微观经济学Ch.docx

微观经济学ChChapter 4: Individual and Market Demand CHAPTER 4 INDIVIDUAL AND MARKET DEMAND QUESTIONS FOR REVIEW 1. Explain the difference between each of the following terms: a. a price consumption curve and a demand curve; A price consumption curve identifies the utility maximizing combinations of two goods as the price of one of the goods changes. When the price of one of the goods declines, the budget line will pivot outwards, and a new utility maximizing bundle will be chosen. The price consumption curve connects all such bundles. A demand curve is a graphical relationship between the price of a good and the (utility maximizing) quantity demanded of a good, all else the same. Price is plotted on the vertical axis and quantity demanded on the horizontal axis. b. an individual demand curve and a market demand curve; An individual demand curve identifies the (utility maximizing) quantity demanded by one person at any given price of the good. A market demand curve is the sum of the individual demand curves for any given product. At any given price, the market demand curve identifies the quantity demanded by all individuals, all else the same. c. an Engel curve and a demand curve; A demand curve identifies the quantity demanded of a good for any given price, holding income and all else the same. An Engel curve identifies the quantity demanded of a good for any given income, holding prices and all else the same. d. an income effect and a substitution effect; The substitution effect measures the effect of a change in the price of a good on the consumption of the good, utility held constant. This change in price changes the slope of the budget line and causes the consumer to rotate along the current indifference curve. The income effect measures the effect of a change in purchasing power (caused by a change in the price of a good) on the consumption of the good, relative prices held constant. For example, an increase in the price of good 1 (on the horizontal axis) will rotate the budget line down along the indifference curve as the slope of the budget line (the relative price ratio) changes. This is the substitution effect. This new budget line will then shift inwards to reflect the decline in purchasing power caused by the increase in the price of the good. This is the income effect. 3. Explain whether the following statements are true or false. a. The marginal rate of substitution diminishes as an individual moves downward along the demand curve. This is true. The consumer will maximize his utility by choosing the bundle on his budget line where the price ratio is equal to the MRS. Suppose the consumer chooses P1=MRS. As the price of good 1 falls, the the quantity of goods 1 and 2 such that P2price ratio becomes a smaller number and hence the MRS becomes a smaller number. This means that as the price of good 1 falls, the consumer is willing to give up fewer units of good 2 in exchange for another unit of good 1. b. The level of utility increases as an individual moves downward along the demand curve. This is true. As the price of a good falls, the budget line pivots outwards and the consumer is able to move to a higher indifference curve. 41 Chapter 4: Individual and Market Demand c. Engel curves always slope upwards. This is false. The Engel curve identifies the relationship between the quantity demanded of a good and income, all else the same. If the good is inferior, then as income increases, quantity demanded will decrease, and the Engel curve will slope downwards. 5. Which of the following combinations of goods are complements and which are substitutes? Could they be either in different circumstances? Discuss. a. a mathematics class and an economics class If the math class and the economics class do not conflict in scheduling, then the classes could be either complements or substitutes. The math class may illuminate economics, and the economics class can motivate mathematics. If the classes conflict, they are substitutes. b. tennis balls and a tennis racket Tennis balls and a tennis racket are both needed to play a game of tennis, thus they are complements. c. steak and lobster Foods can both complement and substitute for each other. Steak and lobster can compete, i.e., be substitutes, when they are listed as separate items on a menu. However, they can also function as complements because they are often served together. d. a plane trip and a train trip to the same destination Two modes of transportation between the same two points are substitutes for one another. e. bacon and eggs Bacon and eggs are often eaten together and are, therefore, complementary goods. By considering them in relation to something else, such as pancakes, bacon and eggs can function as substitutes. 7. Which of the following events would cause a movement along the demand curve for U.S.