Dominick Salvatore Schaums Outline of Microeconomics, 4th edition Schaums Outline Series 2006
68 CONSUMER DEMAND THEORY [CHAP. 4The consumer would like to reach indifference curve III in Fig. 4-5, but cannot because of limited income and priceconstraints. The individual could consume at point N or at point R on indifference curve I, but doing so would not maximizethe total satisfaction from expenditures. Indifference curve II is the highest indifference curve this individual can reach withthis budget constraint line. In order to reach equilibrium, this consumer should spend $5 of his or her income to purchase 5units of Y and the remaining $5 to purchase 5 units of X. Note that equilibrium occurs where the budget line is tangent to anindifference curve. Thus, at point E, the slope of the budget line is equal to the slope of indifference curve II.4.8 EXCHANGEIn a two-individual (A and B), two commodity (X and Y) world, there is a basis for mutually advantageousexchange as long as the MRS xy for individual A differs from the MRS xy for individual B. As the quantityexchanged increases, the values of the MRS xy for the two individuals approach each other until they becomeidentical. When this has occurred, there is no further basis for mutually advantageous exchange and thetrading will come to an end (see Problems 4.24 to 4.27).4.9 THE INCOME-CONSUMPTION CURVE AND THE ENGEL CURVEBy changing the consumer’s money income while keeping constant personal tastes and the prices of X andY, we can derive the consumer’s income-consumption curve and Engel curve. The income-consumption curveis the locus of points of consumer equilibrium resulting when only the consumer’s income is varied. The Engelcurve shows the amount of a commodity that the consumer would purchase per unit of time at various levels oftotal income.EXAMPLE 12. If the consumer’s tastes are given by the indifference curves of Fig. 4-2, if P x ¼ P y ¼ $1, and if the consumer’smoney income (M) rises from $6 to $10 and then to $14 per time period, then the consumer’s budget lines are given,respectively, by lines 1, 2, and 3 in Fig. 4-6. Thus, when M ¼ $6, the consumer reaches equilibrium at point F on indifferencecurve I by purchasing 3X and 3Y. When M ¼ $10, the consumer reaches equilibrium at point E on indifference curve IIby purchasing 5X and 5Y. When M ¼ $14, the consumer is in equilibrium at point S and purchases 7X and 7Y. By joiningthese points of consumer equilibrium, we get income-consumption curve FS in Fig. 4-6.Fig. 4-6
CHAP. 4] CONSUMER DEMAND THEORY 69Fig. 4-7EXAMPLE 13. Line F 0 S 0 in Fig. 4-7 is the Engel curve for commodity X for the consumer of Example 12. It shows that whenM ¼ $6, the consumer purchases 3X; when M ¼ $10, he or she purchases 5X, and when M ¼ $14, he or she purchases 7X. Sincethe Engel curve is positively sloped, e M . 0 and commodity X is a normal good. When the Engel curve is negatively sloped,e M , 0 and the good is inferior. We can further add that when the tangent to the Engel curve at a particular point is positivelysloped and cuts the income axis, e M . 1 and the commodity is a luxury at that point. If the tangent to the Engel curve is positivelysloped and cuts the quantity axis, e M is between zero and 1 and the commodity is a necessity (see Problem 4.29).4.10 THE PRICE-CONSUMPTION CURVE AND THE CONSUMER’S DEMAND CURVEBy changing the price of X while keeping constant the price of Y and the consumer’s tastes and moneyincome, we can derive the consumer’s price-consumption curve and demand curve for commodity X. Theprice-consumption curve for commodity X is the locus of points of consumer equilibrium resulting whenonly the price of X is varied. The consumer’s demand curve for commodity X shows the amount of X thatthe consumer would purchase at various prices of X, ceteris paribus.EXAMPLE 14. In Fig. 4-8 we see that when P x ¼ P y ¼ $1 and M ¼ $10, the consumer is in equilibrium at point E onindifference curve II. This is the same as in Fig. 4-6. If P x falls to $0.50 while P y and M remain unchanged, the budget line ofthe consumer rotates counterclockwise from KL to KJ. With this new budget line, the consumer is in equilibrium at point Twhere budget line KL is tangent to indifference curve III. By joining these points of consumer equilibrium, we get priceconsumptioncurve ET in Fig. 4-8.Fig. 4-8
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CHAP. 4] CONSUMER DEMAND THEORY 69
Fig. 4-7
EXAMPLE 13. Line F 0 S 0 in Fig. 4-7 is the Engel curve for commodity X for the consumer of Example 12. It shows that when
M ¼ $6, the consumer purchases 3X; when M ¼ $10, he or she purchases 5X, and when M ¼ $14, he or she purchases 7X. Since
the Engel curve is positively sloped, e M . 0 and commodity X is a normal good. When the Engel curve is negatively sloped,
e M , 0 and the good is inferior. We can further add that when the tangent to the Engel curve at a particular point is positively
sloped and cuts the income axis, e M . 1 and the commodity is a luxury at that point. If the tangent to the Engel curve is positively
sloped and cuts the quantity axis, e M is between zero and 1 and the commodity is a necessity (see Problem 4.29).
4.10 THE PRICE-CONSUMPTION CURVE AND THE CONSUMER’S DEMAND CURVE
By changing the price of X while keeping constant the price of Y and the consumer’s tastes and money
income, we can derive the consumer’s price-consumption curve and demand curve for commodity X. The
price-consumption curve for commodity X is the locus of points of consumer equilibrium resulting when
only the price of X is varied. The consumer’s demand curve for commodity X shows the amount of X that
the consumer would purchase at various prices of X, ceteris paribus.
EXAMPLE 14. In Fig. 4-8 we see that when P x ¼ P y ¼ $1 and M ¼ $10, the consumer is in equilibrium at point E on
indifference curve II. This is the same as in Fig. 4-6. If P x falls to $0.50 while P y and M remain unchanged, the budget line of
the consumer rotates counterclockwise from KL to KJ. With this new budget line, the consumer is in equilibrium at point T
where budget line KL is tangent to indifference curve III. By joining these points of consumer equilibrium, we get priceconsumption
curve ET in Fig. 4-8.
Fig. 4-8
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