1.X is a Stackelberg market leader with its "cash cow" product C which is produced with constant marginal cost c=o. There is one follower (F) which use the same production technology. The market demand is Q(P)=56-4*P, where P is the market price. The industry undergoes major changes and F proposed to X formation of a cartel and sharing profits 2/3 for X and 1/3 for F. The cartels are illegal, but without collusion industry could evaluate to:

a.Cournot oligopoly: calculate the equilibrium price and quantities and compare the new equilibrium to the initial market set-up.

b.Bertrand oligopoly: calculate the equilibrium price and quantities and compare the new equilibrium to the initial market set-up.

c.Each of the two outcomes are equally probable and probability of maintaining status-quo is 40%. The probability of cartel detection 40% and fines are up-to 10% of each cartel member revenues. Advice the board on the profit-maximizing strategy. Preferably use the decision tree to support your reasoning.