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Session 5: Consumer Choice: Ch 6 & Appendix Tips for Navigation in the presentation: Right mouse click to advance, or Use the arrow keys to navigate in the presentation : the up or right arrow to advance, the down or left arrow to go back; This image house appears on every slide in the upper left and operates as a hyper link to the slide “Lecture Outline” Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 1 End Illustration Indifference Curve Analysis How many internet minutes will you consume when the choices are travel to a location for free WIFI of pay for a service on location? At http://intel.jiwire.com, you can type in a zip code and get a list of hotspots within a mile radius. You can also specify a kind of location (like "hotel") and/or a service provider (like T-Mobile or Boingo). The site also tells you about any fees, which can run up to $10 a day. For a list of free hotspots, WifiFreeSpot.com covers everything from hotels to gas stations. Source: WSJ “Quick Fix” about Dec 30, 2003, Rob Turner Begin 2 Utility This diagram shows how the usage changes for a hypothetical adult as they pass from unemployed student to working graduate and their income increases (the budget lines shifts out when the become employed) 3 U. Max 4 Demand 5 I. Curves 6 U. Max End Session 5: Lecture Outline 1 First Slide 2 Definition of Utility 3 Rule for Maximization of Utility: 4 Market Demand Curve: 5 Indifference Curves, Budget Lines 6 Utility Maximization Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 3 End 2.0 Definitions of Utility 2 Definition of Utility 2.1 Utility: Cardinal and Ordinal 2.2 Total Utility (TU) and Marginal Utility (MU = TU/ q) 2.3 Diminishing Marginal Utility (DMU) • Example- A Table • Example: Mr. Cresote Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 4 End 2.1 Cardinal and Ordinal Utility Cardinal Utility : consumers can assign a number (say a scale of 1 to 10) that represents the amount of satisfaction received from consumption o f a good. Ordinal Utility. Consumers do not assign numbers, rather, consumers make relative comparisons--I prefer this to that. This economic model is an improvement by the principle of Occum’s Razor, because it is simpler! Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 5 End 2.2 Total and Marginal Utility Let’s now distinguish between total utility and marginal utility Total utility (TU) is the total satisfaction a person derives from consumption Marginal utility (MU) is the change in total utility resulting from a one-unit change in consumption of a good MU = TU/ q Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 6 End 2.3a Law of Diminishing Marginal Utility The more of a good an individual consumes per time period, other things constant, the smaller the increase in total utility from additional consumption Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 7 End 2.3b: Utility Derived from Water Units of Water Consumed Total Marginal (8 ounce glass) Utility Utility 0 0 1 40 40 2 60 20 3 70 10 4 75 5 5 73 -2 The first column lists possible quantities of water a person might consume after running on a hot day. The second column presents the total utility derived from that consumption and the third column presents the marginal utility of each additional glass of water consumed change in total utility from consuming an additional unit. Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 8 End 2.3cTotal and Marginal Utility: Mr Creosote Because of diminishing marginal, each glass adds less to total utility total utility increases for the first four glasses but at a decreasing rate In our example, diminishing marginal utility begins with the first unit as seen by the pattern of marginal utility Monty Python The Meaning of Life Total Utility In this clip Mr. Creosote is at an elegant buffet restaurant enjoying an fixed price all you can eat dinner. The law of diminishing utility implies that consumption has linits. In this clip Mr Creosote eats his way in to the negative portion of the MU curve. Many people over eat at buffet restaurants because additional servings are free. But few eat into the negative region of MU. Marginal Utility What about Mr. Creosote’s 5th glass of water? (clip 12 is 2:00 mins but is for a fee, the free link is 6:46 mins, and fast forward