When the price of a good rises (falls) and all other variables affecting the

Transcription

1 ONLINE APPENDIX 1 Substitution and Income Effects of a Price Change When the price of a good rises (falls) and all other variables affecting the consumer remain the same, the law of demand tells us that we will observe consumers buying less (more) of the good. The total change in the amount of the good consumed can be attributed to two separate effects caused by the changing price: the substitution effect and the income effect. Although we can observe only the total effect of price changes on the amount consumed, we can theoretically and even experimentally, under controlled conditions isolate and measure the two component effects, which together add up to the total change in the number of units consumed. In this appendix we explain the conceptual process by which the total effect of a price change can be separated into substitution and income effects. substitution effect The change in consumption of a good that would result if the consumer remained on the same indifference curve after the relative price of the good changes. The Substitution Effect When the relative price of a good increases, consumers will substitute away from the relatively higher priced good into other relatively lower priced goods. And, as you would expect, the opposite substitution occurs when a good becomes relatively less expensive. This is called the substitution effect of a price change and is formally defined as the change in consumption of a good that would result if the consumer remained on the original indifference curve after the relative price of the good changes. Obviously, the consumer will in fact move to a higher or lower indifference curve in order to reach a new equilibrium after a price falls or rises, respectively. However, for the purpose of measuring the substitution effect, we must theoretically force the consumer to make substitutions in consumption that will keep the consumer s utility constant (i.e., force substitution to occur along the original indifference curve).

2 FIGURE 1 Substitution and Income Effects When Price of X Increases L 21 Temporary budget line Quantity of Y A 15 F G E II T I S I R Z B Quantity of X To see how we can isolate the substitution effect, suppose a consumer begins with $150 of income and faces market prices for goods X and Y of $6 and $10, respectively. Figure 1 shows this beginning budget line as AB. The consumer is originally in equilibrium where budget line AB is tangent to indifference curve II at 10 units of X (point E ). Now let the price of X increase from $6 to $15 so that the new budget line gets steeper and pivots inward to AR. The consumer is worse off after the price increase because the inward pivot of the budget line reduces the number of bundles that meet the new budget constraint AR, and the consumer moves to a lower indifference curve (bundle G on indifference curve I ). Since the substitution effect is measured holding the consumer s utility constant, we must hypothetically compensate the consumer for the loss of utility caused by the increase in the price of X. Suppose we temporarily give the consumer just enough income to get back to the original indifference curve II. At the now higher price of X, this will require giving the consumer enough income to shift budget line AR in a parallel fashion up to LZ. We must stress that budget line LZ is a temporary budget line constructed solely for the purpose of theoretically isolating the substitution effect. You can see in the figure that giving the consumer the compensating extra income to shift AR to LZ makes it possible for the buyer to reach point F on the original indifference curve II and purchase 5 units of X. The substitution effect, which results from the movement along II from E to F, is equal to 25 (i.e., 5 fewer units of X ) and is represented by the arrow labeled S in the figure. It is most important to see that the substitution effect is negative an increase in price must result in a decrease in consumption of the good when utility is held constant. The substitution effect must be negative because indifference curves are downward sloping, regardless of whether the relative price of the good is increasing (as we show here) or decreasing (as you can now demonstrate for yourself).

