Two firms, Bertrand & Cournot, dominate the global market for Hawaiian Tetra Chloride (HiCl₄).Production of this commodity chemical requires a large upfront investment as well as access to the raw materials (specifically Hawaiian Oxide, HiO₂, whose natural deposits are tightly controlled by Bertrand & Cournot.

The market demand curve for HiCl₄ is given by Q = 7500 - 100P where Q is in kg/day and P is in $USD.Both firms have identical marginal costs of production equal to $15 per kg.

a.Assume the two firms have unlimited capacities AND that the entire market demand goes to the firm with the lower price (or is split 50-50 if the prices are equal.)Determine the Nash Equilibrium in the short-run pricing game.[Unnecessary Hint:we called this the undifferentiated Bertrand Equilibrium.]

b.Now assume the two firms do not have unlimited capacities as in part a.Instead, assume the two firms will each determine their capacities, Q_b & Q_c, independently and the market price will be determined based on the demand curve above and their combined capacities.Specifically, P = 75 - .01(Q_b+Q_c).Determine the Nash Equilibrium of this long-run capacity game.[Even Less Necessary Hint:In class, we called this the Cournot Equilibrium.]

c.Now assume the two firms have merged or founded a cartel in order to act as a monopoly.Determine the monopoly price and quantity for this market.