Maximum Social Welfare and Perfect Competition (Analysis with Indifference Curves)

Readers might be very familiar with Indifference Curve technique, studied under elementary economics, for maximization of satisfaction or maximization of production with available resources. Similar technique can be used for analyzing the concept of maximum social welfare with available resources to indicate that perfect competition is a necessary condition for achieving Pareto’s efficiency of Optimum Welfare.

We can start with household equilibrium in consumption with
Indifference Curve technique, as indicated in the Figure 4.2 below. In the figure, WC1, WC2, WC3 etc., indicate levels of welfare (satisfaction in consumption of two commodities of the household X and Y) with given quantum resources for the household.

The assumption is that the household behaves rationally and attempt to maximize their economic welfare by selecting the largest and best collection of goods X and Y with its resources. Further, we assume perfect competition in the market, and prices of X and Y remain constant.

Higher WC indicates higher levels of satisfaction, i.e., welfare. The consumption possibility line with given prices of X and Y is AB which is called the budget line of the household.

Fig. 4.2 Household Equilibrium : Maximum Social Welfare and Perfect Competition

The household can allocate the resources in any way it likes by moving on the budget line AB, selecting X and Y commodities. The convex nature of the indifference curves (i.e., Welfare Curves WC1, WC2, etc.) indicates that the significance of X commodity diminishes, as it chooses more of X rejecting some of Y commodity and vice versa. The marginal rate of substitution between X and Y commodities diminishes, as the household chooses to travel down on the WC.

In the indifference curve technique, we know that the equilibrium point of the consumer can be found out by superimposing the indifference map on the budget line, spotting the point where the budget line is tangential to the indifference curve.

In the same manner, here too, we spot out the equilibrium point E on the curve WC2 where the budget line is tangential. The household cannot reach WC3 (higher welfare) with the available means and prices of the two commodities. Though the household can choose a lower point, the assumption of rationality and maximization of satisfaction takes us to the point E the maximum attainable point in the welfare curves.

In indifference curve analysis, the slope of the budget line or the price line represents the ratio of the prices of two commodities, i.e., X and Y. In the figure:

OA /OB=Px / Py (P, is the price of X commodity and Py the price of Y commodity).

Further, at the point E (Equilibrium), the slope of budget line AB and the slope of WC2 are the same. We have studied under ‘Indifference Curve’ analysis that the slope of the indifference curve represents the marginal rate of substitution of X and Y commodities and the slope of the price line, i.e., budget line indicates the ratio of prices of two goods.

Hence, at equilibrium point, the marginal rate of substitution between two goods is equal to the ratio of their prices.

That is at equilibrium MRSxy = Px/Py

In the same way, in this analysis, we take the optimal point E on the WC2 (welfare curve) where the slope of the welfare curve is equal to the slope of the budget line. To restate, we can say:

Price of X commodity/Price of Y commodity= Marginal welfare of X /Marginal welfare of Y

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