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

2 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 con- ditions fully satisfactory and must resort to appropriate means in order to render them less unsatisfactory.”

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

4 Choice: Indifference Curves Characteristics 1.Fixed preferences 2.Negatively-sloped 3.Convex 4.Non-intersecting 5.Slope = Marginal Rate of Substitution (MRS xy ) 6.Higher indifference curve represents greater utility Y/time X/time U3U3 U2U2 U1U1

5 Choice: Indifference Curves The Marginal Rate of Substitution represents a trade-off ratio; the marginal benefit from a unit of one good in terms of another. Y/time X/time U2U2 If the individual is at point A, an additional unit of X is worth 2Y. A B If the individual is at B, an additional X is worth 0.2 Y.

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

7 QyQy QxQx I > P x Q x + P y Q y The amount of good Y that can be purchased is the budget divided by the price of good Y I PyPy For an I = $90, and P y = $ = 18 = The amount of good X that can be purchased is I PxPx For an I = $90, and P X = $ = 30 = 0 A C Choice: Budget Constraint

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

9 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.

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

11 Choice: Combining Indifference Curves with Production Possibilities Here, MRSx,y > Px/Py. The individual can buy an additional X for less than the additional unit is valued. Y/time X/time U3U3 U2U2 U1U1 12 Here, MRSx,y < Px/Py. The individual would have to pay more than the additional unit of X is valued. MB MC

12 Choice Y/time X/time U3U3 U2U2 U1U1 13 1Y 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.

13 Choice Y/time X/time U3U3 U2U2 U1U1 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. Y* X* He will have maximized his utility!

14 Choice Y/time X/time U3U3 U2U2 U1U1 Y* X* 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. MRSx,y = MUx/MUy !!!!!

15 Changes in the Budget Constraint Y/time X/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… The budget constraint rotates outward “around” the original Y-intercept

16 Changes in the Budget Constraint Y/time X/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… The budget constraint rotates inward “around” the original Y-intercept

17 Changes in the Budget Constraint Y/time X/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… The budget constraint rotates outward “around” the original X-intercept

18 Changes in the Budget Constraint Y/time X/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… The budget constraint rotates inward “around” the original X-intercept

19 Changes in the Budget Constraint Y/time X/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… The budget constraint shifts outward. Does the slope change? NO.

20 Changes in the Budget Constraint Y/time X/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… The budget constraint shifts inward. Does the slope change? NO.

21 Changes in Indifference Curves Start from an original set of Indifference Curves (only one of which is shown). Y/time X/time U2U2 If the individual is at point A, an additional unit of X is worth 2Y. A 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 2Y, say 5Y… 6 The set of indifference curves will become steeper…

22 Changes in Indifference Curves Start from an original set of Indifference Curves (only one of which is shown). Y/time X/time U2U2 If the individual is at point A, an additional unit of X is worth 2Y. A 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 2Y, say 1Y… The set of indifference curves will become flatter…

23 Changes in Behavior: Price Y/time X/time U3U3 U2U2 U1U1 Beginning from equilibrium, Y* X* The budget constraint rotates outward around the Y-intercept… The consumer chooses a new X, Y combination: X**, Y** X** Y** suppose that Px falls.

24 Changes in Behavior: Price Y/time X/time U3U3 U2U2 U1U1 Beginning from equilibrium, Y* X* The budget constraint rotates outward around the Y-intercept… The consumer chooses a new X, Y combination: X’, Y’ X’ Y’ suppose that Px rises.

25 Changes in Behavior: Income Y/time X/time U3U3 U2U2 U1U1 Beginning from equilibrium, suppose that Income rises. Y* X* The budget constraint shifts outward and the slope doesn’t change (why?) The consumer chooses a new X, Y combination: X**, Y** X** Y**

26 Changes in Behavior: Income Y/time X/time U3U3 U2U2 U1U1 As this graph what kind of goods are X and Y? Y* X* X** Y** Both are normal goods.

27 Changes in Behavior: Income Y/time X/time U3U3 U2U2 U1U1 Suppose, that instead, money income had fallen. Again that means a new equilibrium, and a new equilibrium combination of X’ and Y’. Y* X*X’ Y’

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