to 5:30 for the illustration Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 9 End 3.0 Utility Maximization Rule for Maximization of Utility: 3.1 Two goods and an income constraint (1,2,3) 3.2 Law of Demand (1, 2, 3) 3.3 Example: Pizzas and Videos • Goal: purchase the utility maximizing bundle • Start out buying 5 pizzas: TU =142 • By trail and error, end up with 2 pizzas and 4 videos: TU = 212 3.4 Utility Maximizing Condition: MU/Price (1,2) 3.5 Derive A Demand Curve (1, 2, 3) Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 10 End 3.1a Utility Maximization with 2 Goods Now we will learn about an algebraic model using ordinal utility to show how an ecomomist’s model of how a consumer chooses a consumption bundle that maximizes total utility. So here are the details of a specific illustration: The price of pizza is $8 The rental price of a movie video is $4 A budget of $40 per week By trial and error we will continue to make adjustments as long as utility can be increased when no further utility-increasing moves are possible, we have arrived at the equilibrium combination Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 11 End 3.1b Two Goods: Pizza & Video Rentals Marginal Utility of Pizza Pizza Total Marginal per Dollar Video Total Marginal Consumed Utility Utility Expended Rentals Utility of Utility of Per Week of Pizza of Pizza (price=$8) per Week Videos Videos (1) (2) (3) (4) (5) (6) (7) $32 $40 0 1 2 3 4 5 6 0 56 88 112 130 142 150 56 32 24 18 12 8 7 4 3 2¼ 1½ 1 0 1 2 3 4 5 6 0 40 68 88 100 108 114 40 28 20 12 8 6 Marginal Utility of Videos per Dollar Expended (price=$4) (8) 10 7 5 3 2 1½ $8 To get the process going, suppose you start off spending your entire budget of $40 on pizza 5 pizzas per week, (5 x$ 8 = $40) at a total utility of 142. If you give up one pizza, you free up enough money ($8) to rent 2 videos (2 x $4). Would total utility increase from this reallocation? You give up 12 units of utility – the marginal utility of the 5th unit of pizza, to get 68 units of utility (40 + 28) from the first 2 videos total utility increases from 142 to 198 (198 = 130 + 68). Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 12 End 3.1c Two Goods: Pizza & Video Rentals Marginal Marginal Utility Utility of Pizza of Videos Pizza Total Marginal per Dollar Video Total Marginal per Dollar Consumed Utility Utility Expended Rentals Utility of Utility of Expended Per Week of Pizza of Pizza (price=$8) per Week Videos Videos (price=$4) (1) (2) (3) (4) (5) (6) (7) (8) 0 1 2 3 4 5 6 0 56 88 112 130 142 150 56 32 24 18 12 8 7 4 3 2¼ 1½ 1 0 1 2 3 4 5 6 0 40 68 88 100 108 114 40 28 20 12 8 6 10 7 5 3 2 1½ If you reduce consumption of pizza to 3 units, you give up 18 units of utility from the 4th unit of pizza but gain a total of 32 units (20 + 12) of utility from the 3rd and 4th videos, another utility-increasing move. TU would rise from 198 =( 130 + 68) to 212=(112 + 100). Further reductions in pizza would reduce total utility because you would give up 24 units of utility from the 3rd pizza but gain only 14 (8 + 6) from the 5th and 6th video rentals. TU would fall from 212 (112 + 100) to 202 ( 88 + 114). Thus, by trial and error, we find that the utility-maximizing equilibrium condition is 3 pizzas and 4 videos per week, for a total utility of 212 and an outlay of $24 on pizza and $16 on videos Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 13 End 3.1d Utility-Maximizing Condition Consumer equilibrium is achieved when the budget is completely spent and the last dollar spent on each good yields the same utility MUp MUv Pv Pp Where MUp is the marginal utility of pizza, pp is the price of pizza, MUv is the marginal utility of videos, and pv the price of videos Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 14 End 3.1e Two Goods : Pizza & Video Rentals Marginal Marginal Utility Utility of Pizza of Videos Pizza Total Marginal per Dollar Video Total Marginal per Dollar Consumed Utility Utility Expended Rentals Utility of Utility of Expended Per Week of Pizza of Pizza (price=$8) per Week Videos Videos (price=$4) (1) (2) (3) (4) (5) (6) (7) (8) 0 1 2 3 4 5 6 0 56 88 112 130 142 150 56 32 24 18 12 8 7 4 3 2¼ 1½ 1 0 1 2 3 4 5 6 0 40 68 88 100 108 114 40 28 20 12 8 6 10 7 5 3 2 1½ The utility-maximizing bundle is 3 pizzas and 4 videos, a total utility of 212 and a total