Consumer Equilibrium Under Indifference Curve Analysis

“A consumer is said to be in equilibrium at a point where the price line is touching the highest attainable indifference curve from below”

 “The term consumer’s equilibrium refers to the amount of goods and services which the consumer may buy in the market given his income and given prices of goods in the market, that give maximum satisfaction to consumer”.

The aim of the consumer is to get maximum satisfaction from his money income, given the price line or budget line and the indifference map.

Assumptions of Consumer’s Equilibrium

  1. The consumer has Indifference Map of good X and Good Y
  2. The consumer have a fixed money income which are spend on X and Y
  3. The Prices of good X –Px and good Y – Py are given
  4. Good are homogenous
  5. Goods are divisible
  6. The consumer acts rationally and tries to maximise his satisfaction.
  7. No change in tastes and habits of consumer
  8. Perfect competition.

Conditions of Consumer’s Equilibrium under Indifference Curve Analysis

First order condition :  Necessary Condition

Budget Line Should be Tangent to the Indifference Curve: A given price line should be tangent to an indifference curve or marginal rate of substitution of good X for good Y (MRSxy=∆Y/∆X) must be equal to the price ratio of the two goods. i.e.

MRSxy = Px / Py

Slope of the Price Line to be Equal to the Slope of Indifference Curve

: Price of X / Price of Y = MRS of X for Y

Second order condition: Sufficient Condition

The second order condition is that indifference curve must be convex to the origin at the point of tangency. It means marginal rate of substitution of good X for good Y (MRSxy=∆Y/∆X) is diminishing.                                     

Income, Substitution and Price Effect:

Consumer’s equilibrium is affected by change in his income, change in the price of substitutes, and change in the price of good consumed. These changes are known as (1) Income effect (2) Substitution effect and (3) Price effect, respectively.

1. Income Effect

The income effect may be defined as the effect on the purchases of the consumer caused by change in income, if price remains constant. Income effect indicates that, other things being equal, increase in income increases the satisfaction of the consumer. As a result, equilibrium point shifts upward to the right. On the contrary, decrease in income decrease the satisfaction of the consumer and his equilibrium point shifts downwards to the left.

In this diagram consumer’s initial equilibrium is at point E2 on price line A2B2. When his income increases, his equilibrium point shifts to the right i.e. E3 on price line A3B3. With decrease in his income, his equilibrium point shifts to the left i.e. E1 on price line A1B1.

Locus of all these equilibrium points is called income consumption curve. It starts from the point of origin 0 meaning thereby that when the income of the consumer is zero, his consumption of apples and oranges will also be zero.

Income Consumption Curve:

This curve is a locus of tangency points of price lines and indifference curves.

Income consumption curve refers to the effect of change in income on the equilibrium of the consumer.

Slope of income consumption curve is positive in case of normal goods, but it is negative in case of inferior goods.

Kinds of Income Effect

(i) Positive Income Effect: Income consumption curve is positive in case of normal goods. In other words, consumption of both normal goods (x and y) increases with increase in income. As shown in the diagram, income consumption curve (ICC) of normal goods slopes upwards from left to right signifying that more of both the goods will be bought when income increases. ICC curve indicates that expenditure on both the goods will increase in almost the same ratio.

(ii) Negative Income Effect:

Income effect of inferior goods is negative. It means inferior goods are brought in less quantity when income of the consumer increases. Suppose x-good ( Wheat) is inferior and y-good( Rice) is normal. This decline in quantity demanded reflects negative income effect.

By joining together different equilibrium points one gets income consumption curve which slopes backward to the left. It indicates negative income effect.

(iii) Zero Income Effect: With the change in income, there is no change in the quantity purchased of a commodity.

Income Effect with change in real income change

The real income effect rests on the observation that a change in price affects the purchasing power of a given amount of income.

  • Higher Price: An increase in price causes a decrease in the purchasing power of income. This restricts the ability to purchase a good and the quantity demanded decreases.
  • Lower Price: A decrease in price causes an increase in the purchasing power of income. This enhances the ability to purchase a good and the quantity demanded increases.
  1. Substitution Effect:

Given the constant income, if with the change in the prices of goods, the consumer will substitute relatively lower-priced good for higher-priced ones. Consequently, it will affect the quantity purchased of both the goods. This effect is known as substitution effect.

Substitution effect shows the change in the quantity of the goods purchased due to change in the relative prices alone while money income remains constant.

For instance, a consumer consumes burgers and hot dogs. If the price of burgers goes up, but the price of hot dogs stays the same, you might be more inclined to buy a hotdog. This tendency to change your purchase based on changes in relative price is called the substitution effect.

When the price of burgers goes up, it makes burgers relatively expensive and hot dogs relatively cheap, which influences you to buy fewer burgers and more hot dogs than you usually would. Likewise, a decrease in burger price would cause you to eat more burgers and fewer hot dogs, according to the substitution effect.

In figure 2, the initial equilibrium of the consumer is E1, where indifference curve IC1is tangent to the budget line AB1. At this equilibrium point, the consumer consumes E1X1 quantity of commodity Y and OXquantity of commodity X.

Assume that the price of commodity X decreases (income and the price of other commodity remain constant). This result in the new budget line is AB2. Hence, the consumer moves to the new equilibrium point E3, where new budget line AB2 is tangent to IC2.

Thus, there is an increase in the quantity demanded of commodity X from X1 to X2.

An increase in the quantity demanded of commodity X is caused by both income effect and substitution effect. Now we need to separate these two effects. In order to do so, we need to keep the real income constant i.e., eliminating the income effect to calculate substitution effect.

According to Hicksian method of eliminating income effect, we just reduce consumer’s money income (by way of taxation), so that the consumer remains on his original indifference curve IC1, keeping in view the fall in the price of commodity X. In figure 2, reduction in consumer’s money income is done by drawing a price line (A3B3) parallel to AB2. At the same time, the new parallel price line (A3B3) is tangent to indifference curve IC1 at point E2.

Hence, the consumer’s equilibrium changes from E1 to E2. This means that an increase in quantity demanded of commodity X from X1 to X3 is purely because of the substitution effect. AA3 or B2B3 is called compensating variation in income.

  1. Price – Effect:

Price effect means change in the consumption of goods when the price of either of the two goods changes, while the price of the other good and the income of the consumer remain constant.

When the price of a commodity changes, it has two effects:

(i) There is change in the real income of the consumer leading to change in his consumption. It is called income effect;

(ii) Secondly, due to change in relative prices, the consumer substitutes relatively cheaper goods for the dearer ones. It is called substitution effect. The combination of this income and substitution effect is called price effect.

Supposing IC1 is the original indifference curve and AB the original price line and consumer is in equilibrium at point T1. As the price of Good X falls, price line will shift to AC which touches higher indifference curve IC2 at point T2. It means fall in price of any good will increase the satisfaction of the consumer.

On the contrary, if the price of Good X falls further, the new price line will be AD which will touch the higher indifference curve IC3at point T3, the new equilibrium point.

By joining together different equilibrium points T1, T2 and T3 one gets the price consumption curve (PCC). The price consumption curve for commodity X is the locus of points of consumer’s equilibrium when the price of only X varies, the price of Y and income of the consumer remaining constant.

Unrelated Goods

Substitution Effect will always be non-positive (i.e., negative or zero). Unlike the Substitution Effect, the Income Effect can be both positive and negative depending on whether the product is a normal or inferior good.

Price Effect is the Sum of Substitution Effect and Income Effect

Thus, Price Effect = Income Effect + Substitution Effect.

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By Hassham

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