Download Advanced Microeconomic Theory II - Fall 2011 Outline – Short

Advanced Microeconomic Theory II - Fall 2011
Outline – Short-Run Price Competition [Chapter 5]
In this chapter, we assume firms meet only once, and simultaneously and non-cooperatively choose
their quantity or price.
5.1 – Bertrand Paradox – firms in industries, even duopolists, never succeed in establishing a market
price that generates profit. (This seems not reasonable, hence, the paradox.)
Conclusions of the model: symmetric firms price at marginal cost; symmetric firms do not make
profits; asymmetric firms both charge price equal to the higher marginal cost; only the low-cost
firm earns profit.
5.2 - Solutions to the Bertrand Paradox
The paradox can be resolved by relaxing any of the three main assumptions of the Bertrand
model: that the firm always supplies the demand it faces (i.e., it is not capacity constrained); that
firms choose prices simultaneously and non-cooperatively; and that firms produce identical goods.
5.2.1 – The Edgeworth Solution
Edgeworth introduced capacity constraints. With such constraints, Bertrand is no longer
and equilibrium.
5.2.2 – The Temporal Dimension
When the possibility of a reaction is introduced, a firm would have to compare the shortrun gain from lowering its price and gaining market share, to the longer-run loss from
engaging in a price war.
5.2.3 – Product Differentiation
Firms will keep some consumers who are located nearer to them even when the price of
the competing good is lower.
5.3 - Decreasing Returns to Scale and Capacity Constraints
In the extreme case, the marginal cost of production becomes infinite at some output (capacity
level.)
5.3.1 – Rationing Rules
Not all consumers who want to buy from the lowest-priced firm are able to do so because
of the capacity constraint on the firm’s production. This leaves the other firm with residual
demand to serve.

Efficient-Rationing Rule is called efficient because it maximizes consumer surplus.

The Proportional-Rationing Rule is not efficient for consumers; some with valuation
below the higher price buy the good because they can obtain the good for the lower
price. The higher-priced firm does get greater demand at each price.
5.3.2 – Price Competition
A firm that raises its price slightly above the competitive level loses some demand;
however this is only a second-order effect. At the same time, that firm raises the price on
al the inframarginal units and gets a first-order increase in profit. In the equilibrium, both
firms’ prices exceed the competitive price (formalizing the idea that decreasing returns to
scale soften price competition.
5.4 – Traditional Cournot Analysis
This is a one-stage game in which firms choose quantities simultaneously. When choosing its
output, firm 1 takes into account the adverse effect of the market-price change on its own output,
so each firm chooses higher output than optimal for them.
5.5 –Concentration Indices and Industry Profitability

m-firm concentration ratio (adds the m highest chares in the industry (typically four)

Herfindahl index (sum of the squares of market shares

Entropy index (sum of the shares times their logarithm)
With symmetric firms, the Bertrand model tells us that market price and industry profits are
independent of the number of firms in the industry. Profitability and concentration are not
related. Cournot shows a negative correlation between the number of firms and profitability.
With asymmetric firms, industry profitability is related to concentration.
Note: “Concentration indices have no systematic relationship with economic variables of interest
for assessing changes in cost, demand, or policy.” (page 223)