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Prof. Luigi Benfratello luigi.benfratello@polito.it

**Perfect competition, monopoly,
Market Power and Market
**

**Failures**

2

**Review of Perfect Competition
**

Hypotheses: 1. Large number of buyers and sellers 2. Homogenous product 3. Perfect information

Firm is a price taker

**Solution
** P = (L)MC = (LR)AC
«Normal profits» or «zero economic profits» in the

long run

3

**Review of Perfect Competition**

4

**Microeconomics: a review**

5

**Individual demand: consumer
behavior
**

Under the local nonsatiation assumption, the optimal
consumer demanded bundle of goods (*i = 1, .., n) *is given by
the following problem:

where *p *is the vector of market prices and *m *the income level
of the consumer.

*v*(*p*, *m*) is the maximum utility achievable at given prices and
income and is called *indirect utility function*. The optimal ** x(p,
m) **is therefore the consumer’s

**.**

*demand function**mpxts
*

*xumpv
x
*

..

)(max),(

6

**Individual demand: consumer
behavior
**

The Lagrangian for the Utility maximization problem can be written as:

The FOC is given by:

And it can be re-elaborated as:

)()( *mpxxuL *

*nip
x
xu
*

*i
i
*

,...1for 0)(

*nji
p
p
*

*x
xu
*

*x
xu
*

*j
*

*i
*

*j
*

*i *,...1,for
*)(

*)(

7

**Individual demand: consumer
behavior
**

The indirect utility, i.e. the maximum utility as
a function of *p *and *m *has the following
properties:

1. It is non increasing in *p*, that is if *p’ ≥ p*, then
*v*(*p*’, *m*) ≤ *v*(*p*, *m*). Similarly, *v*(.,.) is non
decreasing in *m.
*

2. It is continuous and quasi-convex

8

**The quasi-linear utility function
** ** Partial equilibrium analysis**: analyse the market

functioning of a “good” that has a relatively low weight on the global economy.

Hence, we can introduce two simplifying assumptions: 1. the impact of a change in consumers’ income on the

expenditure of the “good” is limited (*no income effect*);
2. the substitution effect on the other goods is small too.

The prices of the rest of goods can then be considered as fixed and we can be assume them as a numeraire, normalised to 1.

We can then simplify our utility function in the following
way (*y *is the “rest of goods”, i.e. the numeraire):

*yxuyxU * )(),(

9

**The quasi-linear utility function
**

*u*(*xi*) is a continuous, increasing, twice-differentiable,
and concave function (square root, log,…)

The optimization problem becomes:

FOCs:

This leads to the following optimal condition:

*mypxts
yxuyxU
*

.. )(),(

01

0)(

*y
L
*

*p
x
xu
*

*x
L
*

*pxu
x
xu
*

)()(

10

**Surplus: a review
**

**Consumer surplus **is the total benefit
or value that consumers receive beyond
what they pay for the good

**Producer surplus **is the total benefit or
revenue that producers receive beyond
what it costs to produce a good

11

**Consumer and Producer
Surplus
**

**Between 0 and Q0
producers receive
**

**a net gain from
selling each product--
**

**producer surplus.
**

**Consumer
Surplus
**

**Quantity
**

**Price
**

*S
*

*D
*

*Q0
*

**5
**

**9
**

**Between 0 and Q0
consumers receive a
net gain from buying
**

**the product--
consumer surplus.
**

**Producer
Surplus
**

**3
**

*QD QS*

12

**Marginal effects of a price/quantity
changes on Consumer Surplus
**

Consumer surplus, as a function of price, is given by:

Hence, it results:

*Intutition*: the demand has a negative slope, the minus
sign is needed in order to have a positive quantity

*

)()(
*p
*

*dppqpVCS
*

)()( *pq
dp
*

*pdV
*

13

**Marginal effects of a price/quantity
changes on Consumer Surplus
**

Consumer surplus, as a function of quantity, is given by:

As

it results:

*

0 where

)(
*q
*

*p(q)dq=S(q)
*

*p(q)qS(q)qV=CS
*

)()( *qp
dq
*

*qdS
*

*q
dq
dp=
*

*dq
qdV
*

)(

14

**Perfect competition and Welfare**

15

**Welfare economics
** What are the welfare properties of the perfect

competitive equilibrium?
The **representative consumer approach**: suppose

that the market demand, *x*(*p*), is generated by
maximizing the utility of a single representative
consumer who has a quasi linear utility function *u*(*x*)+*y*,
where *x *is the good under examination and *y
*“everything else”.

Under this utility function, we know that:
Hence, the direct demand function *x*(*p*) is simply the

inverse of the above condition Note that in case of a quasi-linear utility the demand

function is independent of income!!

