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What are the four basic assumptions about individual preferences?
(1) Preferences are complete: this means that the consumer is able to compare and rank all possible baskets of goods and services. (2) Preferences are transitive: this means that preferences are consistent, in the sense that if bundle A is preferred to bundle B and bundle B is preferred to bundle C, then bundle A is preferred to bundle C. (3) More is preferred to less: this means that all goods are desirable, and that the consumer always prefers to have more of each good. (4) Diminishing marginal rate of substitution: this means that indifference curves are convex, and that the slope of the indifference curve increases (becomes less negative) as we move down along the curve. As a consumer moves down along her indifference curve she is willing to give up fewer units of the good on the vertical axis in exchange for one more unit of the good on the horizontal axis. This assumption also means that balanced market baskets are generally preferred to baskets that have a lot of one good and very little of the other good.
Can a set on indifference curves be upward sloping? If so, what would this tell you about the two goods?
A set of indifference curves can be upward sloping if we violate assumption number three: more is preferred to less. When a set of indifference curves is upward sloping, it means one of the goods is a "bad" so that the consumer prefers less of that good rather than more. The positive slope means that the consumer will accept more of the bad only if he also receives more of the other good in return. As we move up along the indifference curve the consumer has more of the good he likes, and also more of the good he does not like.
Explain the difference between each of the following terms: an Engel curve and a demand curve
An Engel curve shows the quantity of one good that will be purchased by a consumer at different income levels. The quantity of the good is plotted on the horizontal axis and the consumer's income is on the vertical axis. A demand curve is like an Engel curve except that it shows the quantity purchased at different prices instead of different income levels.
Explain the difference between each of the following terms: an individual demand curve and a market demand curve
An individual demand curve plots the quantity demanded by one person at various prices. A market demand curve is the horizontal sum of all the individual demand curves. It plots the total quantity demanded by all consumers at various prices.
Explain the difference between each of the following terms: an income effect and a substitution effect
Both the substitution effect and income effect occur because of a change in the price of a good. The substitution effect is the change in the quantity demanded of the good due to the price change, holding the consumer's utility constant. The income effect is the change in the quantity demanded of the good due to the change in purchasing power brought about by the change in the good's price.
Explain whether the following statements are true or false: Engel curves always slope upward
False. If the good is an inferior good, quantity demanded decreases as income increases, and therefore the Engel curve slopes downward.
Jon is always willing to trade one can of Coke for one can of Sprite, or one can of Sprite for one can of Coke. c) Draw two budget lines with different slopes and illustrate the satisfaction-maximizing choice. What conclusion can you draw?
Jon's indifference curves are linear with a slope of 1. Jon's budget line is also linear, and will have a slope that reflects the ratio of the two prices. If Jon's budget line is steeper than his indifference curves, he will choose to consume only the good on the vertical axis. If Jon's budget line is flatter than his indifference curves, he will choose to consume only the good on the horizontal axis. Jon will always choose a corner solution where he buys only the less expensive good, unless his budget line has the same slope as his indifference curves. In this case any combination of Sprite and Coke that uses up his entire income will maximize Jon's satisfaction. The diagrams below show cases where Jon's budget line is steeper than his indifference curves and where it is flatter. Jon's indifference curves are linear with slopes of 1, and four indifference curves are shown in each diagram as solid lines. Jon's budget is $4.00. In the diagram on the left, Coke costs $1.00 and Sprite costs $2.00, so Jon can afford 4 Cokes (if he spends his entire budget on Coke) or 2 Sprites (if he spends his budget on Sprite). His budget line is the dashed line. The highest indifference curve he can reach is the one furthest to the right. He can reach that level of utility by purchasing 4 Cokes and no Sprites. In the diagram on the right, the price of Coke is $2.00 and the price of Sprite is $1.00. Jon's budget line is now flatter than his indifference curves, and his optimal bundle is the corner solution with 4 Sprites and no Cokes
Jon is always willing to trade one can of Coke for one can of Sprite, or one can of Sprite for one can of Coke. a) What can you say about Jon's marginal rate of substitution?
Jon's marginal rate of substitution can be defined as the number of cans of Coke he would be willing to give up in exchange for a can of Sprite. Since he is always willing to trade one for one, his MRS is equal to 1.
Draw a budget line and then draw an indifference curve to illustrate the satisfaction maximizing choice associated with two products. Use your graph to answer the following questions. b) Suppose that the price of one of the products is fixed at a level below the current price. As a result, the consumer is not able to purchase as much as she would like. Can you tell if the consumer is better off or worse off?
