Supplement to Unit – II BEHIND THE DEMAND CURVE: THE THEORY OF CONSUMER CHOICE Here, the purpose is to explain the derivation of the demand function and to provide an understanding of the consumer decision-making process. Consumer Preferences Individuals make choices based on their personal tastes and preferences. Tastes and preferences are shaped by many factors. Some of the factors are family environment, physical condition, age, sex, education, religion, and location.
In the analysis that follows, tastes and preferences will be viewed as a given, and discussion will focus on how those tastes and preferences are transformed into consumption decisions. Bundle B 2 units of X 6 units of Y Bundle A 5 units of X 2 units of Y In the well-established tradition of economics, four basic assumptions are made developing the theory of consumer choice. First, it is assumed that individuals can rank their preferences for alternative bundles of goods and services. Consider a world in which only two goods X and Y are available.
Suppose that a consumer is confronted with the following combinations of those two goods: Bundle C 4 units of X 4 units of Y The ability to rank means that the individual can assess the relative amount of satisfaction that would result from each bundle of goods. For example, suppose that B is considered the most desirable bundle, and that C and A are viewed as providing equal but lesser amount of satisfaction than B. Using the terminology of the theory of consumer choice, it is said that B is preferred to both C and A, and that the consumer is indifferent between C and A. Bundle D units of X 7 units of Y The second assumption is non-satiation. This means that individuals consider themselves better off if they have more of a good or service than if they have less. Consider bundle D that consist of The non-satiation assumption implies that this bundle would be preferred to bundle B because it includes more X and more Y. Transitivity is the third assumption. It can be thought of as requiring that preferences be consistent. Transitivity stated that if bundle D is preferred to bundle B and if B is preferred to both A and C, bundle D must be preferred to bundles A and C.
Finally, it is assumed that in order to get additional unit of one good, consumers are willing to give-up successively fewer units of other goods. For example, a consumer may be willing to give up the purchase of five units of Y to obtain the first unit of X. However, if the person already has three units of X, the value of another unit of X in terms of Y is likely to be less than 5 units. Key Concepts Four assumptions form the basis for the theory of consumer choice. They are 1. Individuals can rank their preferences 2. Non-satiation – people prefer more to less 3. Transitivity – ranking are consistent
Indifference Curves Recall that bundles A and C were viewed as being equally desirable. That is, an individual would be indifferent to having A rather than C. Now suppose that other bundles, designated as E, F, G and H, are also considered equivalent to A and C. If these bundles are plotted on a graph as shown in Figure – 1, the points can be joined to form an indifference curve that represents all bundles of goods that provide an individual with equal levels of satisfaction. Units of Y Units of X O A C E F B · · · · · · · G D Figure – 1 Note that Figure – 1 shows several indifference curves.
All points on the curve through B are considered equivalent to that bundle. Because B is preferred to A, the assumption of transitivity guarantees that all the points on the indifference curve passing through B are preferred to all the points on the curve passing through A. Similarly since D provides more satisfaction than B, all points on the curve passing through D are preferred to those on the curve passing through B and C. Because of non-satiation higher indifference curve denote higher level of satisfaction. Units of Y Units of X O Figure – 2 R · · S · J L K · ·
The four assumptions stated earlier determine the basic characteristics of indifference curves. The assumption that individuals are capable of ranking their preferences implies that indifference curves exist. The assumption of non-satiation assures that the curves will have a negative slope. This is easily shown by considering a curve with positive slope, such as the curve passing through point S in Figure – 2. Pick any point on the curve, such as R. Note that point S denotes a bundle with more of both goods X and Y than point R. But because of the non-satiation assumption, having more of both goods implies that S is preferred to R.
Thus, the two points cannot be on the same indifference curve. Hence, indifference curves must be downward sloping. Transitivity and non-satiation guarantee that two indifference curves will not intersect. This can also be seen from Figure – 2, which shows two indifference curves crossing at point J. Consider points K and L. The bundle denoted by K has more of both goods than L and hence must be preferred to L. Because J and L are on the same indifference curve, transitivity requires that K be preferred to J. But this is not true; J and K are on the same indifference curve.
Thus the assumption of transitivity has been violated because preferences are not consistent. The assumption of transitivity is always violated when indifference curves intersect. The assumption that consumers will be willing to give up successively fewer units of one good in order to get additional units of another good assures that indifference curves will have the convex shape shown in Figure – 1. The slope at any point on an indifference curve is the tangent to the curve at that point. This slope represents the units of good Y that will be given up to get one more unit of good X, while still remaining on the same indifference curve.
