Exercises for ECON31002 - Managerial Economics II
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Exercises for ECON31002 - Managerial Economics II
Assignment 2
• Questions:
1. 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+Pj
ipj . 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). [max: 50 words]
(e) Without doing any additional calculations, determine whether a competition au-
thority would be likely to block this merger. [max: 50 words]
2. There are n ≥ 2 profit-maximising firms producing a homogeneous good, competing in quantity, and facing the inverse demand function P(Q) = 10 − Q, where Q = P
qi is the total quantity produced in the market. Each firm i faces the same linear cost function: C(qi) = 2qi .
(a) Find the total quantity produced and the equilibrium price.
Suppose that the n firms form a cartel that chooses a total quantity Q to produce. To avoid lengthy court proceedings, the competition authority has decided to allow cartels to be formed but issue them with a tax equal to 50% of the revenue that firms make above the competitive price. That is, letting P ∗ be the competitive price (found in (a)) and letting Q be the quantity that the cartel chooses, the cartel has to pay max{0,Q(P(Q) − P∗ )/2}. (We assume that the competition commission knows P ∗ and is able to collect the tax.)
(b) Write down the formula for the profit of the cartel as a function of Q.
(c) If the cartel maximises its profit, what will be the total quantity produced and the equilibrium price?
(d) For what values of n are consumers strictly worse off under the cartel than under competition?
(e) Comparing the competitive price (found in (a)), the cartel price (found in (c)),
and the price that the cartel would set if there were no competition authority, how effective is the competition authority at keeping the price low?
2022-04-27