outlay of $40 comprised of $24 on pizza and $16 on videos The return (MUp/Pp ) on the consumption of 3 Pizzas is $3 (24/$3) equals the return (MUv/Pv ) on the renting of 4 videos, which is $3 (12/$4) Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 15 End 3.2 a Law of Demand and Marginal Utility The preceding example can be used to generate a single point on the demand curve for pizzas at a price of $8, the quantity demanded is 3 pizzas per week, based on an income of $40 per week, a . price of $4 per video rental. To generate another point on the demand curve for pizza, lets reduce the price of pizza to $6 Exhibit 4 is the same as Exhibit 3 except that the price of pizza has been reduced Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 16 End 3.2b Two Goods : Pizza & Video Rentals Marginal Utility of Pizza Pizza Total Marginal per Dollar Consumed Utility Utility Expended Per Week of Pizza of Pizza (price=$6) (1) (2) (3) (4) 0 1 2 3 4 5 6 0 56 88 112 130 142 150 56 32 24 18 12 8 9 1/3 5 1/3 4 3 2 1 1/3 Marginal Utility of Videos Video Total Marginal per Dollar Rentals Utility of Utility of Expended per Week Videos Videos (price=$4) (5) (6) (7) (8) 0 1 2 3 4 5 6 0 40 68 88 100 108 114 40 28 20 12 8 6 10 7 5 3 2 1½ The above table is the original example, except column 4 is recomputed at a price of $6 per pizza. For the original consumer equilibrium of 3 pizzas and 4 video rentals, the marginal utility per dollar expended on the third pizza rises to 4, while the marginal utility per dollar on the fourth video remains at 3. Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 17 End 3.2c Two Goods : Pizza & Video Rentals Marginal Marginal Utility Utility of Pizza of Videos Pizza Total Marginal per Dollar Video Total Marginal per Dollar Consumed Utility Utility Expended Rentals Utility of Utility of Expended Per Week of Pizza of Pizza (price=$6) per Week Videos Videos (price=$4) (1) (2) (3) (4) (5) (6) (7) (8) 0 1 2 3 4 5 6 0 56 88 112 130 142 150 56 32 24 18 12 8 9 1/3 5 1/3 4 3 2 1 1/3 0 1 2 3 4 5 6 0 40 68 88 100 108 114 40 28 20 12 8 6 10 7 5 3 2 1½ Additionally, based on the new lower price of pizza we would have $6 unspent, because 3 pizzas cost $18 (3x$6) and 4 videos cost $16 (4x$4) for a total of $34 instead of $40 Based on this new lower price for pizza, we would increase our consumption to 4 pizzas per week total utility increases by the 18 units derived from the 4th pizza, and we are now spending $40 ($24 + $16). ($6 x4 pizzas + $4x4 videos). We are once again in equilibrium and the MU/P ratios are equal.. Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 18 End 3.2d Demand Curve for Pizza Demand Curve Generated from Marginal Utility Model After the price of pizza declines to $6, the consumer purchases 4 units of pizza as shown by point b. 2 Utility b 6 4 2 0 Begin a $8 Price per pizza The original position of consumer equilibrium at the price of $8 is shown as point a where the consumer purchased 3 units of pizza. D 1 2 3 U. Max 4 Demand 3 4 5 I. Curves Pizzas per week 6 U. Max 19 End 4.0 Market Demand 4.1 Market Demand Curve Horizontal Summation 4.2 Consumer Surplus The Diagram Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 20 End 4.1a Market Demand We can now talk more generally about the market demand for a good The market demand is simply the horizontal sum of the individual demand curves for all consumers in the market Tne next slide shows this process for three consumers Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 21 End 4.1b Summing Individual Demands to Derive Market Demand The market demand shows the total quantity demanded per period by all consumers at various prices. (d) Market demand (b) Brittany (c) Chris for Subways Price (a) You $6 $6 $6 $6 4 4 4 4 2 0 dY 2 0 2 4 6 Subways per month dB 2 4 2 0 dC 2 dA + dB + dC = D 2 0 2 6 12 At a price of $6, you demand 2 per month, Brittany 0, and Chris 0. market demand is 2 At a price of $4, you demand 4 Subways, Brittany 2, and Chris none. the market demand at a price of $4 is 6. At a price of $2, you demand 6 per month, Brittany 4, and Chris 2. market demand is 12 Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 22 End 4.2a Consumer Surplus: What is it? Consumer surplus is the net benefit consumers get from market exchange That is, it a measure of the consumer satisfaction from a good