Three companies, 1, 2 and 3, compete in a homogeneous oligopolistic product market by selecting quantities at the same t

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Three companies, 1, 2 and 3, compete in a homogeneous
oligopolistic product market by selecting quantities at the same
time. The quantity of company i is denoted by qi = 1,2,3. The
companies produce with a fixed marginal cost given as c1 = 1, c2 =
1 and c3 = 0. Fixed costs are zero for all businesses. The inverse
market demand function is given as P = 3-Q, where P is the price of
the product and Q is the total quantity (Q = q1 + q2 + q3).
a) Calculate the equilibrium quantities of the three companies, the
total equilibrium quantity to be offered to the market, the
equilibrium price, and the consumer surplus (CS).
b) Suppose firms 1 and 2 merge to form a new firm on 12. Calculate
the equilibrium quantities of the two firms in the market (12 and
3), the total equilibrium quantity, the equilibrium price, and the
corresponding consumer surplus is formed in this case.
c) Based on the amount of consumer surplus you calculated in the
above questions, do you consider that the Competition Authority
should or should not allow this merger?
Document your answer in detail.