Subject Paper No and Title Module No and Title Module Tag 3: Fundamentals of Microeconomic Theory 5: Applications of Indifference curve ECO_P3_M5
TABLE OF CONTENTS 1. Learning Outcomes 2. Introduction 3. Measuring income effects of income and excise taxes 4. Measuring effect of excise and income subsidies 5. Income and substitution effects of price change: normal goods 6. Income and substitution effects of price change: Inferior goods 7. Giffen paradox 8. Summary
1. Learning Outcomes After studying this module, you shall be able to Know the effect of government taxation and subsidization policies with the help of IC Learn how income tax and excise duty affect the welfare of the society Learn how the subsidies (income and price) affects the economic welfare of the society Evaluate the price effect as per Hicksian and Slutsky approach Analyse the Giffen paradox 2. Introduction Indifference curve approach can be used to get the solution of the problems of the real world. It can be used to evaluate the government policies, e.g., taxation, subsidy and rationing policies; determining the gain from exchange of commodities between the individuals, sectors and countries, derivation of labor supply curve, indexing cost of living, etc. Hence, in this chapter, we will demonstrate the applications of indifference curve technique to some real world problems. 3. Measuring income effects of income and excise taxes Choice between taxes There are two types of taxes which government imposes on its citizens. One is direct tax like the income tax and the other is indirect tax like the excise duty. It has been argued that direct taxes are always better and preferable than the indirect taxes because income tax put a lower burden on the taxpayer than the indirect tax of equal amount, i.e. the negative welfare effect of direct tax is lower than that of indirect tax. The relative burden of income and indirect tax is shown in the following diagram with the help of IC. Let us suppose that the consumer has OM money income which he spends for buying commodity X. Given the price of X, his budget line is MT. Now in the absence of any tax, the consumer would be in equilibrium at point E3 on indifference curve IC3 as shown in fig 1 below. Now suppose the government imposes excise duty on X, due to which the price of X will rise so that his budget line MT shifts to MR. As a result, consumer's equilibrium will shift to E1 on a lower indifference curve IC1. At equilibrium E1, the consumer buys OQ units of X and pays MP =JE1 for it. In the absence of the excise tax, OQ (=NK) units
of X could have been purchased only for JK (=MN) of consumer's income. It means that the excess payment that equals JE1 JK = KE1 is the excise tax. Fig 1: Direct tax v/s indirect tax Now, let s replace the excise tax with income tax so that the same amount of revenue (i.e., KE1) can be collected through the income tax. This can be shown by drawing an imaginary budget line NS passing through the equilibrium point E1 which is also parallel to the original budget line MT. Since budget line NS is parallel to the initial budget line MT, therefore income tax MN equals excise tax KE1. Now the budget line NS indicates that the consumer pays income tax which is equal to the excise duty but he moves on to an upper indifference curve IC2 where his equilibrium point becomes E2. Thus, income tax of an equal amount brings the consumer on a higher indifference curve than does the excise tax, because an excise tax, which changes the price structure, imposes both income and substitution effects on the consumer's choice whereas income tax imposes only income effect. Therefore, an excise tax reduces consumer's satisfaction or welfare due to both income and substitution effects whereas income tax reduces it only to the extent of income effect. Thus, clearly the income tax is better from the point of view of the consumers where the government gets equal amount of revenue in both the cases.
4. Measuring effect of excise and income subsidies Let us suppose that the government is planning to raise the standard of living of the poor people by providing them subsidy. Now the subsidy could be given in two ways. First in the form of income subsidy which comprises of lump sum money grant and the second is the excise subsidy provided in the form of food subsidy, rent subsidy or loan subsidy. Now the main task is to evaluate which one would cost less to the government and which subsidy is preferable by the consumers? For this let us take a case of the choice between the income subsidy and excise subsidy on commodity X In the following fig 2, x- axis evaluates the quantity of X and y- axis indicates the income. In the absence of any subsidy, the consumer s budget line is MN1 and he is initially at E1 equilibrium point where his IC is tangent on his budget line and thus he consumes OX1 units of X for which he pays MP of his income and retains OP for other goods. Fig 2: Income subsidy v/s Excise subsidy Now if the government reduces the price of X by half i.e. 50% then the budget line will move to MN3 and the consumer equilibrium will be at E3 where he consumes OX3 units of X for which he pays DM of his income. However, if this subsidy would not have been given to him then he would have paid MB of his income for the purchase of the same quantity of X i.e. OX3. Hence DB (MB MD) is the cost of subsidy which the government pays to the consumer for commodity X.