That is, it is the rate at which the individual is willing to trade Y for X. This trade-off is referred to as the marginal rate of substitution (MRS). For example, in Figure – 1, if the slope of the tangent to the indifference curve at point A is -8, the individual will be willing to substitute eight units of Y for one unit of X. To satisfy the fourth assumption, the absolute value of the MRS must decrease when moving down an indifference curve. Indifference curves that are convex to the origin have this property. Note that the absolute value of the slope of the curve in Figure – 1 decrease from point A to point G.
If the slope of the tangent at point H is -1/8, the individual is now willing to give-up eight units of X to get one unit of Y. An indifference curve must be convex in order to depict this declining marginal rate of substitution. Key Concepts * Indifference curves are downward sloping, convex, and do not intersect. Higher indifference curves reflect greater levels of satisfaction. * The slope of an indifference curve is called the marginal rate of substitution (MRS). It denotes the rate at which an individual is willing to trade two goods or services. * Convex indifference curves depict a declining marginal rate of substitution.
Budget Constraints Want reflect individual tastes and preferences. But actual purchases are strongly influenced by income and prices. Let I be income and PX and PY be the prices of Goods X and Y, respectively. In a two-good world, possible purchases are defined by the following expression: I? PX QX+PY QY (1) Where QX and QY are the quantities of good X and good Y. The interpretation of equation (1) is straightforward. It states that the sum of money spent on good X plus the sum spent on good X must be less than or equal to the total income available.
If equation (1) is treated as equality, it denotes the possible bundles of goods X and Y that can be purchased if all the income is spent. Solving this equation for QX yields QX =IPX – PY PX QY (2) which expresses possible purchases of good X in terms of income, prices, and the quantity of good Y purchased. Equation (2) can be graphed as shown in Figure – 3. Units of Y Units of X O A B · · Figure – 3 IPY IPX Slope=-PXPY The line in Figure – 3 is called a budget constraint. All the points to the left of the curve, such as point A, represent quantities of goods X and Y that can be purchased using less than available income.
Points to the right of the budget constraint, such as point B, are bundles that cannot be purchased with the available income. Note that the vertical intercept of the budget constraint is IPY. It represents the number of units of good Y that could be purchased if all income was spent on that commodity. The horizontal intercept is IPX and has a similar interpretation. The slope of the budget constraint is -PXPY. It represents the rate at which one good can be substituted for another in the marketplace. For example, if -PXPY = ? , two units of good X must be given up to get one unit more of good Y. Utility Maximization
It is assumed that individuals strive to achieve the most satisfaction possible from their purchase choices. This objective is often referred to as utility maximization. It involves consideration of both indifference curves and the budget constraint. Suppose that a consumer is contemplating the purchase of bundle R as shown in Figure – 4. Point R lies on the budget constraint, indicating that it is an affordable bundle. But R is not the bundle that will maximize the individual’s utility. Note that E is also on the budget constraint but is on a higher indifference curve. Thus the bundle E is preferred to R.
Units of good Y Units of good X Figure – 4 O T R E · · · Point E lies at the point of tangency between the budget constraint and the indifference curve. That is, point E is the only point on the curve that touches the budget constraint. Note that a point such as T on any higher indifference curve is above the budget constraint and hence is not affordable. Thus the bundle represented by point E is the utility-maximizing point. Given the individual’s tastes, preferences, and income, and the prices of the two goods, there is no other point that will provide the same level of utility or satisfaction as point E.
Because E is the point of tangency between the indifference curve and the budget constraint, the slope of the two lines is equal at that point. Remember that the slope of an indifference curve is the marginal rate of substitution, and the slope of the budget constraint is the negative of the price ratio, -PXPY. Hence the utility maximizing bundle is the point where -PXPY=MRSXY (3) Equation (3) is easily interpreted. The price ratio represents the rate at which the market requires consumers to substitute the two goods.
The MRS is the rate at which the individual desires to substitute the goods. Utility maximization occurs where the rate at which the consumer wants to substitute is just equal to the rate at which he or she must substitute. If these two rates are not equal, purchase can be rearranged in such a way as to increase satisfaction or utility. Key Concepts * The utility-maximizing point occurs where the highest indifference curve is tangent to the budget constraint. * At the utility-maximizing point, the rate that products must be traded in the market is just equal to the rate at which the individual is willing to substitute one good for another.
