Indifference Curve Analysis Intermediate Microeconomics Professor Dalton ECON

Indifference Curve Analysis Intermediate Microeconomics Professor Dalton ECON 303 – Fall 2008 1

Ludwig von Mises “Man acts because he is dissatisfied with the state of affairs as it prevails in the absence of his intervention. Man acts because he lacks the power to render conditions fully satisfactory and must resort to appropriate means in order to render them less unsatisfactory. ” 2

Terminology Warning! § Economists use the terms value, utility and benefit interchangeably when speaking of individual choice. Marginal utility = Marginal value = Marginal benefit 3

Choice: Indifference Curves Y/time Characteristics 1. 2. 3. 4. 5. U 3 U 2 U 1 Fixed preferences Negatively-sloped Convex Non-intersecting Slope = Marginal Rate of Substitution (MRSxy) 6. Higher indifference curve represents greater utility X/time 4

Choice: Indifference Curves Y/time 11 9 The Marginal Rate of Substitution represents a trade-off ratio; the marginal benefit from a unit of one good in terms of another. A If the individual is at point A, an additional unit of X is worth 2 Y. B 3. 2 3 U 2 34 11 12 If the individual is at B, an additional X is worth 0. 2 Y. X/time 5

Choice: Budget Constraint The budget constraint can be expressed: Qy C Any combination inside area 0 AC can be purchased. I > P x Q x + P y. Q y Any combination outside area 0 AC can not be purchased. A 0 Qx 6

Choice: Budget Constraint I > P x Q x + P y. Q y For an I = $90, and Py = $5 Qy 90 5 I = 18 = Py For an I = $90, and PX = $3 C The amount of good Y that can be purchased is the budget divided by the price of good Y The amount of good X that can be purchased is 0 90 3 = 30 = I Px A Qx 7

Choice: Budget Constraint I > P x Q x + P y. Q y Qy The amount of good Y that can be purchased is I Py 0 C Any combination inside area 0 AC can be purchased for less than $90. The amount of good X that can be purchased is I Px A Qx 8

Budget Constraint § A budget constraint is negatively-sloped, reflecting the notion of opportunity cost one must give up one good to get more of another. § The slope of a budget constraint measures the opportunity cost of one additional unit of a good in terms of the foregone units of the other good. 9

Choice: Budget Constraint What is the slope of the budget constraint? Slope equals rise over run. Slope equals I/Py divided by I/Px. Qy I Py C The slope of the budget constraint equals the price ratio Px/Py I/Py/I/Px = Px/Py 0 I Px A Qx 10

Choice: Combining Indifference Curves with Production Possibilities Y/time Here, MRSx, y > Px/Py. The individual can buy an additional X for less than the additional unit is valued. MB MC U 3 U 2 Here, MRSx, y < Px/Py. The individual would have to pay more than the additional unit of X is valued. U 1 1 2 X/time 11

Choice Y/time 1 Y U 3 U 2 U 1 1 3 X/time When the MRSx, y > Px/Py, the individual can make himself better off by selling a unit of Y to purchase additional units of X, since a unit of X is valued more highly than a unit of Y at the going prices. So long as this remains true, the individual continues to move “down” his budget constraint. 12

Choice Y/time Y* When MRSx, y = Px/Py, the individual will have reached a point where he can make himself no better off by a rearrangement of resources in X and Y consumption. U 3 U 2 U 1 X* He will have maximized his utility! X/time 13

Choice Y/time Y* U 3 U 2 Note: In marginal utility analysis, equilibrium occurs where MUx/Px = MUy/Py. If we multiply both sides by Px and divide both sides by MUy, we get MUx/MUy = Px/Py. U 1 X* X/time MRSx, y = MUx/MUy !!!!! 14

Changes in the Budget Constraint Y/time Starting from an original budget constraint … Suppose that the price of X falls… The consumer can now buy more X if all income is spent on X… But can buy no more Y if all income is spent on Y… X/time The budget constraint rotates outward “around” the original Y-intercept 15

Changes in the Budget Constraint Y/time Starting from an original budget constraint … Suppose that the price of X increases… The consumer can now buy less X if all income is spent on X… But can buy no more Y if all income is spent on Y… X/time The budget constraint rotates inward “around” the original Y-intercept 16

Changes in the Budget Constraint Y/time Starting from an original budget constraint … Suppose that the price of Y falls… The consumer can now buy more Y if all income is spent on Y… But can buy no more X if all income is spent on X… X/time The budget constraint rotates outward “around” the original X-intercept 17

Changes in the Budget Constraint Y/time Starting from an original budget constraint … Suppose that the price of Y increases… The consumer can now buy less Y if all income is spent on Y… But can buy no more X if all income is spent on X… X/time The budget constraint rotates inward “around” the original X-intercept 18

Changes in the Budget Constraint Y/time Starting from an original budget constraint … Suppose that money income I increases… The consumer can now buy more Y if all income is spent on Y… and can buy more X if all income is spent on X… X/time The budget constraint shifts outward. Does the slope change? NO. 19

Changes in the Budget Constraint Y/time Starting from an original budget constraint … Suppose that money income I decreases… The consumer can now buy less Y if all income is spent on Y… and can buy less X if all income is spent on X… X/time The budget constraint shifts inward. Does the slope change? NO. 20

Changes in Indifference Curves Y/time 11 9 Start from an original set of Indifference Curves (only one of which is shown). If the individual is at point A, an additional unit of X is worth 2 Y. A 6 U 2 34 X/time Suppose that the individual’s preferences change so that X is now valued more highly (he prefers X relatively more)… Now the individual will value an additional unit of X at more than 2 Y, say 5 Y… The set of indifference curves will become steeper… 21

Changes in Indifference Curves Y/time 11 10 Start from an original set of Indifference Curves (only one of which is shown). If the individual is at point A, an additional unit of X is worth 2 Y. A U 2 34 11 12 X/time Suppose that the individual’s preferences change so that Y is now valued more highly (he prefers X relatively less)… Now the individual will value an additional unit of X at less than 2 Y, say 1 Y… The set of indifference curves will become flatter… 22

Changes in Behavior: Price Y/time Beginning from equilibrium, Y** Y* suppose that Px falls. The budget constraint rotates outward around the Y-intercept… U 3 U 2 U 1 X* X** X/time The consumer chooses a new X, Y combination: X**, Y** 23

Changes in Behavior: Price Y/time Beginning from equilibrium, Y’ Y* suppose that Px rises. The budget constraint rotates outward around the Y-intercept… U 3 U 2 U 1 X’ X* X/time The consumer chooses a new X, Y combination: X’, Y’ 24

Changes in Behavior: Income Y/time Beginning from equilibrium, suppose that Income rises. Y** Y* U 3 U 2 U 1 X* X** X/time The budget constraint shifts outward and the slope doesn’t change (why? ) The consumer chooses a new X, Y combination: X**, Y** 25

Changes in Behavior: Income Y/time As this graph what kind of goods are X and Y? Both are normal goods. Y** Y* U 3 U 2 U 1 X* X** X/time 26

Changes in Behavior: Income Y/time Suppose, that instead, money income had fallen. Again that means a new equilibrium, and a new equilibrium combination of X’ and Y’. U 3 Y* Y’ U 2 U 1 X’ X* X/time 27

Changes in Behavior: Preferences Y/time Y* Start from an original equilibrium, A. Suppose preferences become more favorable to X…the IC steepen. A B Y** X* X** The individual now moves to a bundle favoring more X and Less Y, at B. X/time 28