8 Indifference Curve Analysis-II

Kamal Singh

 

INSTRUCTIONAL OBJECTIVES

 

At the end of this chapter, learner should be able to understand:

  • 1) Price Effect
  • a) Price consumption curve
  • 2) Income effect
  • a) Income consumption curve
  • b) Normal and Inferior goods
  • 3) Substitution effect
  • 4) Decomposition of Price effect into Income and Substitution effect
  • 5) Giffen goods

(Keyword: Indifference curves, Budget Line, Price effect, Income effect, Inferior goods, Normal goods, Giffen goods and Substitution effect)

 

Breaking Price effect into Income effect and Substitution Effect

 

Under Indifference curve analysis, you have studied that under Indifference curve analysis , consumer equilibrium can be attained with the help of indifference curve analysis . Consumer equilibrium can be achieved if two conditions are fulfilled, one at the point of equilibrium indifference curve (IC) should be tangent to budget line or the slope of IC = slope of budget line i.e. MRSXY = − . Second at the point of tangency indifference curve should be convex to the origin.

 

In the proceeding sections we will study once the consumer equilibrium is attained , if certain changes occurs say consumer income changes or prices of relative good changes how consumer adjust to these changes .When the consumer money income changes alone , prices of goods , taste etc remain same the resultant effect is called as income effect . When the price of only one good varies alone keeping the income, other good price and other factors constant the effect is called price effect. So price effect shows that when price of good changes its demand also changes example with fall in price of good its demand increases according to law of demand. Further we will discuss how the price effect consists of two effects one is income effect and other is substitution effect. We also discuss how price effect is decomposed and income effect and substitution effect are isolated from price effect. The study of these effects and decomposition will lead to understand the different types of goods which we use and study in economics along with new insight into law of demand will be studied.

 

Price Effect and Price Consumption Curve

 

In the following section, we shall study about price effect, price consumption curve and how demand curve can be derived using price consumption curve.

 

According to law of demand, price and quantity demanded are inversely related i.e. when the price of good changes its quantity demanded also changes but in opposite direction keeping other factors constant. When the price of good changes but the price of another good and money income of the consumer remains constant, quantity demanded also changes but in opposite direction of price changes, this effect is called price effect. Example, Let us take two goods X and Y, Px and Pyare the prices of good Xand good Y , M is consumer money income . Now if the price of good X changes , keeping the price of Y and M constant, the quantity demanded of X will also change, if price of good falls, quantity demanded will increase and vice versa. So, Price effect is the change in the consumption basket of the consumer, which takes place due to change in the price alone. Price effect is explained in the following figure number 1.

 

FIGURE 1

 

Good X and Good Y is measured along horizontal and vertical axis, initially BL is the Budget line and U1 is the Indifference curve, consumer is at equilibrium at point E, where indifference curve is tangent to budget line and at the point of tangency IC is convex to the origin.At point E, consumer is consuming OX of good X and OY of Y good. Now the price of good X falls but the price of good Y and his money income M is constant. Now the budget line tilts outward and becomes BL1 and new consumer equilibrium is formed at point E1 , where new IC , U2 becomestangent to new budget line BL1 at this point consumer consumes OX1 of good X and OY1 of good Y , similarly when again price of good X fall again the price of good Y and consumer money income is constant , another equilibrium is formed at E2, where budget line is BL2 and IC is U3. If we join all the equilibrium point i.e E, E1 and E2 we get a curve called price consumption curve (PCC) which is the locus of points of consumer equilibrium resulting from changes in the price of good X alone other things remaining constant.

 

Derivation of Demand Curve

 

Price consumption curve traces the effect of changes in price when all other factors affecting demand remain same. Through Price consumption curve demand curve can also be derived. Derivation of demand curve is shown in figure 2

 

FIGURE 2

 

The above figure has two panel panel A and panel B, in panel A price effect is explained and in panel B , demand curve is derived. Price effect is explained in above paragraph, PCC was formed by joining three equilibrium points i.e E, E1 and E2 . In panel B ,price of good X is plotted in vertical axis and quantity demanded of good X is plotted in horizontal axis. All the three points of panel A are traced vertically in panel B, so we can see that at Point E , 2 units of good X are consumed at point E1 ,4 unit and at E2 , 6 units of good X are demanded. Corresponding to point E ,  E1 and E2 in vertically axis price is Rs 6, Rs 4 and Rs 2. When all these points are joined we get a downward sloping curve DD which shows that as price of good X falls, quantity demanded of good X increases vice versa and ceteris paribus. This curve is demand curve for good X.

