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consumer equilibrium in case of double commodity

October 15, 2025 admin Other 0

Consumer equilibrium in the case of two commodities (also known as the Law of Equi-Marginal Utility in the cardinal utility approach, or the Indifference Curve Analysis in the ordinal utility approach) refers to the point where a consumer maximizes their total satisfaction (utility) given their limited income and the prices of the two goods.1

This concept is explained using two main approaches:

1. Utility Analysis (Cardinal Approach)

This approach assumes utility can be measured in units (utils).2 The consumer attains equilibrium when the marginal utility per unit of money spent is equal for both commodities.3

Conditions for Equilibrium:

  1. The ratio of Marginal Utility to Price is the same for both goods:4Where:
    • = Marginal Utility of good X5
    • = Price of good X
    • = Marginal Utility of good Y6
    • = Price of good Y7
    • = Marginal Utility of Money (the constant utility derived from the last rupee/dollar spent).8
  2. The Law of Diminishing Marginal Utility (DMU) must operate: As the consumer consumes more of a good, its Marginal Utility must fall.9 This condition is necessary to ensure that the consumer actually reaches a state of rest (equilibrium).

Explanation:

  • If Px​MUx​​>Py​MUy​​:The marginal utility derived from the last rupee spent on good X is greater than that from good Y.10 The consumer is encouraged to buy more of X and less of Y.11 As consumption of X increases, 12MUx​ falls (due to DMU), and as consumption of Y decreases, 13MUy​ rises.14 This adjustment continues until 15Px​MUx​​=Py​MUy​​.16
  • If Px​MUx​​<Py​MUy​​:The marginal utility derived from the last rupee spent on good Y is greater than that from good X. The consumer is encouraged to buy more of Y and less of X.17 As consumption of Y increases, 18MUy​ falls, and as consumption of X decreases, 19MUx​ rises.20 This adjustment continues until 21Px​MUx​​=Py​MUy​​.22

2. Indifference Curve Analysis (Ordinal Approach)

This approach assumes utility can only be ranked (ordinal), not measured. Equilibrium is achieved at the point where the consumer’s budget allows them to reach the highest possible indifference curve.23

Conditions for Equilibrium:

  1. The Marginal Rate of Substitution (MRS) is equal to the Price Ratio:This occurs at the point where the Budget Line is tangent to the Indifference Curve.24
    • is the rate at which the consumer is willing to give up good Y for an additional unit of good X (the slope of the Indifference Curve).25
    • is the rate at which the market requires the consumer to give up good Y for an additional unit of good X (the slope of the Budget Line).26
  2. The Indifference Curve must be convex to the origin at the point of equilibrium:27This implies that the MRS is continuously diminishing as the consumer substitutes one good for the other.28 This condition ensures the point of tangency is a point of maximum satisfaction (equilibrium) and not a point of minimum satisfaction.

Graphical Representation:

The point of tangency between the budget line and the highest attainable indifference curve represents the consumer equilibrium.29 At this point, the consumer is spending all their income and maximizing their satisfaction.30