3 Principle The substitution effect is the change in the consumption of a good after a change in its price, when the consumer is forced by a change in income to consume at a point on the original indifference curve. Considering the substitution effect only, the amount of the good consumed must vary inversely with its price. The Income Effect income effect The change in consumption caused by the change in purchasing power accompanying a price change, measured at the new relative price ratio. total effect The sum of the substitution and income effects. A change in the price of a good causes the purchasing power of the consumer s income to change even though the amount of income is the same. When the price of a good falls, buyers feel like they have more income because they can buy the same bundle of goods and have some income left over. Of course the opposite happens when the price of a good increases: consumers feel poorer because after the price increase they cannot buy the same bundle of goods even though they still have the same amount of income. The income effect of a price change is the change in consumption caused by the change in purchasing power accompanying a price change, measured at the new relative price ratio. In Figure 1, once the substitution effect is identified we can reduce the consumer s purchasing power by taking back the temporary compensation. This causes purchasing power to fall, as indicated by the downward shift in budget line LZ to AR. In so doing, the consumer moves from tangency point F to tangency point G as purchasing power falls with the relative prices ratio remaining constant at 3/2 (5 P x /P y 5 $15/$10). Thus the income effect of the price increase from $6 to $15 is 2. This is the reduction in consumption of good X by 2 units from 5 to 3 units as shown by the arrow labeled I in the figure. The total effect of a price change is the sum of the substitution and income effects. The total effect of the increase in the price of X from $6 to $15 is 27: Total effect of price increase 5 Substitution effect 1 Income effect (22) Notice that the substitution and income effects both cause a reduction in consumption of X when the price of X increased. In this example, good X is a normal good, since the decrease in purchasing power caused a decrease in consumption of X. When the price of X falls, the substitution effect is positive (more X is consumed), and the income effect is also positive if the good is normal. Therefore, when good X is normal, the substitution and income effects always move in the same direction or reinforce each other. Alternatively, if good X is an inferior good and the price of X increases, then the reduction in purchasing power increases consumption of X, and the income effect is positive and partially offsets the substitution effect. Relation Considering the substitution effect alone, an increase (decrease) in the price of a good causes less (more) of the good to be demanded. For a normal good, the income effect from the consumer being made better or worse off by the price change adds to or reinforces the substitution effect. The income effect in the case of an inferior good offsets or takes away from the substitution effect.

4 Why Demand Slopes Downward In the case of a normal good, it is clear why price and quantity demanded are inversely related along demand. As we explained, the substitution effect always involves price and quantity moving in opposite directions. For normal goods, the income effect always reinforces the substitution effect and further strengthens the inverse relation between price and quantity demanded. In the case of inferior goods, it is theoretically possible to violate the law of demand. For inferior goods, the income effect does not reinforce the substitution effect, and the income effect offsets the substitution effect. As long as the income effect only partially offsets the substitution effect, quantity demanded will vary inversely with price, and the demand curve will be downward sloping. The substitution effect almost always dominates the income effect, because the income effect of a price change is almost always relatively small. After all, consumers buy many different goods, and a change in price of any one of them is not going to have a large effect on the purchasing power of household income. Strictly speaking, it is indeed theoretically possible for the income effect of an inferior good to completely dominate the substitution effect and cause demand to slope upward. Economists call this theoretical exception to the law of demand a Giffen good. While experimental economists believe they have found a Giffen good for an individual consumer in an experimental setting, we have seen no convincing evidence of the existence of a Giffen good for a group of consumers. TECHNICAL PROBLEMS 1. In the following graph the consumer begins in equilibrium with an income of $2,000, facing prices of P x 5 $5 and P y 5 $ Quantity of Y I II Quantity of X

5 a. In equilibrium, units of X are consumed. Now let the price of X rise to $10. b. In the new equilibrium, units of X are consumed. c. In order to isolate the substitution effect, $ must be given to the consumer. d. The total effect of the price increase is. The substitution effect is. The income effect is. e. Good X is a good. 2. In the following graph the consumer begins in equilibrium with an income of $5,000, facing the prices P x 5 $50 and P y 5 $ Quantity of Y 120 II I Quantity of X 250 a. In equilibrium, units of X are consumed. Now let the price of X fall to $20, income and the price of Y remaining constant. b. In the new equilibrium, units of X are consumed. c. In order to isolate the substitution effect, $ must be taken away from the consumer. d. The total effect of the price decrease is. The substitution effect is. The income effect is.

6 ANSWERS TO TECHNICAL PROBLEMS 1. a. 300 b. 125 c. $1,250 d. 175 units of X ; 75 units of X ; 100 units of X e. normal 2. a. 50 units of X b. 80 units of X c $25 5 $2,000 d. Total effect units of X Substitution effect units of X Income effect 5 10 units of X