No, the consumer could be better off or worse off. When the price of one good is fixed at a level below the current (equilibrium) price, there will be a shortage of that good, and the good will be effectively rationed. In the diagram below, the price of good 1 has been reduced, and the consumer's budget line has rotated out to the right. The consumer would like to purchase bundle B, but the amount of good 1 is restricted because of a shortage. If the most the consumer can purchase is G*, she will be exactly as well off as before, because she will be able to purchase bundle C on her original indifference curve. If there is more than G* of good 1 available, the consumer will be better off, and if there is less than G*, the consumer will be worse off.
Suppose that an individual allocates his or her entire budget between two goods, food and clothing. Can both goods be inferior? Explain
No, the goods cannot both be inferior; at least one must be a normal good. Here's why. If an individual consumes only food and clothing, then any increase in income must be spent on either food or clothing or both (recall, we assume there are no savings and more of any good is preferred to less, even if the good is an inferior good). If food is an inferior good, then as income increases, consumption of food falls. With constant prices, the extra income not spent on food must be spent on clothing. Therefore as income increases, more is spent on clothing, i.e., clothing is a normal good.
What is the difference between ordinal utility and cardinal utility? Explain why the assumption of cardinal utility is not needed in order to rank consumer choices.
Ordinal utility implies an ordering among alternatives without regard for intensity of preference. For example, if the consumer's first choice is preferred to his second choice, then utility from the first 34 Pindyck/Rubinfeld, Microeconomics, Eighth Edition Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall. choice will be higher than utility from the second choice. How much higher is not important. An ordinal utility function generates a ranking of bundles and no meaning is given to the magnitude of the utility number itself. Cardinal utility implies that the intensity of preferences may be quantified, and that the utility number itself has meaning. An ordinal ranking is all that is needed to rank consumer choices. It is not necessary to know how intensely a consumer prefers basket A over basket B; it is enough to know that A is preferred to B.
Jon is always willing to trade one can of Coke for one can of Sprite, or one can of Sprite for one can of Coke. b) Draw a set of indifference curves for Jon
Since Jon is always willing to trade one can of Coke for one can of Sprite, his indifference curves are linear with a slope of 1. See the diagrams below part c.
The price of computers has fallen substantially over the past two decades. Use this drop in price to explain why the Consumer Price Index is likely to overstate substantially the cost-of-living index for individuals who use computers intensively.
The Consumer Price Index measures the cost of a basket of goods purchased by a typical consumer in the current year relative to the cost of the basket in the base year. Each good in the basket is assigned a weight, which reflects the importance of the good to the typical consumer, and the weights are kept fixed from year to year. One problem with fixing the weights is that consumers will shift their purchases from year to year to give more weight to goods whose prices have fallen, and less weight to goods whose prices have risen. The CPI will therefore give too much weight to goods whose prices have risen, and too little weight to goods whose prices have fallen. In addition, for nontypical individuals who use computers intensively, the fixed weight for computers in the basket will understate the importance of this good, and will hence understate the effect of the fall in the price of computers for these individuals. The CPI will overstate the rise in the cost of living for this type of individual.
Explain why an MRS between two goods must equal the ratio of the price of the goods for the consumer to achieve maximum satisfaction.
The MRS describes the rate at which the consumer is willing to trade off one good for another to maintain the same level of satisfaction. The ratio of prices describes the trade-off that the consumer is able to make between the same two goods in the market. The tangency of the indifference curve with the budget line represents the point at which the trade-offs are equal and consumer satisfaction is maximized. If the MRS between two goods is not equal to the ratio of prices, then the consumer could trade one good for another at market prices to obtain higher levels of satisfaction. For example, if the slope of the budget line (the ratio of the prices) is 4, the consumer can trade 4 units of Y (the good on the vertical axis) for one unit of X (the good on the horizontal axis). If the MRS at the current bundle is 6, then the consumer is willing to trade 6 units of Y for one unit of X. Since the two slopes are not equal the consumer is not maximizing her satisfaction. The consumer is willing to trade 6 but only has to trade 4, so she should make the trade. This trading continues until the highest level of satisfaction is achieved. As trades are made, the MRS will change and eventually become equal to the price ratio.
What happens to the marginal rate of substitution as you move along a convex indifference curve? A linear indifference curve?
The MRS measures how much of a good you are willing to give up in exchange for one more unit of the other good, keeping utility constant. The MRS diminishes along a convex indifference curve. This occurs because as you move down along the indifference curve, you are willing to give up less and less of the good on the vertical axis in exchange for one more unit of the good on the horizontal axis. The MRS is also the negative of the slope of the indifference curve, which decreases (becomes closer to zero) as you move down along the indifference curve. The MRS is constant along a linear indifference curve because the slope does not change. The consumer is always willing to trade the same number of units of one good in exchange for the other.
