Create a linear demand model of a single item with two sellers. “linear demand” means pi is a linear function of qi and qj, but please make a numerical demand function of your choice. Assume the marginal cost is zero.

 [Collusive] Solve the collusive price and quantity of the model.

 [Static] Solve the static game of quantity competition.

 [Dynamic] Change the model to a Stackelberg game, and solve the equilibrium prices, quantities, and profits of both players (the leader and the follower).

 Compare 3) and 4), why does the leader set a higher quantity (or a lower quantity) in the Stackelberg setting? Use 1-2 sentences to discuss your intuition.

 In 4), Why does the leader’s profit higher (or lower) than the profit of the follower? Use 1-2 sentences to discuss your intuition.

Without calculating the real values, rank consumer welfare in 2), 3) and 4), and use 1-2 sentences to discuss the reason.