# Monopoly Market, Power Market, Formulas and forms for Economics. Politeknik Pos Indonesia

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Prof. Luigi Benfratello [email protected]

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

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