Monopoly Market, Power Market, Exercises of Economics

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Prof. Luigi Benfratello

luigi.benfratello@polito.it

Perfect competition, monopoly,

Market Power and Market

Failures

Review of Perfect Competition



Hypotheses:

1. Large number of buyers and sellers2. Homogenous product3. Perfect information 

Firm is a price taker 

Solution



P = (L)MC = (LR)AC 

«Normal profits» or «zero economic profits» in thelong run

Microeconomics: a review

Individual demand: consumerbehavior 

Under the local nonsatiation assumption, the optimalconsumer 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

.

m

px t s

x u

m p v

x 

 . .

) (

max

)

, (

Individual demand: consumerbehavior 

The indirect utility, i.e. the maximum utility asa function of

p

and

m

has the following

properties:

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.

It is continuous and quasi-convex

The quasi-linear utility function 

Partial

equilibrium

analysis

:^

analyse

the

market

functioning of a “good” that has a relatively low weighton the global economy. 

Hence, we can introduce two simplifying assumptions:^ 

1. the impact of a change in consumers’ income on theexpenditure 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 consideredas fixed and we can be assume them as a numeraire,normalised to 1. 

We can then simplify our utility function in the followingway (

y

is the “rest of goods”, i.e. the numeraire):

y x u y x U 



) (

) , (

Surplus: a review 

Consumer surplus

is the total benefit

or value that consumers receive beyondwhat they pay for the good



Producer surplus

is the total benefit or

revenue that producers receive beyondwhat it costs to produce a good

Consumer and ProducerSurplus

Between 0 and

Q

0

producers receive

a net gain from selling each product--

producer surplus.

ConsumerSurplus

Quantity

Price

S

D

Q

0

5 9

Between 0 and

Q

0

consumers receive anet gain from buying

the product-- consumer surplus.

ProducerSurplus

3

Q

D^

Q

S

Marginal effects of a price/quantitychanges on Consumer Surplus 

Consumer surplus, as a function of quantity, isgiven by: 

As it results:



0

where

q

p(q)dq

S(q)

p(q)q

S(q)

q

V

CS

) (

) (

q p

dq

q

dS



q dp dq

=

dq

q

dV



) (

Perfect competition and Welfare

Welfare economics 

Consider

now

a

representative

firm

having

a

cost

function

c

( x

), with

c’ >

c’’

0 and

c

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 issimply 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 marginalcost of production.

) (

) (^

x c

x

u







Welfare analysis 

What

is

the

optimal

amount

of

output

that

maximizes

the

representative consumer’s utility? Let’s use market mechanism todetermine 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 maximizetotal 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

,

x c w y t s

y

x u y x





^ ) (

) (

max

,

x c w x u y x





(^

x c

x u

Welfare analysis: a generalization 

Suppose there are

i

n

consumers and

j

m

firms. Each consumer has a quasi-linear utility function u

( i

x

)+ i

y

i^

and each (perfectly competitive) firm has a cost

function

c

( j x

). j

An

allocation

describes

how

much

each

consumer

consumers of x-good and the y-good, (

x

, i y

), i

i

n

and how much each firm produces of the x-good,

z

, j j

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

i

i

i^

y

x

u

1

1

Welfare analysis: a generalization 

The total amount of the y-good is the sum ofinitial endowments, minus the amount used upin production: 

Observing that the total amount of the x-goodproduced

must

equal

the

total

amount

consumed, we have

















m j

j j

n i

i

n i

i^

z c

w

y

1

1

1

) (





















m j

j

n i

i

m j

j j

n i

i

n i

i i

z x

z

x

t

s

z c w x u j i

1

1

1

1

1

max