-produced clothing, and which would cause a shift in the demand curve? a. the removal of quotas on the importation of foreign clothes The removal of quotas will shift the demand curve inward for domestically-produced clothes, because foreign-produced goods are substitutes for domestically-produced goods. Both the equilibrium price and quantity will fall as foreign clothes are traded in a free market environment. b. an increase in the income of U.S. citizens When income rises, expenditures on normal goods such as clothing increase, causing the demand curve to shift out. The equilibrium quantity and price will increase. c. a cut in the industrys costs of producing domestic clothes that is passed on to the market in the form of lower clothing prices A cut in an industrys costs will shift the supply curve out. The equilibrium price will fall and quantity will increase. There is a movement along the demand curve. 9. Suppose that the average household in a state consumes 800 gallons of gasoline per year. A 20-cent gasoline tax is introduced, coupled with a $160 annual tax rebate per household. Will the household be better or worse off under the new program? If the household does not change its consumption of gasoline, it will be unaffected by the tax-rebate program, because in this case the household pays 0.20*800=$160 in taxes and receives $160 as an annual tax rebate. The two effects would cancel each 42 Chapter 4: Individual and Market Demand other out. To the extent that the household reduces its gas consumption through substitution, it must be better off. The new budget line (price change plus rebate) will pass through the old consumption point of 800 gallons of gasoline, and any now affordable bundle that contains less gasoline must be on a higher indifference curve. The household will not choose any bundle with more gasoline because these bundles are all inside the old budget line, and hence are inferior to the bundle with 800 gallons of gas. 11. Explain which of the following items in each pair is more price elastic. a. The demand for a specific brand of toothpaste and the demand for toothpaste in general. The demand for a specific brand is more elastic since the consumer can easily switch to another brand if the price goes up. b. The demand for gasoline in the short run and the demand for gasoline in the long run. Demand in the long run is more elastic since consumers have had more time to adjust to the change in price. EXERCISES 1. An individual sets aside a certain amount of his income per month to spend on his two hobbies, collecting wine and collecting books. Given the information below, illustrate both the price consumption curve associated with changes in the price of wine, and the demand curve for wine. Price Wine Price Book Quantity Wine Quantity Book Budget $10 $12 $15 $20 $10 $10 $10 $10 7 5 4 2 8 9 9 11 $150 $150 $150 $150 The price consumption curve connects each of the four optimal bundles given in the table above. As the price of wine increases, the budget line will pivot inwards and the optimal bundle will change. 4. a. Orange juice and apple juice are known to be perfect substitutes. Draw the appropriate price-consumption (for a variable price of orange juice) and income-consumption curves. We know that the indifference curves for perfect substitutes will be straight lines. In this case, the consumer will always purchase the cheaper of the two goods. If the price of orange juice is less than that of apple juice, the consumer will purchase only orange juice and the price consumption curve will be on the “orange juice axis” of the graph (point F). If apple juice is cheaper, the consumer will purchase only apple juice and the price consumption curve will be on the “apple juice axis” (point E). If the two goods have the same price, the consumer will be indifferent between the two; the price consumption curve will coincide with the indifference curve (between E and F). See the figure below. 43 Chapter 4: Individual and Market Demand Apple JuicePA < POEPA = POPA > POUFOrange JuiceAssuming that the price of orange juice is less than the price of apple juice, the consumer will maximize her utility by consuming only orange juice. As the level of income varies, only the amount of orange juice varies. Thus, the income consumption curve will be the “orange juice axis” in the figure below. Apple JuiceBudgetConstraintIncomeConsumptionCurveU3U2U1Orange Juice4.b. Left shoes and right shoes are perfect complements. Draw the appropriate price-consumption and income-consumption curves. For goods that are perfect complements, such as right shoes and left shoes, we know that the indifference curves are L-shaped. The point of utility maximization occurs when the budget constraints, L1 and L2 touch the kink of U1 and U2. See the following figure. 