Download measuring welfare: marshallian surplus

JEM081
ADVANCED ECONOMICS OF EUROPEAN INTEGRATION:
Microeconomic Aspects
Lecture 2
Topic 2a, Welfare Effects of Trade
MEASURING WELFARE:
MARSHALLIAN SURPLUS
Dr. Wadim Strielkowski
IES FSV CUNI
October 1, 2013
Contents
•
•
•
•
•
Measuring market effects
Marshallian surplus
Consumers’ surplus
Producers’ surplus
Welfare in closed economy.
2
Reading
Turnovec, F.: Political Economy of European
Integration. Karolinum, Charles University Press,
Prague, 2003, chapter 3, pp. 30-52.
Strielkowski, W. and F. Turnovec,: Labour Migration
and Welfare Effects of Free Mobility of Labour in the
Common Market. In: Mejstřík M. et al., SocioEconomic Models and Policies to Support Active
Citizens: Czech Republic and Europe. Matfyzpress,
Prague 2008, pp. 105-120.
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Measuring market effects
• To be able to evaluate effects of
different positions of a country in an
international division of labour we
need a measure, a way how to
assess a quality of changes
• Economic theory provides us with a
concept of welfare.
4
Demand and supply functions
• market for one commodity
• demand curve q = D(p) as a decreasing
function of the price p, or inverse demand
function as a decreasing function p = D(q)
of the quantity q
• supply curve as an increasing function q =
S(p) of the price p, or inverse supply curve
as an increasing function p = S(q) of the
quantity q
5
Inverse demand function
p
D
F
inverse demand
function
p = D(q)
p*
how much to
pay for q*
p*q* = q*D(q*)
0
q*
q
6
Inverse supply function
p
inverese supply
function p=S(q)
S
p*
revenues from q*
p*q* = q*S(q*)
0
q*
q
7
Equilibrium in a closed economy
• no trade assumed
• the intersection of supply and demand
function defines an equilibrium point E
• equilibrium price p* and equilibrium
quantity q* of the given commodity clearing
the market)
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Equilibrium in a closed economy
p
D
Market equilibrium
S(q) = D(q)
S
E
p*
0
q*
q
9
Measuring welfare of consumers
• Demand function: for any quantity q demand
function provides price p = D(q) for which
this quantity will find buyers
• for example, a person is willing to pay a
tremendous amount for water which
represents a basic measure of survival,
however since there are competing suppliers
of water on the market the water is available
for less than a consumer is willing to pay
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Nash Equilibrium
• Preplay Communication
– Before the game, discuss their options. Note only NE are
suitable candidates for coordination as one player could
profitably violate any agreement.
• Rational Introspection
– Based on what each player knows about the other players,
reason what the other players would do in its own best interest.
(Best Response - tomorrow) Points where everyone would be
playing “correctly” are the NE.
• Focal Point
– Some distinguishing characteristic of the tuple causes it to stand
out. The NE stands out because it’s every player’s best
response.
• Trial and Error
– Starting on some tuple which is not a NE a player “discovers”
that deviating improves its payoff. This continues until no player
can improve by deviating. Only guaranteed to work for Potential
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Games (couple weeks)
How much consumers are ready to
pay?
p
p0
D
how much
consumers are
ready to pay
E
p*
0
q*
S
equilibrium
q
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Individual consumer’s surplus
• an individual consumer’s surplus is the
difference between the price a consumer is
ready to pay for a product and the actual
price of the product
• if a consumer is ready to pay more than the
actual price of the product, her benefit from
the eventual transaction is how much she
saved when she did not pay that price but
the price prevailing on the market
13
Aggregate consumers’ surplus
• the difference between the price a
consumer is willing to pay and the
price she pays is the individual
consumer’s surplus.
• consequently, the aggregate
consumers' surplus is the sum of all
individual consumer’s surpluses.
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Consumers’ surplus
p
D
consumers' surplus
CS
S
E
p*
0
q*
equilibrium
q
15
Measuring producers welfare
• an individual producer‘s surplus is
used to measure the welfare of a group
of firms selling a particular product at a
particular price
• an individual producer‘s surplus is
defined as the difference between what
the producer actually receives for
selling her product and the amount she
would be ready to accept for the
product unit.
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For how much producers are ready
to produce
p
D
S
E
p*
equilibrium
for how much
producers are
ready produce
0
q*
q
17
Aggregate producers’ surplus
• Summing up all individual producer‘s
surpluses we get aggregate
producers’ surplus
• difference between what producers
get in equilibrium and for what they
are ready to produce
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Producers’ surplus
p
D
producers' surplus
PS
E
p*
0
q*
S
equilibrium
q
19
In the case of no mobility of the factor we have equilibrium
EH in country H and EP in country P and different
equilibrium factor prices in H and P, namely rH* and rP*
Interpretation of the graph
Definite integral!
Why do we have to use definite integral?
20
The Area Problem
Find the area of the following region:
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22
23
24
25
Definite integral
26
27
Properties of the Definite
integral
Reversing the limits
 f  x  dx    f  x  dx changes the sign.
b
a
a
b
a
If the upper and lower limits are equal,
then the integral is zero.
b
b
a
 f  x  dx  0

a

b
a
k  f  x  dx  k  f  x  dx
a
c dx  c(b  a ),
b
Constant multiples can be
moved outside.
where c is any constant
b
b
 f  x   g  x   dx   f  x  dx   g  x  dx
a
a
a