However, if the government would have provided the income subsidy to the consumers instead of the excise subsidy then the effect would have been different on both the consumer and on the government. For this suppose, the government supplements consumer's income by an amount that makes the consumer to move from IC1 to his indifference curve IC2 which he had reached after subsidization of commodity X. This effect can be shown by drawing a budget line TN2, which is parallel to MN1. The consumer reaches his equilibrium at point E2 on this new budget line and consumes OX2 units of X for which he pays TS of his income, of which TM is the subsidy provided by the government If we now compare the cost of the two subsidies to the government then we have already seen through the above diagram that the cost of excise subsidy is DB and that of income subsidy is TM; where DB = E3k and TM = JK. Moreover, E3k > JK therefore the government s cost of providing excise subsidy is more than the cost of providing income subsidy, however, both the policy measures leads to an increase in the consumer s level of satisfaction as in both the case the consumer moves to an higher IC. Thus, income subsidy is more efficient and always preferable than the excise subsidies. But if we look this analysis from a different angle then we find out that it depends upon the objective of the government to implement which policy. As in, if the policy objective is to encourage consumption of a commodity then excise subsidy is preferable because income subsidy may reduce the consumption of food. As has been seen in the above diagram that income subsidy reduces consumption of X from OX3 to OX2 or it increases food consumption only marginally from OX1 to OX2. On the other hand, income subsidy would encourage people to actually increase their standard of living as now they can consume less or same amount of food and can spend their money income (provided by the government in the form of income grant or income subsidy) on other goods and services like on education, home, clothes etc. 5. Income and substitution effects of price change: normal goods As we have already seen in our previous module that a change in the price of a good causes a change in the demand of the good, ceteris paribus, and is known as the price effect. Further this price effect is divided into income effect and substitution effect for the consumer to make his choices wisely. Income effect arises because of a change in a consumer's real income or purchasing power, which is caused by the change in its price i.e. a rise in the price, reduces and a fall in price increases a consumer's real income. Furthermore, a change in the real income leads to a change in the consumer's consumption basket; which is also known as the income effect of price change. On the other hand, when the price of one commodity decreases, it becomes relatively cheaper than the other and the consumer substitute cheaper goods for relatively costlier ones. This is known as substitution effect.
The total of these two effects is known as price effect. There are two methods to evaluate the price effect: Hicksian method Slutskian method Hicksian Method: Income and substitution effect for a fall in the price of X Let the consumer is initially be in equilibrium at point P on IC1 with MN budget line, where he consumes PX1 of Y and OX1 of X. Now if the price of X will fall then the budget line will pivot to MN. On this new budget line the consumer will be at equilibrium at point Q as IC2 is tangent on MN at point Q. Now since the price of X has fallen down and correspondingly the consumer I also moves to point Q as his equilibrium so now he will consume more of X as compare to his previous selected basket of good. At this point, he will buy an additional X1X3 of X. Thus, the total price effect on the consumption of X is X1X3. The next step is to split this price effect into substitution and income effect. According to hicks, first measure the income effect then the residue would be the substitution effect. For this he reduced the income of the consumer (by the way of taxation) so that the consumer would again reach back to his original IC1 in accordance to the new price ratio. Hicks calls it as income compensation approach as when the price of X falls the purchasing power of consumer increases for X so in order to bring the consumer back to his original IC, hicks suggested to reduce his level of income (in order to show the income effect). This is done by drawing an imaginary budget line, M N, which is also tangent to IC1 at point R. Thus R is consumer s new equilibrium point after eliminating the real income effect, which in turn means that, after income adjustment, the consumer will move from point Q to R. this will lead to a reduction in X by X2X3, which is also known as the income effect.
Fig 3: Price effect when the price of X falls: Hicksian approach Now as per hicks, the substitution effect can be derived by subtracting this income effect from the total price effect. In other words, SE = PE IE SE = X1X3 X2X3 = X1X2 Income and substitution effect for an increase in the price of X Suppose that the consumer's initial budget line is given by AB and the consumer is in equilibrium at point E2 on the indifference curve IC2 where he consumes OX3of commodity X. When the price of X increases, the budget line shifts from AB to AD and the consumer moves to a new equilibrium point E1 on a lower indifference curve IC1. This decrease in consumption of X, that is, OX3 OX1 =X1X3, is the price effect.
Fig 4: Price effect when the price of X increases: Hicksian approach Now as per the Hicksian method i.e the income compensation approach, let us suppose that the government grants dearness allowance (DA) to the consumer which is just sufficient to compensate him for the loss of his real income due to the rise in price of X so that he could move on to his original indifference curve, IC2. This will also shifts the consumer's budget line AD to HC, which will be tangent to the original indifference curve IC2 at point E3, which is the consumer's equilibrium point after income compensation. The consumer's movement from point E1 to point E3 shows a rise by X1X2 in the consumption of X. This rise in consumption of commodity X is the result of a rise in the real income after the grant of compensatory DA. Therefore, X1X2 is the income effect. Now since, PE = X1X3 and IE = X1X2, SE = X1X3 X1X2 =X2X3. The consumer moves (after the grant of DA) from equilibrium point E2to E3. This movement indicates a decrease in the consumption of commodity X by X2X3. This means that the consumer reduces the consumption of commodity X when its price rises. Thus, X2X3 is the substitution effect.
