Economics 121

Zvika Neeman

Spring 2015

Yale University

Monday, March 23: Competitive Markets

How does this lecture fit?

This lecture begins the third part of our semester, the study of compet-

itive markets. Studying competitive markets is important both because

some markets in our economy are reasonably modeled as competitive, and

because this is a useful point of comparison for other markets.

This lectures explores a “partial equilibrium” view of competitive markets,

meaning that we examine the supply (or firm) side of the market while

holding fixed the demand (or consumer) side. Our next topic, a “general

equilibrium” view of these markets, will integrate the two.

Outline

I. INDIVIDUAL CHOICE

I.1 The Basic Model of ”Consumer” Choice

I.1.1 Modeling Choice: Preferences and Constraints

I.1.2 The Mathematics of Optimization

I.1.3 Demand Functions

I.1.4 Elasticity

I.1.5 Maximizing Utility

I.2 Applications

I.2.1 Labor Supply

I.2.2 Time

I.2.3 Consumer Surplus

I.2.4 Uncertainty

I.2.5 Uncertainty: Risk Pooling and Insurance

I.2.6 Uncertainty and Valuing Life

I.3 Utility: Does It Make Sense?

II. FIRMS

II.1 Profit Maximization

III. COMPETITIVE MARKETS

III.1 A Partial Equilibrium Model of Competitive Markets

IV MARKET FAILURE

(Competitive) Markets

“The market is not an invention of capitalism. It has existed for centuries.

It is an invention of civilization.” (Mikhail Gorbachev, June 8, 1990)

“The moment that government appears at market, the principles of the

market will be subverted.” (Edmund Burke, 1729–1797)

“We Are The 99% that will no longer tolerate the greed and corruption of

the 1%.” (occupywallst.org)

Intuitively, a competitive market has:

1. Many firms

2. Homogeneous outputs,

3. Perfect information

4. No transactions costs.

Formally, in a competitive market, R(q) = pq.

A Partial Equilibrium Model of Competitive Markets

First, the demand side. To look at markets, we need to aggregate individual

behavior. Suppose there are m consumers in the market, indexed by k =

1, . . . , m. Then the market demand is the sum of the k individual demands.

In particular, Market demand for good xi equals∑m

k=1 xi(p1, p2, . . . , pn, I(k), k).

We will typically be interested in the case of two goods, so that the market

demand for good x1 equals∑m

k=1 x1(p1, p2, I(k), k).

We will typically write this market demand as x1(p1, p2). Notice that there

is no income variable here, which is the sign that this is a market demand

and not an individual demand.

We would like to have a criterion for measuring the “performance” of a

market.

The consumer surplus is given by:

∫ p′′

p′x1(p1, p2)dp1

This differs from our pervious measure of consumer surplus by using market

rather than individual demand. It is the sum of the individual consumer

surpluses.

What determines the outcome in a competitive market? This depends on

the time horizon.

In the market period or very short run the quantity supplied is fixed.

In the short run, some inputs are fixed and some variable. Firms are unable

to either enter or exit the market.

In the long run, all inputs are variable. Firms can enter and exit.

Notice that these are measured in terms of “economic time,” not calendar

time.

In the short run, the firm’s supply curve is given by the appropriate part

of its marginal cost curve. Market supply is the sum of the firms’ supply

curves. The firm’s profit maximization problem is

maxq

pq − C(q),

with first-order condition

p−dC(q)

dq= 0.

C( ) C’( )C(q) C’(q)

pp

q qq(p)

Second order condition:

d2C(q)

dq2> 0

Interiority condition:

pq(p)− C(q(p)) ≥ −C(0).

In the long run, all inputs are variable. In particular, firms can enter and

exit the market.

The relevant cost curves are now long-run cost curves.

The short-run and long-run cost curves emerge from similar-looking max-

imization problems, with the difference being the variables over which the

maximization is performed.

Short run:

C(q) = minx1

p1x1 + p2x2

s.t. f(x1, x2) = q.

Long run:

C(q) = minx1,x2

p1x1 + p2x2

s.t. f(x1, x2) = q.

Once we have the cost function, the long-run profit maximization problem

looks familiar:

maxq

pq − C(q)

p−dC(q)

dq= 0.

The difference is in the shape of the cost function:

C( ) C’( )C(q) C’(q)

]

pp

q qq(p)

Second order condition:

d2C(q)

dq2> 0

The interiority condition is now:

pq(p)− C(q(p)) ≥ 0.

The short-run and long-run also differ in terms of entry and exit decisions.

In the short-run, there is no entry and exit, and profits may be positive or

negative.

In long-run equilibrium, firms in a competitive market earn zero profits.

This initially sounds absurd. Why would firms earn negative profits, and

who would enter a market, only to earn zero profits?

The answer requires distinguishing normal from excess (or economic) profit.

Firms in a competitive industry earn zero excess profit.

What is the equilibrium long-run firm size, price, and number of firms?

This depends on the shape of the cost functions and whether there are

indivisibilities in inputs.

Do firms enter and leave markets? Some data:

We must now distinguish constant (or increasing, or decreasing) costs for

a firm and for an industry.

Costs that are decreasing everywhere are inconsistent with perfect compe-

tition. The result is often a “natural” monopoly.

R(q)

C(q)

q

(Eventually) increasing costs are consistent with perfect competition.

Constant costs are a knife-edge case.

Competitive markets are often viewed as leading to desirable outcomes.

Producer surplus:

∫ p′′

p′C′(q(p))dp.

Competitive markets maximize the sum of consumer and producer surplus.

Things to read:

Nicholson and Snyder cover this topic in chapter 12. Pages 409-431 de-

velop the theory, and the remainder of the chapter explores some applica-

tions. See Chapter 8 in Perloff and Chapters 22-23 in Varian.

The organization of markets is a topic with important political as well as

economic implications. A nicely accessible and often entertaining discus-

sion of how markets work is given by John McMillan in Reinventing the

Bazaar (Norton, 2002).