In a monopoly market, the profit-maximizing monopolist will produce 500 units and make $1000 in profits. Suppose there are exactly two sellers in the market, Alpha and Beta. They both collude, split the fixed cost ($1000) and each agrees to produce and sell only 250 units, and charge $5 per unit, each making a profit of $500. But Alpha decides they can earn more profit if they produce 300 units.
a, Assuming the fixed costs are evenly split, construct a normal form representation of the cartel game.
b, Who (if any) has the dominate strategy? If so, what is it?
c, Redraw the cartel game, but not Alpha and Beta both decide to increase production to 350 units (vice 300 units).
d, Who (if any) has the dominate strategy? If so, what is it?
e, What is the Nash Equilibrium (if any)?