RATIONAL CONSUMER CHOICE

Drawing on Chapter 3 Graphics copyright © 2010 The McGraw-Hill Companies, Inc. All rights reserved.

Rational Choice Model given 1. Possibilities 2. Preferences opportunity set of quantities, bought with income M at prices P 2. Preferences preference ordering (indifference curves) or utility function and 3. Rationality, seeking the best affordable bundle of quantities we 4. Predict choices of quantities

2. Preferences (again) Utility Functions Assign a number (indexing utility or satisfaction) to each bundle of goods Assume positive but diminishing marginal utilities (slopes relative to each good’s quantity) Measure utility cardinally, but are better interpreted ordinally Imply indifference curves, each showing bundles providing a given level of utility

Analogy to Topographic Maps References: U.S. Geological Service.

Figure A3-3: A Three-Dimensional Utility Surface

Figure A3-4: Indifference Curves as Projections

Figure A3-1: Indifference Curves for the Utility Function U=FS Cobb-Douglas function in 3-D

Figure A3-2: Utility Along an Indifference Curve Remains Constant

Rational Choice with Utility Functions 3. Rationality (again) Rational Choice with Utility Functions Suppose utility from two divisible goods: U(X,Y) Using more of X and less of Y along an indifference curve, the gain in utility must equal the loss in utility MUX ∆X = -MUY ∆Y So -MUX /MUY = ∆Y/∆X = MRS At the best affordable bundle, this equals the slope of the budget constraint: -MUX /MUY = -PX /PY So MUX /PX = MUY /PY Marginal benefit equals marginal opportunity cost per unit of X or dollar spent on X.

Simple numerical example 4. Predict (again) Simple numerical example Additively separable utility Table rather than formula Compares benefits and costs in MU/P along budget constraint Shows that the scale of the utility function does not affect the rational choice Activities: 03 Example - additively separable utility & consumer choice.xlsx

Figure A3-6: The Optimal Bundle when U=XY, Px=4, Py=2, and M=40 See in 3-D

More Examples of Utility Functions Relatively simple, with assumed properties Activities: 03 Examples - utility functions.xlsx

Review Predict Rational choice of most Preferred Possibility. Adapts to different Possibilities and Preferences, not to non-rational choice. Ordinal ranking is less restrictive. Corresponding utility functions are mathematically convenient, and not misleading if interpreted ordinally.