Week 7Partial Equilibrium
(Jehle and Reny, Ch.4)
Serçin �ahin
Y�ld�z Technical University
6 November 2012
Serçin �ahin (Y�ld�z Technical University)Week 7 Partial Equilibrium (Jehle and Reny, Ch.4)6 November 2012 1 / 22
Perfect Competition
In perfectly competitive markets, buyers and sellers are su�ciently
large in number to ensure that no single one of them, has the power
to determine market price.
Buyers and sellers are price takers, and each decides on a
self-interested course of action in view of individual circumstances and
objectives.
Serçin �ahin (Y�ld�z Technical University)Week 7 Partial Equilibrium (Jehle and Reny, Ch.4)6 November 2012 2 / 22
Perfect Competition
The demand side of a market is made up of all potential buyers of the
good, each with their own preferences, consumption set, and income.
We let I ≡ {1, ..., I} index the set of individual buyers and
qi (p,p, y i )
be i 's non-negative demand for good q as a function of its own price,
p, income, y i , and prices for all other goods, p.
Market demand for q is simply the sum of all buyers' individual
demands
Serçin �ahin (Y�ld�z Technical University)Week 7 Partial Equilibrium (Jehle and Reny, Ch.4)6 November 2012 3 / 22
Perfect Competition
The supply side of the market is made up of all potential sellers of q.
If we let J ≡ {1, ..., J} index those �rms and
qj(p,w)
be j 's short-run supply function for good q as a function of its own
price, and input prices, w.
Then the short-run market supply function is the sum of individual
short-run supply functions:
Serçin �ahin (Y�ld�z Technical University)Week 7 Partial Equilibrium (Jehle and Reny, Ch.4)6 November 2012 4 / 22
Perfect Competition
Market demand and market supply together determine the price and
total quantity traded.
We say that a competitive market is in short-run equilibrium at price
p∗ when
qd(p∗) ≡ qs(p∗)
Serçin �ahin (Y�ld�z Technical University)Week 7 Partial Equilibrium (Jehle and Reny, Ch.4)6 November 2012 5 / 22
Perfect Competition
Serçin �ahin (Y�ld�z Technical University)Week 7 Partial Equilibrium (Jehle and Reny, Ch.4)6 November 2012 6 / 22
Perfect Competition
In the long run, no inputs are �xed for the �rm.
Also, there are possibilities of entry and exit of �rms.
In a long-run equilibrium, we shall require not only that the market
clears but also that no �rm has an incentive to enter or exit the
industry. Namely, no �rm can be earning positive pro�ts in the long
run.
Serçin �ahin (Y�ld�z Technical University)Week 7 Partial Equilibrium (Jehle and Reny, Ch.4)6 November 2012 7 / 22
Perfect Competition
Serçin �ahin (Y�ld�z Technical University)Week 7 Partial Equilibrium (Jehle and Reny, Ch.4)6 November 2012 8 / 22
Imperfect Competition
In pure monopoly, there is a single seller of a product for which there
are no close substitutes in consumption, and entry into the market is
completely blocked by technological, �nancial, or legal impediments.
The monopolist takes the market demand function as given and
chooses price and quantity to maximise pro�t.
Π(q) ≡ r(q)− c(q)
If q∗ > 0 maximises pro�t, then it satis�es the �rst-order conditions
which is equivalent to
mr(q∗) = mc(q∗)
Serçin �ahin (Y�ld�z Technical University)Week 7 Partial Equilibrium (Jehle and Reny, Ch.4)6 November 2012 9 / 22
Imperfect Competition
Because r(q) ≡ p(q)q, di�erentiating to obtain marginal revenue gives
where ε(q) =dq/dp
p/q
Rearranging this, we can obtain an expression for the precentage
deviation of price from marginal cost in the monopoly equilibrium:
Serçin �ahin (Y�ld�z Technical University)Week 7 Partial Equilibrium (Jehle and Reny, Ch.4)6 November 2012 10 / 22
Imperfect Competition
Serçin �ahin (Y�ld�z Technical University)Week 7 Partial Equilibrium (Jehle and Reny, Ch.4)6 November 2012 11 / 22
Imperfect Competition
Many market display an blend of monopoly and competition
simultaneously.
Firms become more interdependent
the smaller the number of �rms in the industry,
the easier entry,
and the closer the substitute goods available to consumers.
When �rms perceive their interdependence, they have an incentive to
take account of their rivals' actions and to formulate their own plans
strategically.
