There are three profit-maximising firms that compete in prices. Each firm i = 1, 2, 3 produces good i and faces the dema
Posted: Wed Apr 27, 2022 1:02 pm
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 + P 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.
(c) How much profit did the merger generate for the firms
involved?
(d) i. Did the outsider (firm 1) benefit from the merger? ii.
Provide intuition for your result in (i).
(e) Without doing any additional calculations, determine whether
a competition authority would be likely to block this
merger.
Each firm i = 1, 2, 3 produces good i and faces the demand function
qi = 12−3pi + P 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.
(c) How much profit did the merger generate for the firms
involved?
(d) i. Did the outsider (firm 1) benefit from the merger? ii.
Provide intuition for your result in (i).
(e) Without doing any additional calculations, determine whether
a competition authority would be likely to block this
merger.