Therefore TR

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```					                WELFARE ECONOMICS

Topic 4. The first fundamental theorem of welfare
economics
Lecture slides, notes & topic handouts for this
module are available from:
http://www.staff.city.ac.uk/n.j.devlin

1. The model of perfect competition

Perfect competition is an extreme form of market
organisation where all firms in an industry are price
takers.

Assumptions required:

   Many firms selling identical products
   No restrictions on entry
   No restrictions on exit
Perfect competition 1a:
Supply and demand for the industry and the firm
Price                                          Price
Market Supply

Firm’s demand

Market Demand

Quantity                               Quantity

Industry:                                     Firms:
Supply is the sum of                           Sell as much as
firms’ supply.                              they wish at the
market price.

For each firm:
 Price = Marginal Revenue
Perfect competition 1b: profit maximising
decisions by each firm.

Price
Marginal cost

P1

Q1
Quantity

For each firm, Profits are maximised if:

 Marginal Revenue = Marginal Cost
And since P = MR, in equilibrium

 P = MC
Perfect competition 1c. Normal profits in
long-run equilibrium.

Price
Marginal cost
Average cost

P

Q
Quantity

   Total Revenue (TR) = P x Q
   Total Cost (TC) = AC x Q
   For profit maximisation, MR = MC
   P = MR = MC = AC
 Therefore TR = TC i.e. zero economic
profits

Principal conclusions of the model of perfect
competition: (1) P = MC, so prices reflect
opportunity cost. (2) Profits are ‘normal’
2. General equilibrium in the perfectly
competitive economy
 An economy comprised entirely of
perfectly competitive markets for goods
and inputs.
For the following exposition, we assume:
 2 goods (X and Y), 2 consumers, 2 firms,
2 inputs (L and K)
 but the theorem is generalisable over n
goods, firms, inputs and consumers

Market for Good X:
Price
Market Supply

Market Demand

Quantity
Market for Good Y:
Price
Market Supply

Market Demand

Quantity
Good
3. Pareto efficiency in consumption

 Each household maximises utility,
thus MRS = PX/PY
Quantity Good Y
10

9

8
Indifference curve, slope =
MRS = ΔY/ΔX
7

6

5

4

3

2

1

0
0     1   2    3   4     5     6      7        8      9     10
Quantity Good X

 Each household faces the same price
for Good X as any other household.
 Each household faces the same price
for Good Y as any other household.

 Thus PX/PY is the same for each
household.
 Thus MRS for any one household =
MRS for any other household…

 Which is the requirement for a
Pareto optimal allocation of goods
between household.

Good
Household 2
X

Slope =
Px/Py

b

Good                         a

Y                                             Good
Y

Household 1           Good
X
4. Pareto efficiency in production

 Each firm maximises profit
 Cost minimising combination of inputs is
where MRTS = PL/PK.
K
10

9

8
Isoquant, slope = MRTS
7
= ΔK/ΔL
6

5

4

3

2

1

0
0    1    2   3   4   5    6     7     8       9   10
L

 Each firm faces the same price for L as
any other firm, and the same price for K
as any other firm.
 Thus PL/PK is the same for both firms
 Thus MRTS for one firm = MRTS for any
other firm…

 …which is the requirement for Pareto
optimality in production

Capital                  Firm 2

b

Labour                         a
Labour

Firm 1                    Capital
5. Pareto optimality in the mix of goods

 PPF = derived from the contract curve in
the production Edgeworth-Bowley box.
Shows the highest feasible
combinations of outputs of goods X and
Y, given the quantities of L and K.
 Slope = marginal rate of transformation
(MRT) = ΔY/ΔX
 ‘isoprofit lines’. Slope = PX/PY
Good Y

Good X
Good Y

Slope = MRT

Slope = PX/PY

Good X

 MRT = MRS
6. Summary
3 requirements for Pareto Optimality in general
equilibrium:
1. MRS of any one household = MRS of any
other household
2. MRTS of any one firm = MRTS of any
other firm.
3. MRT between two goods = MRS between
those two goods

 The first fundamental theorem of welfare
economics is that a competitive market
equilibrium will satisfy each requirement
for Pareto optimality

[The second fundamental theorem,
conversely, is that all Pareto-efficient
allocations are competitive equilibria]
7. Conclusions
 Competitive markets generate an
equilibrium which is optimal in the
Pareto sense i.e. it is impossible to
make a change (in the mix of goods
produced, the inputs used to produce
them, or their allocation between
consumers) without making someone
worse off.
 But may not be optimal in any other
sense e.g. may be very unfair. The
outcome depends entirely on the initial
distribution of endowments
 There are an infinitely large number of
potential equilibria that satisfy each of
the 3 criteria. Each is Pareto-non-
comparable. Choosing between them
requires a further criterion i.e. to
invoke a value judgement stronger
than Pareto.

Next week:

Using Social Welfare Functions to choose the
‘optimum optimorum’
Discussion questions

How would each of the deviations
from perfect competition violate the
requirements for Pareto optimality?

 Price discrimination?
 Monopsony power by a firm in hiring
labour inputs?
 Barriers to entry into an industry?
 Consumers having less than perfect
information?

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