PARETO OPTIMALITY

1Prof. Prabha Panth,

Osmania University,Hyderabad

GENERAL EQUILIBRIUM Partial equilibrium: Marshall -

individual consumer, producer, firm, or factor’s equilibrium analysis.

General equilibrium – Walras and Pareto.

General Equilibrium: all product and factor markets achieve equilibrium simultaneously. What will be the nature of this

equilibrium? Will all economic units benefit from it? How can it be achieved?

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GENERAL EQUILIBRIUM Assumptions:

Free, capitalistic market. Perfect competition in the product

market, product prices are given Perfect competition in the factor

market, factor prices are given. Equilibrium determined simultaneously

in both product and factor markets. Other things remaining constant, Static, no growth. Diminishing returns.

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GENERAL EQUILIBRIUM There is inter connection between

product and factor markets. Partial equilibrium in individual markets,

can lead to general equilibrium. Achieved through adjustments of product

and factor Ps. All resources are allocated in an optimum

manner. Welfare of all units is maximised. Laissez faire, no government interference. Efficient and Equitable market.

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PARETO OPTIMALITY Pareto Optimality: A Market

situation, where in it is not possible to make one person better off, without making another worse off.

Because of Optimum allocation of resources in General equilibrium.

If resources are not allocated optimally, it is possible to increase or improve one unit’s welfare without decreasing another’s.

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PARETO OPTIMALITY Basis of Welfare Economics. Efficiency and Equity or Social

Justice in general equilibrium in a capitalist free market. Efficiency: in terms of allocation of

resources. Equity: in terms of distribution of

income.

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CONDITIONS FOR EFFICIENCY:Three conditions for Efficiency in

the General equilibrium model:1. Production efficiency: Maximum

possible output with the given resources.

2. Consumption efficiency: Maximum utility for all consumers,

3. Product mix efficiency: optimum mix of commodities.Prabha Panth 7

MODEL OF PARETO OPTIMALITY Assume that two commodities are being

produced A and B. Two firms M and N. M produces A, and N

produces B. Two factors of production, K and L. Firms M

and N use both factor inputs to produce A and B.

Two consumers X and Y, who consume both commodities A and B.

Perfect competition, Static analysis, Diminishing returns, and utility

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PRODUCTION EQUILIBRIUM An allocation of inputs (K,L) is

production efficient if it is not possible to increase the output of one commodity (A), without decreasing the output of the other commodity (B). Assume that there are two firms M, N. M produces commodity A, N produces commodity B. Both use K and L as inputs.

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Edgeworth box Isoquants of two firms M,N.Both use K and L.Each tries to achieve its highest IQ. If M moves to higher IQ, then N is forced to move to lower IQ.More K,L for one firm M means less for N.So lowers its output.

1. Efficiency in Production

0M

0N

IQ 1A

IQ2 A

IQ3 A

IQ 4A

LN

IQ2B

IQ3B

IQ4B

KM

IQ1B

LM

KN

a

b

c

d

f

Edgeworth box: Diagrams of isoquants of each individual firm M and N. Rotate that of N, and align the two to form a box.

Firm M’s isoquants are IQ1A, IQ2A, etc. (purple lines)

Firm N’s isoquants are IQ1B, IQ2B, etc. (blue lines).

OM is the origin for M, and ON is the origin for N.

Both firms compete for use of K and L. Each firm tries to reach its highest IQ. If M wants output of IQ4A, then N can

produce only IQ1B. If N wants to produce IQ4B, then M has to

produce IQ1A.Prabha Panth 11

At ‘f’ combination, M producing IQ2A, while N is producing output of IQ2B.

Is it possible to improve the situation? If they move to point ‘c’, then M can increase

output to IQ3A, and N can maintain its output at IQ2B. (all combinations on the same IQ show the same level of output).

Now M is better off, but N is not worse off. Similarly, if they move to point ‘b’, then N’s

output increases to IQ3B, but M’s output remains same at IQ2A as on point ‘f’.

N is better off, but M is not worse off. Such adjustments called “Pareto

improvements” – when it is possible to improve the welfare of one, without reducing another’s welfare.

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At point b and c, IQ of both firms are tangents to each other, (touch).

Similarly points a, b, c, and d. Joining together these points, gives

the “Contact Curve” of production. Moving along the contact curve

leads to improvement of one firm’s welfare (output), but decreases the other’s welfare (output).

Thus all points on the Contact curve are “Pareto Optimal” points.

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At each of these points, a, b, c, d, the slopes of their isoquants are the same.

Also slopes of their isocost curves are the same. We know that at equilibrium, slope of

isoquant = slope of isocost. Slopes of isoquants of M and N = MRTSA

= MRTSB

Slope of isocost of K and L for the two firms: = w/i At each of the equilibrium points ‘a b c d’ on

the contact curve, = MRTSA

= MRTSB = w/i

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PRODUCTION POSSIBILITY CURVE Edgeworth box shows output of A and

B with isoquants in input factor space. To convert to output factor space, the

two goods should be shown on the two axis (instead of K and L).

Can be done using the Production Possibility Curve (PPC), or the Product Transformation Curve (PTC).

The PPC shows the equilibrium outputs of A and B with different inputs of K,L.

It is the transformation of the contract curve on to the outer space.

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Transformation Curve shows alternative combinations of 2 goods that can be produced with given amounts of factor inputs.Points on Contact Curve abcd of Figure 1, shown in outer space.As Q of A rises, Q of B falls. Inverse relationship.PPC is convex outwards, the slope increases with increase in B. Diminishing returns.

Com

mod

ity

B

Commodity A

0

a

b

c

d

A1

A2

A3

A4

B1

B2

B3

B4

2. THE PRODUCTION

POSSIBILITY CURVE OR

TRANSFORMATION CURVE

The PPC shows how one good A is transformed into another B, by transferring resources from the production of A to that of B.

1) PPC is concave to the origin: To produce one more unit of B, more and more of A should be given up. Shows diminishing returns.

2) Slope of PPC: measures the Marginal Rate of Product Transformation : MRPT between the two goods.

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MRPT of A, B, shows the amount by which B has to fall, for A to rise, with the help of resources released by reducing B.

MRPTA,B = - dA = MCB ----------- (1) dB MCA

MRPT is the rate at which the economy can transform one commodity into another, through reallocation of K and L.

There is no unique Pareto optimum situation.

All points on the PPC are Pareto optimum.All points below the PPC are not efficient.

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In P.C. firms equate P = MC, so MCA = PA, MCB= PB.Slope of PPC = MRPTA,B = dB = MCA = PA -----(2) dA MCB PBGiven product prices, production equilibrium is the point where slope of PPC = ratio of product Ps. At point T on the diagram.CC is the Isocost curve, whose slope = Pa/PbAt T, OAT of A is produced and OBt of B is produced.Producers’ equilibrium, and Product Efficiency

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Com

mod

ity

B

Commodity A

0

T

PA/

PBA2

B2

3. PRODUCT EFFICIENCY

C

C

TO BE CONTINUED ----- PARETO OPTIMALITY 2

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