in excess of the price they have to pay for the good. It is used to measure economic welfare and to compare the effects of such concepts as Different market structures: competition v monopoly Different tax structures: sales taxes v income taxes Different public expenditure programs: voting models Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 23 End 4.2b Consumer Surplus At price = $8, the marginal utility of other goods is higher than the marginal utility of a Subway no Subways are purchased. At price = $7, the consumer is willing and able to buy one per month, at price = $6, 2 are purchased the second is worth at least $6. At price = $5, 3 are purchased, and so on. In each case, the value of the last subway purchased must at least equal the price, otherwise it would not be purchased. Along the demand curve, the price reflects the marginal valuation of the good, or the dollar value of the marginal utility derived from consuming each additional unit. $8 7 6 5 4 3 2 1 D 0 1 2 3 4 5 6 7 8 Subways per month Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 24 End 4.2c Consumer Surplus When price = $4, each of the four Subways can be purchased at this price, even though the consumer would have been willing to pay more for each of the first three. For the first sandwich the consumer surplus is $3, i.e. ($7-$4), $2 for the second, i.e. ($6-$4), and $1 for the third. Thus, the dollar value of the total consumer surplus of the first four sandwiches is $3 + $2 + $1 + $0 = $6. A price of $4 confers a consumer surplus of $6, equal to the difference between the maximum amount we would have been willing to pay ($22=$7+$6+5+$4) rather than go without Subways and what we actually paid ($16=$4x4)). $8 7 6 5 4 3 2 1 Later on we will show that in the continuous case the consumer surplus is represented by the red 0 triangle formed by the area below demand and above price and its area of that triangle would be 8=(.5)($4x4subs) Begin 2 Utility D 1 2 3 U. Max 4 Demand 3 4 5 6 5 I. Curves 7 Subways per 8 month 6 U. Max 25 End 4.2d Consumer surplus from sub sandwiches At P=$4: •1st sub valued at $7 •2nd sub valued at $6 •3rd sub valued at $5 •4th sub valued at $4 •Willing to pay $22 for 4 subs •Pays only $16 for 4 subs •Consumer surplus $22-$16 = $6 Price per subs $8 7 6 5 4 3 2 1 0 D 1 2 3 4 5 6 7 8 Subs per month When P drops to $3, consumer surplus increases by $4 Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 26 End 4.2e Market demand and consumers surplus, continuous case Price per unit Consumer surplus at a price of $2 is shown by the blue area. If the price falls to $1, consumer surplus increases to include the green area. At a zero price, consumer surplus increases to the entire area under the D curve. $2 1 D 0 Quantity per period Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 27 End 4.2f Consumer Surplus: Exercise Price $40 $30 $25 $20 To do this exercise you need to leave the “slide show” view, by striking the “Esc” key. Question: Resize and use the triangle below K to identify the Z consumer surplus at G the price of $20 900 at the price of $20, the area of the triangle representing the consumer surplus is one-half base time height, or (.5) times ($20 times 600 units) which equals $6,000. 5 I. Curves 6 U. Max H $10 Demand 300 Your yellow triangle should fill the area between the price of $20 and up to the demand curve. Begin 2 Utility 600 Quantity 3 U. Max 4 Demand 28 End 5.0 Indifference Curves 5.1 Ordinal Utility 5.2 Indifference Curves (ICs) pic 5.3 The Marginal Rate of Substitution Pic, formula 5.4 The Indifference Curve Map 5.5 Non-intersecting 5.6 Summary ICs 5.7 The budget line 5.8 Summary ICs and Budget Lines Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 29 End 5.1. Ordinal Utility: I prefer this to that All this new approach requires is that consumers be able to rank their preferences for various combinations of goods Specifically, the consumer should be able to say whether Combination A is preferred to combination B Combination B is preferred to combination A. or Both combinations are equally preferred Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 30 End 5.2.a Indifference Curves & Properties An Indifference Curve is defined as showing all combinations of goods that provide the consumer with the same satisfaction, or the same utility In other words, along the indifference curve, the consumer finds all combinations on the curve equally preferred Since each of the alternative bundles of goods yields the same level of utility, the consumer is indifferent about which combination is actually consumed Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 31 End Video rentals per week 5.2b Here is an indifference curve An indifference curve (I) shows all combinations of two goods that provide a particular consumer with the same total utility. 