1$) and $TC(q_2) = q_2^2$ (so $MC_2 = 2 q_2$). Firm 1 is lower-cost.

Find the Cournot equilibrium.

Same setup as 3a. Now Firm 1 is the Stackelberg leader. Find equilibrium quantities, price, and profits.

Compare the Cournot and Stackelberg outcomes from 3a/3b. Why is the first-mover advantage smaller than in Q1?

Cournot, cartel, and cheating. Identical firms with $TC(q) = 80 q$ ($MC = 80$), $P = 200 - Q$. (Same numbers as Q2.)

Find the Cournot equilibrium.

Same setup as 4a. The two firms form a cartel to maximise joint profit. Find each firm's quota and profit.

Same setup as 4a/4b. Firm 1 cheats on the cartel agreement by best-responding to Firm 2's cartel quota $q_2 = 30$. Find Firm 1's optimal deviation and profit.

Compare Firm 1's profit across the three scenarios (Cournot, cartel, cheating). Why are cartels unstable?

Instead of colluding, suppose Firm 1 considers acquiring Firm 2. What is the maximum it would pay, and the minimum Firm 2 would accept?

Common fishery (commons with externality). Two countries share a fishery. Country $i$ catches $q_i$; cost $TC_i = (q_i + B q_j)^2$ with $0 < B < 1$ ($B$ = how much the rival's catch raises your cost — congestion / depletion). Utility $U_i = q_i - TC_i$.

Find the Cournot (simultaneous) Nash Equilibrium catches and utilities.

Same fishery setup as 5a. Now Country 1 is the Stackelberg leader. Find $q_1, q_2$ and utilities.

Compare 5a and 5b. Is there really a difference between Cournot and Stackelberg here? Explain why or why not, focusing on the role of the externality parameter $B$.