Explain why the Paasche index will generally understate the ideal cost-of-living index.
The Paasche index measures the current cost of the current bundle of goods relative to the base year cost of the current bundle of goods. The Paasche index will understate the ideal cost-of-living index because it assumes the individual buys the current year bundle in the base period. In reality, at base year prices the consumer would have been able to attain the same level of utility at a lower cost by altering his or her consumption bundle in light of the base year prices. Since the base year cost is overstated, the denominator of the Paasche index will be too large and the index will be too low, or understated.
Tickets to a rock concert sell for $10. But at that price, the demand is substantially greater than the available number of tickets. Is the value or marginal benefit of an additional ticket greater than, less than, or equal to $10? How might you determine that value?
The diagram below shows this situation. At a price of $10, consumers want to purchase Q tickets, but only Q* are available. Consumers would be willing to bid up the ticket price to P*, where the quantity demanded equals the number of tickets available. Since utility-maximizing consumers are willing to pay more than $10, the marginal increase in satisfaction (i.e., the value or marginal benefit of an additional ticket) is greater than $10. One way to determine the value of an additional ticket would be to auction it off. Another possibility is to allow scalping. Since consumers are willing to pay an amount equal to the marginal benefit they derive from purchasing an additional ticket, the scalper's price equals that value.
Describe the equal marginal principle. Explain why this principle may not hold if increasing marginal utility is associated with the consumption of one or both goods.
The equal marginal principle states that to obtain maximum satisfaction the ratio of the marginal utility to price must be equal across all goods. In other words, utility maximization is achieved when the budget is allocated so that the marginal utility per dollar of expenditure (MU/P) is the same for each good. If the MU/P ratios are not equal, allocating more dollars to the good with the higher MU/P will increase utility. As more dollars are allocated to this good its marginal utility will decrease, which causes its MU/P to fall and ultimately equal that of the other goods. If marginal utility is increasing, however, allocating more dollars to the good with the larger MU/P causes MU to increase, and that good's MU/P just keeps getting larger and larger. In this case, the consumer should spend all her income on this good, resulting in a corner solution. With a corner solution, the equal marginal principle does not hold.
Explain why two indifference curves cannot intersect.
The figure below shows two indifference curves intersecting at point A. We know from the definition of an indifference curve that the consumer has the same level of utility for every bundle of goods that lies on the given curve. In this case, the consumer is indifferent between bundles A and B because they both lie on indifference curve U1. Similarly, the consumer is indifferent between bundles A and C because they both lie on indifference curve U2. By the transitivity of preferences this consumer should also be indifferent between C and B. However, we see from the graph that C lies above B, so C must be preferred to B because C contains more of Good Y and the same amount of Good X as does B, and more is preferred to less. But this violates transitivity, so indifference curves must not intersect.
Explain the difference between each of the following terms: a price consumption curve and a demand curve
The price consumption curve (PCC) shows the quantities of two goods a consumer will purchase as the price of one of the goods changes, while a demand curve shows the quantity of one good a consumer will purchase as the price of that good changes. The graph of the PCC plots the quantity of one good on the horizontal axis and the quantity of the other good on the vertical axis. The demand curve plots the quantity of the good on the horizontal axis and its price on the vertical axis.
Upon merging with the West German economy, East German consumers indicated a preference for Mercedes-Benz automobiles over Volkswagens. However, when they converted their savings into deutsche marks, they flocked to Volkswagen dealerships. How can you explain this apparent paradox?
There is no paradox. Preferences do not involve prices, and East German consumers preferred Mercedes based solely on product characteristics. However, Mercedes prices are considerably higher than Volkswagen prices. So, even though East German consumers preferred a Mercedes to a Volkswagen, they either could not afford a Mercedes or they preferred a bundle of other goods plus a Volkswagen to a Mercedes alone. While the marginal utility of consuming a Mercedes exceeded the marginal utility of consuming a Volkswagen, East German consumers considered the marginal utility per dollar for each good and, for most of them, the marginal utility per dollar was higher for Volkswagens. As a result, they flocked to Volkswagen dealerships to buy VWs.
Explain whether the following statements are true or false: The level of utility increases as an individual moves downward along the demand curve.
True. As the price of a good falls, the budget line pivots outward, and the consumer is able to move to a higher indifference curve.
