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### OCB_Inc_Sub_Effect

Course: ECON 1101, Fall 2008
School: Minnesota
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Word Count: 1974

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on Notes the Optimal Consumption Bundle (OCB) and Examples of Graphically Showing Income &amp; Substitution Effects The following notes review some material we covered on Thursday and Friday this week. First it reviews the idea of the optimal consumption bundle (OCB) then presents a couple examples of graphically showing the income and substitution effects. In class on Thursday, 06/19/08, we began to see how...

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on Notes the Optimal Consumption Bundle (OCB) and Examples of Graphically Showing Income & Substitution Effects The following notes review some material we covered on Thursday and Friday this week. First it reviews the idea of the optimal consumption bundle (OCB) then presents a couple examples of graphically showing the income and substitution effects. In class on Thursday, 06/19/08, we began to see how to graphically show the substitution effect. We ran out of time before we could see how to show the income effect, we will do this in lecture on Friday, 06/20/08. This handout may prove helpful when doing Homework 1. I. Tangency A brief review of tangency. Def: A line is tangent to a curve at a point (an (x,y) pair) if the line only touches the curve at this specific point (the slope of the line is equal to the slope of the curve at this point). Ex: y Curve 1 Curve 2 Point A Line x In this example, Curve 1 is not tangent to the Line. In this example, Curve 2 is tangent to the Line at Point A. 1 II. Optimal Consumption Bundle and Tangency We've talked about the idea of affordability (use the budget constraint) and the idea of what a consumer wants, based on preferences (use indifference curves). We combine these two ideas to determine what the consumer would choose. Def: The optimal consumption bundle is the bundle of goods that is both affordable (contained in the budget constraint) and preferred the most by the consumer (highest indifference curve). (The OCB is the bundle that maximizes utility given the budget constraint.) This optimal consumption bundle is the bundle of goods the consumer will choose. At the optimal consumption bundle the indifference curve is tangent to the budget constraint. Otherwise, either the bundle is not affordable or the consumer could do better (get a more preferred bundle). This can be seen in the example below. This means, at the optimal consumption bundle, the MRS of good y for good x is equal to Px (the absolute value of the slope of the budget constraint). Py Example: Two goods, x and y Prices Px and Py Money M Standard preferences (follows from the Four Rules given in class) 2 Good y M/Py Point A Point E IC3 Point C IC2 Point D Point B IC1 Good x M/Px First, notice that Point D and Point E are not affordable. They are outside the budget constraint, and thus cannot possibly be the optimal consumption bundle. Points A, B and C are all affordable (either on the budget constraint or below it). Now we need to consider which of these bundles is most preferred. By Rule 1 of indifference curves, higher indifference curves are preferred to lower indifference curves. Thus, Point C must be preferred to Points A and B. In this example, Point C is the optimal consumption bundle. It is the most preferred of all affordable bundles. NOTE that the optimal consumption bundle is the one bundle such that the indifference curve is tangent to the budget constraint. If you are at a bundle such that the indifference curve is NOT tangent to the budget constraint, either the bundle is not affordable (like Points D and E) or the bundle is not the most preferred (like Points A and B). III. Intuition behind Income & Substitution Effects When the price of a good changes (in this class, only one price will change at a time), we have two effects. The first effect, the substitution effect, is a movement away from the relatively more expensive good. We represent it as the movement between the initial optimal 3 consumption bundle (OCB) and the point on the initial indifference curve that has a slope equal to the new ratio of prices. We graphically find it by constructing a new line parallel to the new budget constraint and tangent to the old indifference curve. The remaining effect is the income effect. The income effect is the movement from where the substitution effect left off to the new OCB. We have an income effect because at the new prices, consumers have different purchasing power. We use our assumptions about how consumers respond to income changes here (normal, inferior goods). The income effect must take this into account. Measuring from the end of the substitution effect, to the new OCB, the normal/"inferiorness" of the good tells us which way to shift our graph. Remember that we assume all goods follow the law of demand. This means that