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Conditions of Paretian Social Optimum

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In this article we will discuss about the conditions of Paretian Social Optimum.

Pareto’s “Manual of Political Economy” (1906) represents a decisive watershed in the history of subjective welfare economics. Pareto broke away from the traditional utilitarian economics. He rejected the hypothesis based on cardinal utility and also the additive utility function and arrived at his welfare conclusions which do not require any inter-personal comparison what so ever. Some have therefore called Paretian welfare economics as “New Welfare Economics”.

Pareto had three objectives in mind in giving his concept of the social optimum:

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1. To clarify and quantify the concept of economic welfare.

2. To develop welfare propositions which are “scientifically” free of value – judgements.

3. To clearly state what it is that economists have to say on matters of public policy.

Social Optimum:

Pareto defined social optimum as a position from which no reorganization of production and exchange can be effected to make anyone better off without making somebody else worse off.

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Pareto’s welfare criterion:

From the Paretian concept of social optimum follows his criterion for judging an increase or decrease in welfare. The criterion may be stated thus: given some form of distribution, a reorganization of production and exchange would increase social welfare, if it makes at-least one person better off without harming anyone else. Since the criterion requires that there should be unanimity among individuals about the maintenance of the condition in which welfare has increased, it is also called “Pareto’s Unanimity Rule”.

Conditions:

The concept of the social optimum given by Pareto was introduced into the English language by A.P. Lerner and J.R. Hicks. Lerner detailed the conditions of production and exchange which are necessary for the attainment of social optimum in the form of marginal equalities and hence are called “Marginal conditions”. Prof. Hicks pointed out that besides these marginal on first order conditions, there are other conditions which must be satisfied to ensure that these marginal conditions define a maximum. These are referred to as total or second order conditions.

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Assumptions:

The assumptions underlying the Pareto social optimum are:

1. Individual ordinal utility functions remain invariant when economic changes are effected.

2. Each individual owns definite quantities of each product and factor.

3. The individual attempts to maximise his satisfaction.

4. Each producer strives to earn maximum profit and is in equilibrium only when producing at the lowest average cost.

5. Each firm has a given transformation function determined by the given technology.

The conditions can be stated geometrically.

I. Optimum allocation of products:

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The allocation of products between individuals can be optimal only when the Marginal Rate of Substitution (MRS) between any two goods is the same for any pair of individuals owning the two goods. If MRS between any two goods is not the same for any two individuals, they can enter into exchange which would increase the satisfaction of both or one without diminishing that of the other.

II. Optimum allocation of factors:

The marginal rate of technical substitution between any pair of factors must be the same for any two firms using both to produce a given product. If this condition is satisfied, it is not possible to produce any more of a good without producing Jess of some other goods, if the condition is not satisfied, there remains a possibility of increasing total production by shifting resources from one firm to the other.

III. Optimum degree of specialization:

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This condition determines the optimum output of each product to be produced by each firm. This will prevail when the marginal rate of transformation between any two goods is the same for any two firms which produce both the products. Marginal Rate of Transformation between two goods is the rate at which one good must be sacrificed to obtain more of the other good without varying the input used. Thus if MRT between two goods is not the same for the two firms, it would always be possible to increase the combined output of both the goods on at-least one of them.

IV. Optimum factor utilisation:

This condition states that the marginal rate of transformation between any factor and any product must be the same for any pair of firms using the factor and producing the product”. It means that the marginal productivity of any factor in producing a particular product must be the same for all the firms. If the marginal productivity of factor to produce a given product is low, the total product would increase by transferring some units of the factor to the high productivity firm.

V. Optimum direction of Production:

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This condition relates to the substitution of products to conform to the structure of consumer’s preferences. The general optimum will be attained only when exchange optimum in the consuming sector and production optimum in the producing sector are simultaneously reached. It requires that the subjective rate of substitution between two products for any pair of individuals must be equal to the objective rate of transformation for all pairs of goods in the economy.

VI. Optimum allocation of a factor — unit’s time:

The condition relates to the substitution of leisure for work on product on intensity of use of factors. It states that the marginal rate of substitution between leisure and work must be the same as the marginal rate of transformation between work and its product for the community as a whole. The private rate of substitution between leisure and work for every factor must equal the social rate.

VII. Optimum inter — temporal allocation of assets:

This condition requires that “The marginal temporal rate of transformation between every pair of factors and products as well as the marginal temporal rate of substitution between every pair of factors and between every pair of products must be equal to the rate of interest on riskless securities”.

It therefore relates to borrowing and lending between producers in the absence of risk or uncertainty. This condition implies that the rate of interest at which an individual producer is willing to lend a given amount of capital must equal its marginal productivity to the borrowing producer.

The Second Order and Total Conditions:

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To ensure that the marginal conditions define a maximum, it should be supplemented with some second order conditions. These second order conditions require that in the neighbourhood of the optimum all indifference curves must be convex to the origin and all transformation curves must be concave to it.

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