PARETO OPTIMALITY Continued -- 2

Prof. Prabha Panth,Osmania University,

Hyderabad

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2. Equilibrium in ConsumptionThere is equilibrium in Consumer Market also.Two consumers X and Y, both consume the two

goods A and B.Prices of both goods are given.Law of Diminishing MU applies.Income of consumers is given,Also tastes, preferences, etc. Total Q of A and B fixed by producing firms M, N.

If X increases his consumption of A&B, Y has to decrease his consumption.

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4. Efficiency in Consumption

0X

0Y

BX

AY

IC 1X

IC2 X

IC3 X

IC4X

BY

IC2Y

IC3Y

IC4Y

AX

IC1Y

1

2

3

4

5

As in the case of production, draw the Edgeworth box for consumption.

Taking Indifference curves of consumers X and Y, for the two goods A and B.

As X increases his consumption from IC1A to IC4A, B has to decrease his from ICB4 to ICB1.

At 5, the ICs of both X and Y intersect, with X on IC1X, and Y on IC3Y.

Is it possible to improve this situation?If X moves to point 2, he will be on a higher IC =

IC2X, while Y will be on the same IC3Y. So X improves his welfare (consumption), but no change in Y. X is better off, Y is not worse off.

So point 5 is not an efficient position.Prabha Panth 4

If Y moves to IC4Y, then he will be on a higher IC at point 1. But X will remain on the same IC2X. So at point 1, Y is better off, but X is not worse off.

This is known as Pareto Improvement.All points where the two IC curves of the two

consumers are tangents to (touch) each other, are points of equilibrium, = 1, 2, 3, 4.

Joining them gives the Contact curve of consumption, OX 1, 2, 3, 4 OY.

These are all Pareto optimal points.Moving from one to another point on the Contact

curve, it is not possible for one consumer to increase his consumption, without another one’s decreasing.

But no unique equilibrium point.Prabha Panth 5

Take any one point on the Contact Curve, e.g. 2 with X on IC2X and Y on IC3Y.

The budget line drawn to it (dotted line) shows the ratio of the prices of A and B.

The slope of the Indifference curves shows the Marginal rate of substitution, MRSA,B.

The slopes of the two IC and that of their Budget lines are same on each point on the Contact curve.

At point 2, the slope of IC2X = IC3Y = PB/PAMRSx = MRSy = PB/PA => Equilibrium And so on for each of the points on the contact

curve. No unique equilibrium.

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General Equilibrium Equilibrium in Production, Consumption, and

Factor markets.Prices of goods (Pa, and Pb) and Factor prices

(w, i) are given.Equilibrium of both consumption and production

to be achieved simultaneously.Superimpose the Edgeworth box of

consumption on the PPC to find the General equilibrium point for a two goods, two consumers, two firms and two factors market.

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Com

mod

ity B

Commodity A0 a

EB

5. GENERAL EQUILIBRIUM

IC1X

IC2 X

IC3 X

IC2Y

IC3Y

IC4Y1

2

3

Pa/ Pb

A

b

p

pPa/

Pb

In figure 5, Commodities A and B are measured on the two axis.

Edgeworth box of consumption is fitted within the PPC of production.

Point E, where it touches the PPC.Shows the maximum A and B that can be produced: 0A

and 0B.These have to be shared between the two consumers

X and Y.Slope of the PPC at point E gives the prices of the two

goods: PA/PB.Draw a line parallel to pp in the inner space.Find the point where it is tangent to any set of IC

curves (e.g. at point 2)

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At point 2, the slope of the Price line pp is same as slope of the two IC curves.

Or, MRSX = MRSY = Pa/PbtPoint E which is on the PPC also shows the ratio

of prices Pa/Pb, This is the equilibrium of Production.Hence E is the point of General Equilibrium Here, both consumption and production are

determined simultaneously.

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But, it is not a unique point.If there is any change in the relative prices, then the

equilibrium will change.This will change allocations, employment, and

output.Is based on given prices of goods and factors.Does not show how they are determined.Based on perfect competition in both product and

factor markets.Not if there is imperfect competition in any market.Difficult to show in the case of multiple goods

markets.

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Questions (both 1 and 2)Short questions:

What is general equilibrium? How does it differ from partial equilibrium?

Explain the meaning of “Pareto optimality” and “Pareto improvement”.

Draw an Edgeworth box of a) production, and b) consumption. Explain how it works.

What is a contract curve? What is its significance?What is a Production Possibility Curve? How is it

derived? And what is its significance?

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Essay Questions:Explain how Production equilibrium is achieved in a

Pareto optimal model.How is equilibrium achieved in the consumer’s market

with two consumers, and two goods?Show with the help of diagrams, how general

equilibrium is achieved in a Pareto model.What are the limitations of the Pareto model of

General Equilibrium?

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