 

Income Effect

 

Income is an important variable which influences the consumption decision of the consumer, level of income of the consumer is the budget constraint within which consumer has to make his consumption decision. When the consumer income increases, he/she can consume more of goods and services and when the income falls he is forced to consume less provided that other factors which influence the demand are constant. Changes in the consumer consumption decision are traced by income effect and income consumption curve. Income effect is the effect in the consumption equilibrium or his consumption basket which results because of changes in consumer real income keeping the prices of goods and services , consumer taste and preferences as constant. Income effect and income consumption curve is explained in figure 3

 

Good X and Y are plotted in horizontal and vertical axis. Initially U1 is the indifference curve and BL1 is the budget line. Consumer equilibrium is at point E1 , where two conditions of consumer equilibrium are attained, consumer consumes OX of good X and OY of good Y. Let the consumer income changes (increases) but other factors remains same, so the budget line shifts upward to B1 L1 and new consumer equilibrium is attained at E2 , with new IC i.e. U2 where consumer consumes more of good X and good Y i.e. OX1 and OY1 . Similarly again when consumer income increases new budget line B2 L2 is formed and new consumer equilibrium is formed with IC, U3at point E3 here again consumer consumes more of good X and good Y. When all the three consumer equilibrium points i.e. E1 , E2 and E3 are joined a curve is derived called Income Consumption Curve which traces the changes in consumer equilibrium which is result of changes in consumer income ceteris paribus .Income effect can be both positive and negative. Income effect for a good is called positive, if with increase in income of the consumer he consumes more of that good. The goods which exhibit positive income effect are called normal good or superior goods, means their demand increases as the income of the consumer increases. Similarly income effect for a good is called negative if with increase in income, consumer consumes less of that good. The goods which have negative income effect are called inferior goods example bajra, millet etc. So in case of inferior good (and giffen goods), there demand falls with increase in the income of consumer. Income effect for inferior good is explained in Figure 4

 

FIGURE 4

 

In figure 4, initially budget line is BL and indifference curve is U1 consumer equilibrium occurs at point I, here the consumer consumes OX of X good, now the income of the consumer increases so budget line shifts to MN and new IC is U2 and new consumer equilibrium occurs at point H , here the consumption of good X becomes OX1 , similarly further when income increases new equilibrium is at point K , with budget line RS and IC U3 . here consumption of X is OX2 , in this figure ICC bends towards Y axis which represent that when the income of consumer increases, consumption of good X falls , so we may say that good X is inferior because the demand for good X falls with increase in income of the consumer . Similar diagram can be drawn for if we consider good Y as inferior in this ICC will bends towards X axis.

 

Substitution Effect

 

Substitute goods and complementary goods are two important categories of goods in economics. Substitute goods are also called competitive good and they can be used in place of one another. If the price of one good changes it has impact on the demand of another good e.g Tea and Coffee, when the price of tea falls relative to price of coffee (price of coffee remains same) , demanded for tea increases and that of coffee falls. Substitution effect traces this effect of change in price of one good and effect on demand for another good. Substitution effect takes places because of change in the relative prices. Under substitution effect when the price of one good fall (or Increases) it become relatively cheaper ( or dearer) than the other, in this case consumer will substitute cheaper good to dearer good or he will buy more of cheap good and less of expensive good which has become expensive because of fall in the price of its substitute. Substitution effect is always negative which means that relative price of a commodity and its quantity demanded they change in opposite direction. It measures the increase in the quantity demanded of a good when its price falls resulting only from the relative price decline and is independent of change in real income.

 

Decomposition of Price Effect into Income and Substitution effect

 

In the previous paragraph we studied about price effect. This effect explains that when price changes consumer equilibrium changes and more specifically when the price of a good fall all other factors remaining same its demand increases. This is happens because of two effects, income effect and other substitution effect. These two effects are of immense important in economics because on the basis of these effect we can distinguish between different types of goods namely normal, inferior and giffen goods and this is also used to explain why in certain cases demand curve slopes upward or why in certain cases law of demand does not holds valid.

 

There are two approaches to decompose the price effect into income and substitution effect. For the decomposition it is imperative to hold real income constant. Once we are able to hold the real income constant, we can measure the change in quantity demanded due to substitution effect and the remaining change in quantity represent the change due to income effect. To keep the real income constant, there are mainly two methods suggested in economic literature:

  1. The Hicksian Method
  2. The Slutskian method

 

According to Hicksian method of eliminating income effect, we reduces the consumer’s money income i.e. by taxation, so that the consumer remains on his original indifference curve IC1. The decomposition of price effect into income and substitution effect with the help of Hicksian approach is explained in the following figure .