*pxu * )(

16

**Welfare economics
** Consider now a **representative firm **having a cost

function *c*(*x*), with *c’ > *0, *c’’ *> 0 and *c*(0) *= *0.
In a perfect competitive market, the profit maximizing

(inverse) supply function of a representative firm is
given by *p *= *c*’(*x*).

In equilibrium demand = supply Hence, the equilibrium level of output of the x-good is

simply the solution to the equation:

This is the level of output at which the marginal willingness to pay for the x-good just equals its marginal cost of production.

)()( *xcxu *

17

**Welfare analysis
**

What is the optimal amount of output that maximizes the representative consumer’s utility? Let’s use market mechanism to determine the final output.

Let *w *be the consumer’s initial endowment of the y-good. The
consumer’s problem is:

Intuition: the welfare maximizing problem is simply to maximize
total utility consuming x-good and y-goods. Since *x *units of the x-
good means giving up – in a competitive market - *c*(*x*) units of the
y-good, our social objective function becomes:

The FOC is given by (as before):

*The competitive market results in exactly the same level of
production and consumption as does maximizing utility directly*.

)( ..

)(max ,

*xcwyts
*

*yxu
yx
*

)()(max ,

*xcwxu
yx
*

)()( *xcxu *

18

**Welfare analysis
** Another way to look at the same problem.
Let *CS*(*x*) = *u*(*x*) - *px *be the consumer’s surplus and *PS*(*x*)

= *px *– *c*(*x*) be the producer’s surplus.
The **total surplus**, or **welfare**, is:

Same FOC as before:
We can conclude saying that **the competitive equilibrium
**

**level of output maximizes total surplus**!

)()(

)()(

)()(max

*xcxu
xcpxpxxu
*

*xPSxCSW
x
*

)()( *xcxu *

19

**Welfare analysis: a generalization
**

Suppose there are *i *= 1,…,*n *consumers and *j *= 1,…,*m
*firms. Each consumer has a quasi-linear utility function
*ui*(*xi*)+*yi *and each (perfectly competitive) firm has a cost
function *cj*(*xj*).

An **allocation **describes how much each consumer
consumers of x-good and the y-good, (*xi*, *yi*), *i *= 1,…,*n*,
and how much each firm produces of the x-good, *zj*, *j *=
1,…,*m *.

The **initial endowment **of each consumer is taken to be
some given amount of the y-good and 0 of the x-good.

The sum of utilities of all consumers is given by:

*n
*

*i
*

*n
*

*i
iii yxu
*

1 1 )(

20

**Welfare analysis: a generalization
**

The total amount of the y-good is the sum of initial endowments, minus the amount used up in production:

Observing that the total amount of the x-good produced must equal the total amount consumed, we have

*m
*

*j
jj
*

*n
*

*i
i
*

*n
*

*i
i zcwy
*

111 )(

*m
*

*j
j
*

*n
*

*i
i
*

*m
*

*j
jj
*

*n
*

*i
i
*

*n
*

*i
iizx
*

*zxts
*

*zcwxu
ji
*

11

111,

..

)()(max

21

**Welfare analysis: a generalization
**

Let the Lagrangian multiplier on the constraint, we have

where *p* = *since the market is perfectly
competitive!

Hence, market equilibrium necessarily
maximizes welfare **for a given pattern of initial
endowments (wi)**.

)(' )('

*jj
*

*ii
*

*zc
xu*

22

**Consumer Equilibrium in a
Competitive Market
**

** First Theorem of Welfare Economics
** If everyone trades in a competitive

marketplace, all mutually beneficial trades
will be completed and the resulting
**equilibrium allocation **of resources will be
**economically efficient
**

Welfare economics involves the **normative
evaluation of markets **and **economic
policy**

23

**Consumer Equilibrium in a
Competitive Market
**

**«Pareto Optimality»
** An outcome is Pareto optimal if it is not possible

to make one person better off without making one another worse off

If this is possibile, we face a *potential Pareto
improvement *(PPI)

The adoption of the PPI criterion means that we can focus on what happens to total surplus.

Hence an outcome that maximizes total surplus is Pareto optimal.

24

**Consumer Equilibrium in a
Competitive Market
**

Difficult to achieve an efficient allocation with many consumers and producers unless all markets are perfectly competitive Efficient outcomes can also be achieved

by **centralized system
**Competitive outcome is preferred since

consumers and producers can better assess their preferences and supplies

25

**«Equity» and Efficiency
**

Although there are many efficient allocations, some may be more fair than others The difficult question is, what is the most

equitable allocation? We can show that there is no reason to

believe that efficient allocation from competitive markets will give an equitable allocation