10 a 8 5 4 3 2 0 Indifference curve: • negative slope • convex to origin b c d 1 2 3 4 5 Begin 2 Utility I 10 Pizzas per week 3 U. Max 4 Demand 5 I. Curves 6 U. Max 32 End 5.3.a Indifference Curves Slope Down Because… For a person to remain indifferent among consumption combinations, the increase in utility from eating more pizza must just offset the decrease in utility from watching fewer videos Thus, along an indifference curve, there is an inverse relationship between the quantity of one good consumed and the quantity of another consumed indifference curves slope down Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 33 End 5.3.b Moving along an Indifference Curve We will show the MRS is: “what you give up” / “what you get” which is the same calculation •Suppose there are only two goods available: pizzas and movie videos •On the indifference curve Point a shows the consumption bundle consisting of 1 pizza and 8 video rentals •On the indifference curve the consumer is indifferent between point a and the other points b,c, and d. 10 “a” to “b” trade 4 videos for 1 pizza •Question: Holding utility constant, how many video rentals would a person be willing to give up to get a second pizza? 5 4 3 •Answer: Moving from point a to point b, she is willing to give up 4 videos to get a second pizza (total utility is the same at points a and b); the marginal utility of another pizza per week is just sufficient to compensate for the utility lost from decreasing video purchases by 4 movies per week. 2 Begin 2 Utility a 8 b c d I 0 1 2 3 4 5 3 U. Max 4 Demand Pizzas per week 5 I. Curves 6 U. Max 10 34 End 5.3.c Moving along an Indifference Curve Question: In moving from point b to c, how many video rentals would a person be willing to give up to get a second pizza? Answer: the person is willing to give up 1 video for another pizza. Once at point c, the person is willing to give up another video only if they get two more pizzas in return, and combination d consists of 5 pizzas and 2 videos Points a, b, c, and d can be connected to form the indifference curve, I, which represents possible combinations of pizza and videos that would keep the person at the same level of total utility. 10 a 8 5 4 3 “b” to “c” ? Trade 1 video for 1 pizza b c d 2 I 0 1 2 3 4 5 10 Pizzas per week Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 35 End 5.3.d Marginal Rate of Substitution Defined The marginal rate of substitution, or MRS measures the consumers willingness to trade one good for another. The MRS P,V , between pizza and videos indicates the number of videos that the consumer is willing to give up to get one more pizza, while maintaining the same level of total utility. MRS P,V =V/P = slope of IC Alternatively, The marginal rate of substitution of pizzas for video rentals can be found from the marginal utilities of pizza and video MRS P,V = MUP / MUV Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 36 End 5.3.e Marginal Rate of Substitution Graphed Mathematically, the MRS is equal to the absolute value of the slope of the indifference curve For example, in moving from combination a to combination b, the consumer is willing to give up 4 videos to get 1 more pizza slope between these two points equals “–4” MRS P,V = 4; by the same logic from b to c, MRS = 1 10 a 8 “a” to “b” MRS=4 5 4 3 “b” to “c” MRS=1 b c d 2 I 0 1 2 3 4 5 Begin 2 Utility 3 U. Max 4 Demand Pizzas per week 5 I. Curves 6 U. Max 10 37 End 5.3.f Marginal Rate of Substitution Declines The law of diminishing marginal rate of substitution says that as a person’s consumption of pizza increases, the number of videos that they are willing to give up to get another pizza declines. MRS P,V =V/P falls as pizza consumption increases This implies that the indifference curve has a diminishing slope as we move down the indifference curve, the