Consider two bars that are the only sellers of beer in San Francisco. Total inverse demand for beer in San Francisco is given by p(Q)= 28-Q where Q= q1+ q2 is the sum of the beers stocked by bar 1 and 2, respectively. The cost function of both bars is given by C(q)= 4q which represents the fact that the bar pays its supplier $4 per bottle of beer. The bars compete by choosing how many beers to stock (i.e. Cournot competition).
(a) What is the profit function of each bar?
(b) Find and draw the best response functions of each bar on a single diagram.
(c) Solve for the Cournot equilibrium quantities of beer stocked by each bar (the intersection point of the best response functions in part (b)).
(d) Suppose bar 1 purchased bar 2 (a merger). What would be the new price of beer in San Francisco?