if the price of a good increases, overall consumption of that good (initial OCB vs. final OCB) will decrease; if the price of a good decreases, overall consumption of that good will increase. You must be careful when drawing the final OCB, it's easy to accidentally violate the law of demand. IV. The Steps for Graphically Showing Income & Substitution Effects This section will present the steps that should be followed when graphically showing the effects (income and substitution) of a price change. The next section will then present examples. Steps to Graphically Show Income and Substitution Effects of a Price Change: (a) Construct Initial Budget Constraint, BC1 (b) Show Initial Optimal Consumption Bundle, OCB1 (c) Now suppose there is a change in price for one good (1) Draw New Budget Constraint, BC2 (2) Show "substitution effect." We are interested in how the price change has changed the tradeoffs between two goods. Only interested in new slope (stay on original indifference curve) (2a) Draw a line parallel to BC2 and tangent to IC1. (Line parallel to BC2 represents new relationship between prices). NOTE: Due to the shape of the indifference curves, at a given point, all points to the left are steeper, all points to the right are flatter. 4 (2b) The point tangent to this parallel line is point B. Vertical distance between A & B represents the change in consumption of the good on the y-axis due to the substitution effect. Horizontal change represents the change in consumption of the good on the x-axis to due the substitution effect. (3) Show "income effect"/ Plot the final Optimal Consumption Bundle (Pt. C) Note if goods are normal or inferior. Also note if income is "increasing" or "decreasing." (3a) The above (normal or inferior, "richer" or "poorer") determine if consumption of each good should rise or fall as you move from B to C. (3b) Make sure the placement of point C (compared to point A) obeys the Law of Demand. The Law of Demand states that the price of a good and consumption of the good are inversely related (if the price of a good increases, the consumption of that good must decrease; if the price of a good decreases, the consumption of that good must increase). To compare initial consumption and consumption after the price change, compare initial OCB (Point A) and the final OCB (Point C). Since the price of only one good will change, we can only compare the position of Point A and Point C along one axis (the x-axis if the price of good x changes, the y-axis if the price of good y changes). The law of demand holds for both normal and inferior goods. This means, for an inferior good, make sure if the price of that good goes down that consumption does not go down. This does not make sense. If price of inferior good goes up, we will not buy more of it. (3c) New optimal consumption bundle, point "C," must be on BC2 (and satisfy above conditions). Draw IC2 tangent to BC2 at point C. The movement from point B to point C represents "income effect." 5 V. Examples Example 1: Two goods: Ramen (inferior good) CD's (normal good) Pram = \$0.50/pack Pcd = \$1.50/CD Money, M = \$15 Consumer has bowed in IC's (a) & (b) Construct the Initial Budget Constraint (BC1) and show the Initial Optimal Consumption Bundle (pt. A). (c) Now suppose, prices change such that Pram = \$1.00/pack Pcd = \$1.50/CD (no change) Money, M = \$15 (no change) (1) Draw BC2 (2) Substitution Effect (2a) Line parallel to BC2 (dashed line) Note: BC2 is flatter than BC1, so tangency to IC1 occurs to the right of point A (2b) Point B is tangent to parallel line Movement from A to B represents substitution effect (fewer packs of ramen, more CD's, because ramen is relatively more expensive) (3) Income Effect CD's are normal, ramen is inferior Consumer feels poorer (less purchasing power) (3a) Consumption of ramen should increase as we move from B to C; Consumption of CD's should fall as we move from B to C (3b) Draw IC2 tangent to BC2 at point C (new OCB). (3c) Make sure point C is below point A due the law of demand (the price of ramen has increased, so overall consumption of ramen must decrease). To begin: 6 Ramen 30 BC1 IC1 BC2 A 15 C B IC2 CD's 10 Movement from B to C represents income effect. Example 2: Two goods: Magazines (normal good) Newspapers (normal good) Pmag = \$2.00/magazine Pnews = \$1.00/paper Money, M = \$10 Consumer has bowed in IC's (a) & (b) Construct the Budget Constraint (BC1) and show the Optimal Consumption Bundle (pt. A). To begin: 7 . Magazines IC1 BC1 5 BC2 A 4 B C IC2 Newspapers 10 (c) Now suppose, prices change such that Pmag = \$2.50/magazine Pnews = \$1.00/paper (no change) Money, M = \$10 (no change) (1) Draw BC2 (2) Substitution Effect (2a) Line parallel to BC2 (dashed line) Note: BC2 is flatter than BC1, so tangency to IC1 occurs below point A (2b) Point B is tangency point between parallel line and IC1 Movement from A to B represents substitution effect (more newspapers, less magazines, because magazin...

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