consumption of pizza increases and the marginal utility of additional pizza declines MRS P,V = MUP / MUV falls as pizza consumption increases Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 38 End 5.4.a Higher Preferred to Lower: Indifference Map We can use the same approach to generate a series of indifference curves, called an indifference map graphical representation of a consumer’s tastes Each curve in the map reflects a different level of utility The next slide illustrates an indifference map for a particular consumer Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 39 End Video rentals per week 5.4.b An indifference curve map Indifference curves I1 through I4 are examples from a consumer’s particular indifference map. 10 5 I4 I2 I3 Indifference curves farther from origin depict higher levels of utility. I1 0 5 10 Pizzas per week A line intersects each higher indifference curve, reflecting more of both goods. Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 40 End If indifference curves crossed, such as point i, then every point on indifference curve I and every point on curve I', would have to reflect the same level of utility as at point i But point k is a combination with more pizza and more videos than point j must represent a higher level of utility Video rentals per week 5.5. Indifference Curves Do Not Intersect k j i I' I 0 Begin 2 Utility 3 U. Max 4 Demand Pizzas per week 5 I. Curves 6 U. Max 41 End 5.6 Summary: Indifference Curves A particular indifference curve reflects a constant level of utility the consumer is indifferent among all consumption combinations along a given curve Because total utility is to constant along an IC, an increase in the consumption of one good must be offset by a decrease in the consumption of the other good indifference curves slope downward Reflects the law of diminishing marginal rate of substitution Higher indifference curves represent higher levels of utility. Indifference curves do not intersect Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 42 End 5.7a The Budget Line Now that we have the consumer’s indifference may, we now need to depict the consumer’s budget. To answer this question, we must consider the relative prices of the two goods and the consumer’s income Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 43 End 5.7b The Budget Line Defined The Budget line depicts all possible combinations of movies and pizzas, given prices and your budget It is drawn from the point of intersection with the vertical axis to the point of intersection with the horizontal axis. Suppose videos rent for $4 and are represented on the vertical axis, and pizza sells for $8 and is represented on the horizontal axis. Suppose the budget is $40 per week. if you spend the entire $40 on videos, the consumer can purchase ($40/$4) = 10 videos—this is the vertical intercept if you spend the entire $40 on pizzas, the consumer can purchase ($40/$8) = 5 pizzas—this is the horizontal intercept Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 44 End Given the prices and budget, the budget line meets the vertical axis at 10 videos and meets the horizontal axis at 5 pizzas These two intercepts are then connected to form the budget line. The budget line defines all possible combinations of the two goods, pizza and videos, that can be purchased, given prices and income can be thought of as a consumption possibilities frontier Video rentals per week 5.7c Slope of Budget Line 10 5 0 Slope of the budget line indicates what it costs the consumer in terms of foregone video rentals to get another pizza =rise/run = -(I / pv )/ (I / pp ) = - pP / pV –pp –$8 Slope = = = –2 pv $4 5 10 Pizzas per week At the point where the budget line meets the vertical axis, the maximum number of videos you can rent equals income divided by the video rental price = I / pv and for the horizontal axis is I / pp . Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 45 End 5.8 Summary: Indifference Curve & Budget Line The indifference curve indicates what the consumer is willing to buy The budget line shows what the consumer is able to buy When the indifference curve and the budget line are combined, we find the quantities of each good the consumer is both willing and able to buy When they are tangent this is the point of Utility Maximization as shown in the next section Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 46 End 6.0 Utility Maximization 6 .1 Utility Maximization: • Tangent, when slopes are equal, MU/P = across all goods 6.2 Deriving a Demand Curve 6.3 The Substitution and Income Effects (challenging) 6.4 Summary Substitution and Income Effects (challenging) 6.5 Exercise (only works in PPT file) 6.5 Self-Review of 6.3 & 6.4 (challenging) Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 47 End The utility-maximizing consumer will select a combination along the budget line that lies on the highest attainable indifference curve Given prices and income, this occurs at point e, where I2 just touches, or is tangent to, the budget line buy 3 pizzas at $8 each and rent 4 videos at $4 each (3x$8 = 4x$4) = $40 Other attainable combinations along the budget line reflect lower levels of utility. For example, point a is on the budget line a combination that can be purchased. However, point a lies on a lower indifference curve. Begin 2 Utility Video rentals per week 6.1a Utility Maximization 10 a 5 4 e I1 0 3 U. Max 4 Demand 3 5 I2 I3 10 Pizzas per week 5 I. Curves 6 U. Max 48 End 6.1b Consumer Equilibrium & Utility Maximization Consumer equilibrium occurs where the slope of the indifference curve is equal to the slope of the budget line Recall that the absolute value of the slope of the indifference curve is the marginal rate of substitution, MRS P,V = MUP / MUV and the absolute value of the slope of the budget line equals the price ratio slope = PP / PV Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 49 End 6.1c Consumer Equilibrium & Utility Maximization Thus, the utility maximization condition MUP PP MUV PV Or rearranging terms, MUP MUV PP PV Which you will recall is the rule we used earlier, spend income until the per unit return from consumption (MU/P) is equalized across all items! Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 50 End 6.2a Deriving the Demand Curve The Indifference Curve analysis is used to derive a demand curve The derivation begins with the question: What happens to the consumer’s equilibrium consumption when there is a change in price? The next slide illustrates the derivation Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 51 6 U. Max End Recall the initial equilibrium is at point e with 3 pizzas ($8 each) and 4 videos ($4 each) with budget of $40. Suppose the price of pizza falls from $8 to $4, other things constant consumer can now purchase a maximum of 10 pizzas with a budget of $40. The budget intercept line rotates out from 5 to 10 pizzas. Since the rental price of videos has not changed, the maximum number of videos that can be rented remains the same at 10. Video rentals per week 6.2b Deriving the Demand Curve: I 10 e* 5 4 e I* I 0 3 5 10 Pizzas per week With the decrease in price, the new equilibrium occurs at e*, where pizza purchases increase from 3 to 5, and video rentals rises to 5. Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 52 End 6.2c Deriving the Demand Curve: II (a) 10 Videos per week To recap, as the price of pizza fell from $8 per unit to $4 per unit, other things assumed constant, the budget line rotates out and the quantity d increases from 3 to 5 . 5 4 e" e I 0 In the price quantity space we plot the information for the indifference curve analysis. Point “e” is the initial point of $8 and 3 pizzas. Point e” is the new equilibrium of $4 and 5 pizzas. Thus, from the indifference curve model we have shown how to derive a down ward sloping demand curve. Price per pizza (b) 3 4 5 7 10 Pizzas per week e $8 e" D 4 0 3 4 5 7 10 Pizzas per week Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 53 End 6.3a Substitution and Income Effects The law of demand was initially explained in terms of a substitution effect and an income effect With indifference curve analysis we have the analytical tools to examine these two effects more precisely The next slide illustrates this process Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 54 End Suppose the price of pizza falls from $8 to $4, other things constant consumer can now purchase a maximum of 10 pizzas with a budget of $40. The budget intercept line rotates out from 5 to 10 pizzas. The increase in the quantity of pizzas demanded can be broken down into the substitution and the income effect of a price change. When the price of pizza falls, the change in the ratio of the price of pizza to the price of video rentals shows up through the change in the slope of the budget line. Video rentals per week 6.3b Substitution and Income Effects 10 e* 5 4 e I* I 0 3 5 10 Pizzas per week To derive the substitution effect, let’s assume that you must maintain the same level of utility after the price change as before consumer’s utility level has not changed but the relative prices you face have changed. Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 55 End A new budget line reflecting the change in relative prices, and holding utility constant, can be shown by constructing the dashed line CF. Given the new set of relative prices, the consumer increases the quantity of pizza demanded to the point on the indifference curve I that is just tangent to the dashed budget line e’ by constraining utility to its initial level (I) and using the new relative prices, we have eliminated the change in real income caused by the price change. The consumer moves down along the indifference curve I to point e', renting fewer videos but buying more pizzas. These changes reflect the substitution effect of lower prices of pizza Video rentals per week 6.3c The Substitution Effect 10 C e* 5 4 e I* e' I 3 4 5 0 F 10 Pizzas per week Substitution effect Since consumption bundle e' represents the same level of utility as consumption bundle e, the consumer is neither better or worse off at point e'. Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 56 End But at point e', the consumer has not spent the full budget. The consumer’s real income has increased because of the lower price of pizza he is able to attain point e* on indifference curve I*. At this point, the consumer buys 5 pizzas and rent 5 videos. Because prices are held constant during the move from e’ to e*, the change in consumption is due solely to a change in real income the change in the quantity demanded from 4 to 5 reflects the income effect of the lower pizza price HENCE: The substitution effect is the move from point e to point e' in response to a change in the relative price of pizza, with utility held constant along I. The income effect is shown by the move from e' to e* in response to a change in real income with relative prices constant Begin 2 Utility Video rentals per week 6.3d The Income Effect 10 C e* 5 4 e I* e' I 3 4 5 0 Substitution effect 3 U. Max 4 Demand F 10 Pizzas per week Income effect 5 I. Curves 6 U. Max 57 End Video rentals per week 6.3e One more time: Substitution and income effects of a drop in P A reduction in the price of pizza moves the consumer from e to e*. 10 Substitution effect: e to e’; consumer’s reaction to a change in relative prices along the original indifference curve. C 5 4 e* e I* e’ I 0 3 4 5 Substitution effect Begin F Income effect 2 Utility Income effect: e’ to e*; moves the consumer to a higher indifference curve at the new relative price ratio. 10 Pizzas per week 3 U. Max 4 Demand 5 I. Curves 6 U. Max 58 End Video rentals per week 6.4 Summary of Substitution and Income Effects 10 C 5 4 3 e* e I* e' I 3 4 5 F 10 Pizzas per week Substitution Income Substitution effect: holding real effect income (total Income effecteffect: holding relative prices constant (after the price of pizza falls), the switch to a higher utility) constant, the switch from videos to indifference curve (more real income). (e’ to e* ) pizza as the price of pizza falls. (e to e’) 0 Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 59 End 6.5 Exercise To do this exercise you need to leave the “slide show” view, by striking the “Esc” key. (Not functional in the Flash Format file.) Y A B C Xin good In the graph above represent the income and substitution effects of the price decrease X: Use A to B as the substitution effect B to C as the income effect Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 60 6 U. Max End 6.6 Self-Review of The Inc. and Sub. Effects Below is a Flash Module that can be used for review. (Note Questions 3 and 4 have incorrect diagrams!) Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 61 End Another Flash Module that can be used for self-review Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max End END OF PRESENTATION Click a pic to review 63 Begin 2 Utility 3 U. Max 4 Demand 5 I. Curves 6 U. Max 63 End