Slutskian Approach: In contrast to the Hicksian approach, Slutsky suggested that consumer's income should be so adjusted that the consumer returns not only to their original indifference curve but also to the original point of equilibrium; that is, they are able to buy the original combination of the two goods after the change in the price ratio. In other words, the consumer's income-adjusted budget line must pass through the initial equilibrium point on the original indifference curve. Suppose that the consumer, given an income and the prices of commodities X and Y, is initially in equilibrium at point P on the indifference curve IC1, where he consumes OX1 of commodity X. When the price of X falls, other factors remaining the same, the consumer moves to a new equilibrium point Q on the indifference curve IC3, which in turn increases the consumer's purchase of X by X1X3. This is the price effect caused by the fall in price of X. Fig 5: Price effect when the price of X falls: Slutsky approach Now in order to split this price effect into substitution and income effect as per slutsky the consumer s real income must be reduced to the level to make them capable of purchasing the original bundle of both the goods at new price ratio. This can be done by drawing an imaginary budget line M N through point P, and is tangent to IC2 at point R. Point R is the consumer's equilibrium after income adjustment, which shows a decrease by X2X3 in the consumption of X. The quantity X2X3 is, therefore, the income effect. The SE, thus, would be X1X3 - X2X3 = X1X2.
6. Income and substitution effect: Inferior goods Inferior goods are those goods whose demand decreases with the increase in the income of the consumers. For example, bajra. If the income of the consumer increases then he substitute the inferior good with that of normal good and so this decreases the consumption of inferior good and increases the consumption of normal good. Suppose a consumer consumes two goods X and Y, where, X is an inferior good. The income and substitution effects of a fall in the price of X are illustrated in the following diagram: Fig 6: Price effect of an inferior good Suppose that the consumer is in equilibrium at point P, where the budget line M1N1 is tangent to the indifference curve IC1. Now, if the price of X fall, other factors remaining the same, the budget line shifts to M1N3 and the consumer moves from equilibrium point P to R. The movement from P to R is the price effect. To eliminate the income effect of the price change, let us draw, following the Hicksian method, a compensatory budget line M2N2 which is tangent to the original indifference curve IC1 at point Q. The consumer's movement from P to Q means an increase by X1X3 in the quantity consumed of X. This is the substitution effect, which results from a fall in the price of X. Note that the substitution effect of a fall in the price of an inferior good (X) is very powerful. It is
so powerful that the substitution effect X1X3 exceeds the total price effect X1X2. This makes the income effect of a change in the price of an inferior good negative. The movement from Q to R shows the negative income effect, that is, a decrease in the quantity of X demanded, where, IE = PE SE IE = X1X2 X1X3 = - X2X3 Thus, while the income effect of a fall in the price of an inferior good causes a decrease in the consumption of the good, the substitution effect increases its quantity demanded i.e. the income and substitution effects work in an opposite directions in the case of an inferior good. Here it is important to note that since inferior goods shows a relation between income of the consumer and the quantity of the inferior good therefore we can derive an Engel curve in this case; demand curve cannot be derived as demand shows a relationship between price and quantity. Moreover since an inferior good has an inverse relationship with the income therefore the Engel curve for inferior goods will be downward sloping. 7. Giffen Paradox Goods where the law of demand does not apply are known as Giffen goods. In the case of Giffen goods, the substitution effect is positive and the income effective is negative, and the negative income effect is greater than the positive substitution effect. Therefore, when the price of an inferior good of the Giffen type decreases, its demand decreases; and vice versa. This phenomenon shows a paradoxical situation, i.e., when the price of an inferior good increases, its quantity demanded increases. This happens because in order to meet the minimum consumption need, the consumer has to cut his expenditure on superior goods and spend the saved amount on the inferior good, which is cheaper even after the rise in its price. As a result, the demand for the inferior good increases, due to increase in its price. This paradox is known as the Giffen paradox. Giffen paradox is an exception to the law of demand. Let us now suppose that the consumer is initially in equilibrium at point P. Now, let the price of inferior good X decrease so that the consumer moves to equilibrium point R on IC2. Because of this movement, the quantity of X demanded decreases by X1X2. This is the price effect. Now in order to separate the income and substitution effects of the price effect in the case of Giffen goods. Let s eliminate the income effect by drawing an imaginary budget line M2N2 parallel to the budget line M2N3 and tangent to the original indifference curve IC1. The imaginary budget line is tangential to IC1 at point Q. The consumer's
movement from P to Q and the consequent increase by X2X3 in the quantity of X demanded is the substitution effect. However the Income effect would be: IE = PE SE IE = X1X2 X2X3 = - X1X3 Fig 7: Giffen paradox According to the above diagram, the income effect is greater than the substitution effect, whose net effect is the fall in the quantity demanded of X due to a fall in its price. This is contrary to the law of demand. However, note that, all Giffen goods are inferior goods but all inferior goods are not the Giffen goods. This is so because in both the cases the substitution effect is positive and income effect is negative but in case of Giffen goods the negative income effect outweighs the positive substitution effect, hence the demand curve slopes upward. However, in the case of inferior goods the negative income effect is less than the positive substitution effect and thus the demand curve for this is downward sloping.
8. Summary Hence, we have seen in our above analysis how the indifference curve could be used in evaluating the other measures either taken by the government or by the consumers. Thus, IC analysis is a very important tool which helps the government and the consumers to decide about their objectives and their preferences.