These notes were prepared based on the lectures and supplemented by information from textbooks and tutorials where parts of the lecture were unclear. Graphs, equations, and bullet-point explanations included. Prepared by a first class Economics and Management student for the FHS Microeconomics pape...
MT5 Industrial Organization & Competition Policy
Lecture 12: Application to Industrial Organisation
Competition with Market Power
Types of competition
o Perfect competition (many firms): Profit is competed away
o Monopoly (one firm): Significant profits
o Most industries: Few firms (but more than one)- we will focus on this
Can firms earn profits in concentrated industries?
How does this depend on the nature of the competition?
Strategic decision-making: Optimal decision depends on other firms’ choices
Bertrand Competition (Benchmark model, price-setting)
In Bertrand competition, there is price competition with homogeneous products
Setting it up
o Two firms
o Identical products (perfect substitutes), same marginal cost c
Assume c = 0. (this assumption is not key to the model)
o Each firm i chooses a price pi ≥ 0.
We assume firms choose a fixed price (pure strategy) not a probabilistic
selection of price (mixed strategy)
o If both choose the same price, demand is split equally between them
Since consumers are indifferent between the firms
o If one firm sets a lower price, all the demand goes to that firm
In this model, Nash equilibrium P1 = P2 = c is eventually reached
o Let Q = 180 − 2P, so P = 90 − 0.5Q.
o The monopoly price is £45.
Monopoly maximises Q*(P – c) = QP = 180P − 2P 2.
At optimum, 180 – 4P = 0 → P = 45
o Best response for firm 1 in price setting given firm 2’s price:
If P2 > £45 then set P1 = £45 (get all the demand and monopoly profit)
If 45 > P2 > 0, say P2 =£10, then set P1 just below P2 (P1 = £9.99).
Otherwise, if P1 > £10, you’d earn 0
If you set P1 = £10, you’d earn (A+B). Setting P1 = £9.99 earns you (2B +
E). Your profit for P1 = £9.99 is more by (B+ E – A > 0).
Setting slightly below is better in general even if the demand curve was
not sloping down (no gain in E). This is because loss of A << gain in B.
, o Knowing this, firm 2 will undercut, which causes firm 1 to undercut, and this means the
unique Nash equilibrium in pure strategies (with prices being continuous) is P 1 = P2 = c.
o Bertrand paradox: the competitive outcome arises with only two firms
Why is {c, c} an equilibrium?
o Suppose P2 = c, and firm 1 sets P1 > P2. It still earns 0.
o Suppose instead P1 < P2 = c. Then firm 1 makes a loss. (Captures the market but loses in
each sale)
o Payoff for firm 1 when P1 = c is at least as high as with any other price.
o Same reasoning applies for firm 2. No individually profitable deviations
Why is the {c, c} equilibrium unique?
o Suppose there’s another equilibrium at a different common price. If P 1 = P2 > c then a
firm benefits by undercutting.
o If P1 = P2 < c then a firm benefits by raising its price (lose less)
If instead prices can only be set in discrete units, eg. whole pennies, then there can be another
equilibrium. In the example there would be two equilibria: {c, c} and {c+0.01, c+0.01}
o Profits = 0 if you lower price to c or raise it above c+0.01
o No individually profitable deviations, so it is an equilibrium. Some profits made.
Resolving the Bertrand paradox: what if the situation were slightly different?
o Benchmark model assumes that firms can supply any quantity to the market.
What if firms choose the quantity that they supply to the market?
o Benchmark model assumes products are perfect substitutes.
What if products are differentiated?
o Benchmark model assumes firms interact only once.
What if firms interact repeatedly?
Cournot Competition (quantity setting)
Setting it up
o There are two firms
o Products are identical (homogeneous goods)
o Firms compete by choosing a quantity to supply to the market
o Price adjusts to clear the market
o Assume that demand is linear:
P(Q) = a − bQ where Q = q1 + q2 and b > 0.
Linearity of demand is important for this model, unlike for Bertrand
o Marginal cost is c ≥ 0, there are no fixed costs, and a > c.
No fixed cost assumption not important for the model. Just to make our
examples easier
a > c so a market exists (otherwise max. WTP < marginal cost, no market)
o Profit for firm i = 1, 2 is π(qi, qj) = (P(Q) − c)*qi
Deriving Cournot Nash Equilibrium
o Taking the quantity qj of the other firm as given, firm i's best response BR i(qj) is to
choose qi to maximize profits π(qi, qj)
, o π(qi, qj) = (a − b(qi + qj) − c)qi.
o FOC:
o SOC: (∴ maximum profit point)
o From FOC, BRi(qj) = (a − c − bqj)/(2b)
o Solving this system of equations gives the Nash equilibrium
o Best response is decreasing in the action of the rival: If competitor becomes more
aggressive (produces more), firm backs down (produces less).
o
How Does this Compare to Perfect Competition & Monopoly?
o If firms behaved as if they were a monopoly they would choose Q to maximise profit =
(P(Q) − c)*Q = (a − bQ − c)*Q
FOC: a – 2bQ – c = 0
∴ Q = (a − c)/(2b), P = c + 0.5(a − c)
π = (P – c)*Q =
o If firms behaved as if they were perfect competitors, then they would produce a total
quantity Q such that P(Q) = c
∴ Q = (a − c)/b, P = c
π=0
o Profit under Cournot is higher than in competitive equilibrium but lower than under
monopoly. Profit under Cournot:
,
Aggregate profit: (less than monopoly profit)
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