Serçin �ahin (Y�ld�z Technical University)Week 7 Partial Equilibrium (Jehle and Reny, Ch.4)6 November 2012 12 / 22
Imperfect Competition
Putting the legality of collusion aside, there is something tempting in
the idea of a collusive equilibrium. However, there is a problem.
Let us consider a simple market consisting of J �rms, each producing
output qj , so that
Now suppose �rms cooperate to maximise joint pro�ts. If q maximisesJ∑
j=1
Πj , it must satisfy the �rst-order conditions:
These together imply
Serçin �ahin (Y�ld�z Technical University)Week 7 Partial Equilibrium (Jehle and Reny, Ch.4)6 November 2012 13 / 22
Imperfect Competition
In a Nash equilibrium, every agent must be doing the very best he or
she can, given the actions of all other agents.
When all agents have reached such a point, none has any incentive to
change unilaterally what he or she is doing.
Serçin �ahin (Y�ld�z Technical University)Week 7 Partial Equilibrium (Jehle and Reny, Ch.4)6 November 2012 14 / 22
Imperfect Competition Cournot Oligopoly
In a Cournot oligopoly, �rms choose the quantities they supply in the
market for some homogeneous good.
Suppose there are J identical �rms, that entry by additional �rms is
e�ectively blocked, and that each �rm has identical costs,
Firms sell output on a common market, so market price depends on
the total output sold by all �rms in the market
Serçin �ahin (Y�ld�z Technical University)Week 7 Partial Equilibrium (Jehle and Reny, Ch.4)6 November 2012 15 / 22
Imperfect Competition Cournot Oligopoly
Then pro�t for �rm j is
We seek a vector of outputs (q1, ..., qJ) such that each �rm's output
choice is pro�t maximising given the output choices of the other �rms.
Such a vector of outputs is called a Cournot-Nash equilibrium.
Serçin �ahin (Y�ld�z Technical University)Week 7 Partial Equilibrium (Jehle and Reny, Ch.4)6 November 2012 16 / 22
Imperfect Competition Bertrand Oligopoly
Bertrand argued it is much more natural to think of �rms competing
in their choice of price, rather than quantity.
Suppose that market demand is linear in total output, Q, and write
Q = α− βpwhere p is market price.
Taking �rm 1 for example, for all non-negative prices below α/β,pro�t will be
Serçin �ahin (Y�ld�z Technical University)Week 7 Partial Equilibrium (Jehle and Reny, Ch.4)6 November 2012 17 / 22
Imperfect Competition Monopolistic Competition
Firms in both Cournot and Bertrand oligopolies sell a homogeneous
product.
In monopolistic competition, a relatively large group of �rms sell
di�erentiated products that buyers view as close, though not perfect,
substitutes for one another.
Each �rm therefore enjoys a limited degree of monopoly power in the
market for its particular product variant.
Serçin �ahin (Y�ld�z Technical University)Week 7 Partial Equilibrium (Jehle and Reny, Ch.4)6 November 2012 18 / 22
Imperfect Competition Monopolistic Competition
Assume a potentially in�nite number of possible product variants
j = 1, 2, ....
The demand for j is
and p = (p1, ..., pj , ...)
Clearly the pro�t depends on the prices of all variants:
Serçin �ahin (Y�ld�z Technical University)Week 7 Partial Equilibrium (Jehle and Reny, Ch.4)6 November 2012 19 / 22
Imperfect Competition Monopolistic Competition
In the short run, a �xed �nite number of active �rms choose price to
maximise pro�t, given the prices chosen by the others.
Let j = 1, ..., J be the active �rms in the short run and suppose
p = (p1, ..., pJ) is a Nash equilibrium in the short run.
If �rm j produces a positive output and p must satisfy the �rst-order
conditions for an interior maximum,
Serçin �ahin (Y�ld�z Technical University)Week 7 Partial Equilibrium (Jehle and Reny, Ch.4)6 November 2012 20 / 22
Imperfect Competition Monopolistic Competition
As usual, long-run equilibrium requires there to be no incentive for
entry or exit.
Consequently, maximum achievable pro�ts of all �rms must be zero.
Suppose that p∗ is a Nash equilibrium vector of long-run prices. Then
the following two conditions must hold for all active �rms j :
Serçin �ahin (Y�ld�z Technical University)Week 7 Partial Equilibrium (Jehle and Reny, Ch.4)6 November 2012 21 / 22
Imperfect Competition Monopolistic Competition
Serçin �ahin (Y�ld�z Technical University)Week 7 Partial Equilibrium (Jehle and Reny, Ch.4)6 November 2012 22 / 22