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
Many buyers
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:
Supply is the sum of
firms’ supply.
For each firm:
 Price = Marginal Revenue
Firms:
Sell as much as
they wish at the
market price.
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
Indifference curve, slope =
MRS = ΔY/ΔX
8
7
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
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.
10
 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
X
Household 2
Slope =
Px/Py
b
Good
Y
Household 1
a
Good
Y
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
= ΔK/ΔL
7
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
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
10
 Thus MRTS for one firm = MRTS for any
other firm…
 …which is the requirement for Pareto
optimality in production
Capital
Firm 2
b
Labour
Firm 1
a
Labour
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-noncomparable. 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?