Integrals can be added (or subtracted).
b
c
c
a
b
a
 f  x  dx   f  x  dx   f  x  dx
Intervals can be added (or subtracted.)
28
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Marshallian surplus
• The idea to measure economic welfare that is
based on the concepts of consumers´ and
producers´ surplus was introduced by Alfred
Marshall
• Marshall originally applied this idea to the
analysis of effects of taxes and price shifts
on market equilibrium
• that is why an aggregate of two components
of welfare, consumers´ and producers´
surplus, is called “Marshallian surplus”
30
Graphics of Marshallian surplus
p
D
Marshallian
surplus MS
MS=CS+PS
S
CS
E
p*
equilibrium
PS
0
q*
q
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Alfred Marshall
• Alfred Marshall (1842–1924), born in London,
England, became one of the most influential
economists of his time.
• His book, Principles of Economics (1890),
brings the ideas of supply and demand, of
marginal utility and of the costs of
production into a coherent whole
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What is it good for?
• Comparing two different market
situations, or equilibrium positions, we
can say:
– the higher consumers' surplus is, the
better for consumers, the higher
producers' surplus is, the better for
producers,
– the higher Marshallian surplus is, the
better for the community.
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What is it good for?
• Changes in regimes of international trade
and international economic cooperation,
including different forms of economic
integration, affect the equilibrium situations
at the markets.
• To evaluate economic implications and
desirability of these changes we can use
the welfare measures and ask about welfare
effects.
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What is it good for?
• Arrangements that increase welfare we
shall assess as economically positive,
while arrangements that decreases welfare
we shall consider economically negative.
• To be able to do that, we have to be able to
“calculate” welfare effects
35
Shift of equilibrium, does it increase
or decrease welfare?
p
Shift of
equilibrium to E2
S
CS
E2
p*
2
p*
1
E1
PS
D2
D1
0
q*1 q*
2
q
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How to calculate welfare?
Area below the curve
from calculus: let y = f(x) be continuously differentiable function,
then
b
 f ( x)dx
a
is equal to the shaded area.
y=f(x)
y
a
b
x
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Area below the curve
Definite integral
Let u(x) is a function such that
du ( x)
 f ( x)
dx
then
du ( x)
f
(
x
)
dx

dx

u
(
x
)

const

 dx
(integral of a function is a function such that its derivative is equal
to the function we are integrating) then
b
 f ( x)dx  u (b)  u (a)
a
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How to calculate welfare?
Consumers’ surplus
a) find function e(x) such that
This image cannot currently be display ed.
de ( q )
 D (q )
dq
where D(q) is an inverse demand function
b) then consumers surplus is equal to
q*
CS   D(q)dq  p*q*  e(q*)  e(0)  p*q *
0
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How to calculate welfare?
Producers’ surplus
a) find function r(q) such that
This image cannot currently be display ed.
dr(q)
 S(q)
dq
where S(q) is an inverse supply function
b) then producers’ surplus is equal to
q*
PS  p * q *   S (q)dq  p * q * r(q*)  r(0)
0
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Marshallian surplus
MS  CS  PS  e( q*)  r ( q*)  r (0)  e(0)
Marshall’s original motivation was to study of welfare
effects of taxation.
Some authors (see for example Viner, 1950) used
concepts of consumers’ and producers’ surplus to
analyse welfare effects of customs unions.
In the 1950s and 1960s Marshallian surplus became one
of the instruments of economics of international trade and
economics of integration (Johnson, 1965; Molle, 1994;
Pelkmans, 1997; Hansen and Nielsen, 1997; Svendsed,
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2003; Turnovec, 2003).
Problems?
Questions?
• CS and PS
• Marshallian surplus
• Calculus and definite integral
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Simple quizz (1):
•
•
Pleas list six founding member states of the EU.
Ger, Fr, It, Be, Ne, Lux
•
List all recent member states of the EU that are the members of
European Monetary Union
17 countries (Be, Est, Fin etc.) and 11 non-Euro states
•
•
•
How many members have been elected to the European Parliament
in 2009 elections?
736
•
•
What is the total size of population of the EU?
503 mil.
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Simple quizz (2):
• Please calculate: ∫(3x2+5x+8 )dx
• x3+5/2x2+8x+c
• Please calculate: ∫((2x+3 )/4)dx
• 1/4x2+3/4x+c
• Please derive: 12x5-2x2+x+7
• 60x4-4x+1
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Problems?
Questions?
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