 

FIGURE 5

 

Initially BL is the budget line and U1 is the indifference curve, consumer equilibrium is at point P, where consumer consumes OX of good X and OY of good Y. Price of good X falls keeping price of good Y and his money income same, now the budget tilts and become BM and new equilibrium is formed at point Z with IC, U2. At point Z, consumer consumes OX2 of good X, the movement from point P to Z is called price effect. This price effect is made of two effect income and substitution effect. Following Hicks approach and to keep his real income constant he is taxed and his increase real income is taxed so that he remains on same indifference curve or his level of satisfaction remains same. We draw another budget line TS which is parallel to new budget line BM which shows that equal amount of income is taken away from consumer (amount equal to increase in real income ) this new budget line is tangent to old indifference curve U1 which shows that consumer level of satisfaction is unaltered he is at old level of satisfaction. Movement from point P to point R is substitution effect because this increase in quantity demanded of good X is result of change in relative price. Means when the price of good X relative good Y, good X become cheaper to its substitute and consumer consumes more of cheap good than costly good. So increase in quantity of good X from OX to OX1 is substitution effect. Movement from point R to point Z is income effect , because if consumer’s income is not held constant he will move from point R to Z means with increase in consumer income his consumption of good X will also increase . So increase in quantity demanded to good X with fall in price of good X is because of income effect.

 

So

 

Price effect is XX2 , Substitution effect is XX1 and Income effect is X1 X2 , so we can show that

Price Effect       =             Substitution Effect      +             Income Effect

XX2                     =                             XX1                      +              X1X2

 

Income effect and substitution effect of price change in case of Normal, Inferior and Giffen goods.

 

Normal goods: In case of normal goods, income effect is positive i.e with increase in income, demand for normal goods also increases. The substitution effect is always negative meaning that when the price of normal good fall it becomes cheaper to its substitute, and consumer will buy more of cheaper good than expensive good so itsthe demand increases. Finally the price effect indicate that when the price of normal good fall its demand increases. So the law of demand holds valid and demand curve slopes downwards.

 

Inferior goods: In case of inferior goods , income effect is negative i.e with increase in income , demand for inferior goods falls as discussed in preceding paragraphs. The substitution effect is always negative meaning that when the price of inferior good fall it becomes cheaper to its substitute, so the demand increases. In case of inferior goods, the substitution effect is strong and outweighs the negative income effect so the final effect i.e. price effect is indicate that when the price of inferior good fall the demand increases . So the law of demand holds valid and demand curve slopes downwards.

 

Giffen goods: Giffen goods are named after British Economist Sir Robert Giffen , these goods are special case of inferior goods. In case of giffen good, income effect is negative i.e with increase in income, demand for giffen good falls. The substitution effect is always negative meaning that when the price of giffen good fall it become cheaper to its substitute, so the demand its increases. In case of giffen good, the substitution effect is weak and is outweighed by the negative income effect; so the final effect i.e. price effect is indicate that when the price of giffen good fall the demand also falls . So the law of demand does not hold valid and demand curve slopes upward.

 

Conclusion

 

Price effect, income effect and substitution effect are one of the most important concepts in the micro economic theory. Income effect traces the effect in consumer consumption decision when the income alone changes keeping other factors constant. This effect help us to understand about the normal and inferior goods. Substitution effect traces the effects in consumer equilibrium when the relative price changes alone other factors are constant. Price effect traces what happens when the price of good alone keeping other factors as constant . The decompostition of price effect into income and substitution effect is of pertinent use. The decompostition highlights that the price effect is in fact the combination of income and substitution effect . When the price of a good changes two changes undertake place. One the consumer real income increases and because of change in his real income he buys more of that good. Second the good whose price has fallen become cheaper in relation to other good , so the consumer purchases more of cheaper good and less of expensive good, so when price falls , demand increases partly due change in real income of consumer and partly because now the good has become cheaper than its substitute. Second important issue which is highlighted by this decomposition is that it traces out the exception to law of demand or in which cases, the demand curve slope upward also . This case is highlighted when the negative income effect outweighs the substitution effect. Similarly we have seen that to decompose the price effect , it is important to isolate the income and substitution effect . For this there are two approaches Hicksian and Slutsky approach which keeps the real income of consumer constant and because of this it becomes very easy to isolate substitution effect from income effect .

 

Sources for Further Reading on Indifference curve analysis.

  • Francis Y. Edgeworth , Mahematical Physics , London, C.R. Paul &Co., 1881
  • Hicks, John, and R. G. D. Allen.(1934), “ A reconsideration of the theory of Value”, Economia , Feb-May, 1934
  • A.W. Stonier and D.C. Hague, A textbook of Economic Theory, London, Longman, 1972
  • Hicks, John R., Value and Capital , 2nd Edition (Oxford University Press, 1946)
  • Maddala ,G.S and Ellen.,Miller., Micro Economics Theory and Practice, Tata McGraw Hill, New Delhi
  • Dwivedi , D.N., Microeconomics Theory and Application , Pearson Education , New Delhi.
  • Pindyck, Robert, D.L , Rubinfeld,., and P.L.Mehta, Microeconomics Sixth Edition, Pearson Education
  • Koutsoyiannis, A. (1990), Modern Microeconomics, Macmillan.
  • Varian H. (2000), Microeconomic Analysis, W.W. Norton, New York.