There are three profit-maximising firms that compete in prices. Each firm i = 1,2,3 produces good i and faces the demand

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There are three profit-maximising firms that compete in prices.
Each firm i = 1,2,3 produces good i and faces
the demand function qi = 12−3pi +􏰀j̸=i pj. For
each firm i, the cost of producing a
quantity q is ciq, where c1 =
2, c2 = 4, and c3 = 6.
(a) Find the equilibrium prices and quantities.
(b) Suppose that firms 2 and 3 merge to become firm A and
that their merger results in efficiency gains that halve the cost
of producing goods 2 and 3; that is, c2 = 2
and c3 = 3. Calculate the new equilibrium prices and
quantities. (Provide every step of reasoning and
calculation.)