Explain whether the following statements are true or false: The marginal rate of substitution diminishes as an individual moves downward along the demand curve
True. The consumer maximizes his utility by choosing the bundle on his budget line where the price ratio is equal to the MRS. For goods 1 and 2, P1/P2 MRS. As the price of good 1 falls, the consumer moves downward along the demand curve for good 1, and the price ratio (P1/P2) becomes smaller. Therefore, MRS must also become smaller, and thus MRS diminishes as an individual moves downward along the demand curve.
Describe the indifference curves associated with two goods that are perfect substitutes. What if they are perfect complements?
Two goods are perfect substitutes if the MRS of one for the other is a constant number. In this case, the slopes of the indifference curves are constant, and the indifference curves are therefore linear. If two goods are perfect complements, the indifference curves are L-shaped. In this case the consumer wants to consume the two goods in a fixed proportion, say one unit of good 1 for every one unit of good 2. If she has more of one good than the other, she does not get any extra satisfaction from the additional units of the first good.
Draw a budget line and then draw an indifference curve to illustrate the satisfaction maximizing choice associated with two products. Use your graph to answer the following questions. a. Suppose that one of the products is rationed. Explain why the consumer is likely to be worse off.
When goods are not rationed, the consumer is able to choose the satisfaction-maximizing bundle where the slope of the budget line is equal to the slope of the indifference curve, or the price ratio is equal to the MRS. This is point A in the diagram below where the consumer buys G1 of good 1 and G2 of good 2 and achieves utility level U2. If good 1 is now rationed at G* the consumer will no longer be able to attain the utility maximizing point. He or she cannot purchase amounts of good 1 exceeding G*. As a result, the consumer will have to purchase more of the other good instead. The highest utility level the consumer can achieve with rationing is U1 at point B. This is not a point of tangency, and the consumer's utility is lower than at point A, so the consumer is worse off as a result of rationing.
Which of the following combinations of goods are complements and which are substitutes? Can they be either in different circumstances? Discuss. a) a mathematics class and an economics class b) tennis balls and a tennis racket c) steak and lobster d)a plane trip and a train trip to the same destination e)bacon and eggs
a)If the math class and the economics class do not conflict in scheduling, then the classes could be either complements or substitutes. Math is important for understanding economics, and economics can motivate mathematics, so the classes could be coFoods can both complement and substitute for each other. b)Tennis balls and a tennis racket are both needed to play tennis, thus they are complements. c)Steak and lobster can be substitutes, as when they are listed as separate items on a menu. However, they can also function as complements because they are often served together. implements. If the classes conflict or the student has room for only one in his schedule, they are substitutes d)Two modes of transportation between the same two points are substitutes for one another. e)Bacon and eggs are often eaten together and are complementary goods in that case. However, in relation to something else, such as pancakes, bacon and eggs can function as substitutes.
Suppose that a consumer spends a fixed amount of income per month on the following pairs of goods: a. tortilla chips and salsa b. tortilla chips and potato chips c. movie tickets and gourmet coffee d. travel by bus and travel by subway If the price of one of the goods increases, explain the effect on the quantity demanded of each of the goods. In each pair, which are likely to be complements and which are likely to be substitutes?
a. If the price of tortilla chips increases, the consumer will demand fewer tortilla chips. Since tortilla chips and salsa are complements, the demand for salsa will drop (the demand curve will shift to the left), and the consumer will demand less salsa. b. If the price of tortilla chips increases, the consumer will demand fewer tortilla chips. Since tortilla chips and potato chips are substitutes, the demand for potato chips will increase (the demand curve will shift to the right), and the consumer will demand more potato chips. c. The consumer will demand fewer movies if the price of tickets increases. You might think the demands for movies and gourmet coffee would be independent of each other. However, because the consumer spends a fixed amount on the two, the demand for coffee will depend on whether the consumer spends more or less of her fixed budget on movies after the price increase. If the consumer's demand elasticity for movie tickets is elastic, she will spend less on movies, and therefore more of her fixed income will be available to spend on coffee. In this case, her demand for coffee increases, and she buys more gourmet coffee. The goods are substitutes in this situation. If her demand for movies is inelastic, however, she will spend more on movies after the price increase, and therefore less on coffee. In this case, she will buy less of both goods in response to the price increase for movies, so the goods are complements. Finally, if her demand for movies is unit elastic, she will spend the same amount on movies and therefore will not change her spending on coffee. In this case, the goods are unrelated, and the demand curve for coffee is unchanged. d. If the price of bus travel increases, the amount of bus travel demanded will fall, and the demand for subway rides will rise, because travel by bus and subway are typically substitutes. The demand curve for subway rides will shift to the right.