Consumer Choice and the Demand Curve F · · E X1 X2 X1 X2 P2 P1 Units of Good Y Units of Good X Units of Good X Price per unit (Rs) IPY D D O O Panel (a) Figure – 5 Panel (b) The price-quantity combinations shown on an individual demand curve are the result of utility maximizing decisions at various prices. This can easily be seen by considering demand of good X. Suppose that tastes and preferences, income, and the prices of goods X and Y generate indifference curves and budget constraint as shown in Figure – 5 (a). If the price of good X (PX) is P1 per unit, the utility-maximizing bundle will be point E, which denotes X2 units of this good.
That is, at price P1, quantity demanded is X2 units. Thus, point E in figure – 5(a) corresponds to one point on the demand curve for good X. If price of good X (PX) changes, E will no longer be the utility-maximizing bundle. Suppose that PX increases to P2. This change causes the budget constraint to shift leftward, as shown in Figure – 5(a). Note that the vertical intercept is the same as before (IPY). But the slope of the budget constraint is(-)PXPY. Thus the increase in PX causes the line to shift leftward. With the new budget constraint, the point E is no longer affordable. Hence the consumer must select a new utility-maximizing bundle.
As before, this point is where the highest indifference curve is tangent to the budget constraint. In Figure – 5 (a) the utility-maximizing point is F. Note that that F is a bundle with less quantity of good X than the point E. The higher price of good X reduced purchasing power and increased the opportunity cost of good X relative to good Y. Point F represents another price – quantity point on the demand curve. It is the quantity demanded when PX = P2. As shown in panel (b) of Figure – 5, the individual demand curve DD is generated by plotting these quantities as a function of price.
Additional points are obtained by changing the price of good X and determining the utility-maximizing quantity of the product. Consumer Choice and Change in Demand Units of good Y Units of good X Figure – 6 O F I1 E · · I2 We have already used the theory of consumer choice to show how changes in the quantity demanded (movement along the demand curve) occur. The theory can also be used to explain changes in demand (i. e. , shifts of the demand curve). Such shifts result from a change in tastes and preferences, a change in income, or a change in the price of other goods.
Consider the impact of an increase in income. When income increases, the budget constraint shifts outward, as shown in Figure – 6. Because the slope of the constraint is determined by prices and not by income, the new budget constraint is parallel to the initial budget constraint. Initially, the utility maximizing point was at E where I1 is tangent to the budget constraint, but the extra income allows movement to a higher indifference curve. The utility-maximizing point is now F, where I2 is tangent to the new budget constraint. Note that bundle F contains more quantity of good X than did E.
At the same price of good X, there is a greater demand for good X than before. The result of this income change would appear as a rightward shift of the demand curve – more quantity of good X would be demanded at each price. Units of good Y Units of good X O F · I2 Figure – 7: Changes in Tastes and Preferences and Utility Maximization I2 After I1 Units of good Y Units of good X O Before I1 E · The effect on demand of changes in tastes and preferences is illustrated by Figure – 7. Initially, let the utility-maximizing point be E, as shown in the “before” panel.
Now, suppose that certain circumstances cause the consumer to view good Y less favorably. This is indicated by a shift in the indifference curve from I1 to I2 and a new utility-maximizing point, F, as shown in the “after” panel. Note that at the new utility-maximizing point, less amount of good Y is selected than before the change in preferences. This would be represented on the demand curve as a leftward shift. That is, less amount of good Y would be demanded at any price. In a similar way, the theory of consumer choice can be used to show how changes in the prices of other goods cause the demand curve to shift.
For example, point E in Figure – 8 is the initially utility-maximizing bundle for given income, tastes and preferences, and prices of goods X and Y. E · · F Units of Good Y O Units of Good X Figure – 8 Changes in the price of Other Goods and Utility Maximization · I2 I1 G Now, suppose that the price of good X decreases. This is shown in Figure – 8. This is shown in Figure – 8 by a rightward shift of the budget constraint. The new utility-maximization bundle is point F, where I2 is tangent to the new budget constraint. Note that this point specifies more amount of good X than was selected before the price reduction.