44 Chapter 4: Individual and Market Demand RightShoesPriceConsumptionCurveU2L1U1L2Left ShoesIn the case of perfect complements, the income consumption curve is also a line through the corners of the L-shaped indifference curves. See the figure below. RightShoesIncomeConsumptionCurveU2U1L1L2Left Shoes6. Two individuals, Sam and Barb, derive utility from the hours of leisure (L) they consume and from the amount of goods (G) they consume. In order to maximize utility they need to allocate the 24 hours in the day between leisure hours and work hours. Assume that all hours not spent working are leisure hours. The price of a good is equal to $1 and the price of leisure is equal to the hourly wage. We observe the following information about the choices that the two individuals make: Price of G 1 1 1 1 Price of L 8 9 10 11 Sam L(hours) 16 15 14 14 Barb L(hours) 14 14 15 16 Sam G($) 64 81 100 110 Barb G($) 80 90 90 88 45 Chapter 4: Individual and Market Demand Graphically illustrate Sams leisure demand curve and Barbs leisure demand curve. Place price on the vertical axis and leisure on the horizontal axis. Given that they both maximize utility, how can you explain the difference in their leisure demand curves? It is important to remember that less leisure implies more hours spent working at the higher wage. Sams leisure demand curve is downward sloping. As the price of leisure (the wage) rises, he chooses to consume less leisure to spend more time working at a higher wage to buy more goods. Barbs leisure demand curve is upward sloping. As the price of leisure rises, she chooses to consume more leisure since her working hours are generating more income. This difference in demand can be explained by examining the income and substitution effects for the two individuals. The substitution effect measures the effect of the change in the price of leisure, keeping utility constant (the budget line will rotate around the current indifference curve). Since the substitution effect is always negative, a rise in the price of leisure will cause both individuals to consume less leisure. The income effect measures the change in purchasing power caused by the change in the price of leisure. Here, when the price of leisure (the wage) rises, there is an increase in purchasing power (the new budget line will shift outwards). Assuming both individuals consider leisure to be a normal good (this is not a necessary assumption for Sam), then the increase in purchasing power will increase demand for leisure. For Sam, the reduction in leisure demand caused by the substitution effect outweighs the increase in demand for leisure caused by the income effect. For Barb, her income effect is larger than her substitution effect. 7. The director of a theatre company in a small college town is considering changing the way he prices tickets. He has hired an economic consulting firm to estimate the demand for tickets. The firm has classified people who go the theatre into two groups, and has come up with two demand functions. The demand curves for the general public (Qgp) and students (Qs) are given below. Qgp=500-5Pa. Qs=200-4PGraph the two demand curves on one graph, with P on the vertical axis and Q on the horizontal axis. If the current price of tickets is $35, identify the quantity demanded by each group. Both demand curves are downward sloping and linear. For the general public, the vertical intercept is 100 and the horizontal intercept is 500. For the students, the vertical intercept is 50 and the horizontal intercept is 200. The general public demands Qgp=500-5(35)=325tickets and the students demand Qs=200-4(35)=60 tickets. b. Find the price elasticity of demand for each group at the current price and quantity. -5(35)=-0.54 and the elasticity for The elasticity for the general public is egp=325-4(35)=-2.33. If the price of tickets increases by one percent the students is egp=60then the general public will demand .54% fewer tickets and the students will demand 2.33% fewer tickets. Is the director maximizing the revenue he collects from ticket sales by charging $35 for each ticket? Explain. No he is not maximizing revenue since neither one of the calculated elasticities is equal to 1. Since demand by the general public is inelastic at the current price, the director could increase the price and quantity demanded would fall by a smaller amount in percentage terms, causing revenue to increase. Since demand by the c. 46 Chapter 4: Individual and Market Demand students is elastic at the current price, the director could decrease the price and quantity demanded would increase by a larger amount in percentage terms, causing revenue to increase. d. What price should he charge each group if he wants to maximize revenue collected from ticket sales? To figure this out, find the formula for elasticity, set it equal to 1, and solve for p