Suppose there are two pizza firms (Firm 1 and Firm 2) selling identical products in an isolated town. They compete as Cournot (price-setting) competitors in a market with a demand of

p = 150 - Q. Denote the quantities produced by these firms with q₁, and q₂. These pizzerias have no fixed costs and the constant marginal cost of each of them is $3 per unit of output.

a. Derive the residual demand functions of each firm.

b. Derive the profit functions of each firm.

c. Compute the best response functions for each seller and the Nash

equilibrium outputs and prices.

d. Also compute the optimal profits earned by each of these firms.

e. Draw the best response functions with q1on the horizontal axis and

q₂on the vertical axis. Denote the Nash equilibrium on the graph.

f. On the same graph, show the effect on the (Nash) equilibrium quantities if second firm (Firm 2) receives a local government subsidy for the quality of their pizza (as they are made from organic ingredients and hence healthier than that of Firm 1). The subsidy is a per-unit subsidy. Explain in words what will happen to the equilibrium quantities.

Now using the same information about the market demand for pizza, and the cost structure, assume that one of the firms (Firm 2) is a Stackelberg leader. That means, Firm 1 is the Stackelberg follower. Find out the equilibrium quantity of output produced by the leader and the follower. In solving this problem, keep in mind that you will need the best response function for Firm 1 (the follower) and then substitute it into the profit function of the leader (Firm 2) to derive the profit maximizing quantity of output produced by the leader.