This is because the opportunity cost of buying good X has declined. The price change would be shown as a movement from one point to another along the demand curve for good X. Note also that point F contains less quantity of good Y than did point E. That is, the decrease in the price of good X resulted in a decrease in the demand for good Y. This change causes a leftward shift in the demand curve for good Y – less will be demanded at each price. The impact of a price change of one good on the demand for the other good depend on the relationship between the two products.
Apparently, good X and good Y were considered by the consumer to be substitutes. Thus a decrease in the price of good X decreased the demand for good Y. If the goods had been complements, analysis using the theory of consumer choice would have predicted and increase in the demand for good Y. In this case, a decrease in the price of good X would have resulted in a utility-maximizing point such as G, which specifies more amount of good Y than before the price change. Income and Substitution Effect The impact of change in the price of a good on consumption can be decomposed into two effects: an income effect and a substitution effect.
To see what these two effects are, consider how the consumer might respond the price of good X has fallen. The decrease in the price of good X makes the consumer better off. If good X and Y both are normal goods, the consumer will want to spread this improvement in his purchasing power over both goods. This income effect tends to make the consumer buy more of goods X and Y. Yet, at the same time, consumption of good X has become less expensive relative to consumption of good Y. This substitution effect tends to make the consumer choose more of good X and less of good Y.
Now consider the end result of these two effects. When the price of good X falls, real income of the consumer would increase. In order to decompose the price effect into income effect and substitution effect, first we have to find out the substitution effect. In order to find out substitution effect the consumer’s money income must be reduced by an amount that cancel out the gain in real income that result from the decrease in price. According to Hicks-Allen, price change is accompanied by so much change in money income that the consumer is neither better off nor worse off than before.
In other words, money income of the consumer is changed by an amount which keeps the consumer on the same indifference curve on which he was before the change in price. The amount by which the money income of the consumer is changed so that the consumer is neither better off nor worse off than before is called Compensating Variation in Income. Substitution effect is illustrated in figure-9. With a given money income and given prices of the goods as represented by the budget line AB, the consumer is in equilibrium at point E on indifference curve I1 and is purchasing OM of good X and ON of good Y.
Suppose that the price of good X falls (price of Y remaining unchanged) so that the budget line shift to AB1, as a result the consumer moves from the initial optimum point E to the new optimum point E1. We view this change as price effect. In order to find out the substitution effect, the gain in real income, which accrues due to the fall in price of X, should be canceled out by reducing the money income of the consumer by such an amount that forces him to remain on the same indifference curve I1 on which he was before.
In fig-9, a budget line CD parallel to AB1 has been drawn at such distance from AB1 that it touches the I1. It means that reduction of consumer’s income by the amount AC (in terms of good Y) or B1D (in terms of good X) has been made so as to keep him on the same indifference curve. AC or B1D is thus just sufficient to cancel out the gain in the real income which occurred due to the fall in the price of X. Therefore AC or B1D is compensating variation in income. Units of Y Units of X O A C E E1 B I1 · · M · D B1 Figure – 9: Decomposition of Price Effect into Income and Substitution Effect E2
M2 M1 N N1 N2 I2 Substitution Effect Income Effect Now, budget line CD represents the new relative prices of goods X & Y since it is parallel to the budget line AB1 which was obtained when the price of good X had fallen. Under the budget line CD the consumer moves from E to E2 on the same indifference curve substituting of X for Y. That is, he will buy more of X and less of Y, which is evident from fig-9. Although the consumer never actually chooses point E2, this hypothetical point is useful to clarify the two effects that determine the consumer’s decision.
Notice that the movement from point E to point E2 is due to the change only in the relative prices of the goods without change in the consumer’s real income. Similarly, the movement from point E2 to point E1 is due to the change only in consumer’s real income without any change in relative prices of the goods. Thus, the movement from E to E2 shows the substitution effect and the movement from E2 to E1 shows the income effect. The price effect (EE1) is the summation of substitution effect (EE2) and income effect (E2E1). Note that according to Hicks-Allen approach the substitution effect always occurs on the same indifference curve.
But income effect may be negative or positive depending on the nature of commodity (i. e. , inferior or normal). Here, in our example, the income effect is negative. But the magnitude of negative income effect is smaller than positive substitution effect. Therefore, the commodity in question is inferior good. If the commodity was Giffen good, the magnitude of negative income effect would have been greater than positive substitution effect. In such situation, price effect would have been also negative; that is, decrease in price of the commodity would lead the decrease in quantity demanded.