1. RATIONAL CONSUMER CHOICE

2. Drawing on Chapter 3
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3. 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

4. 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

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

6. Figure A3-3: A Three-Dimensional Utility Surface

7. Figure A3-4: Indifference Curves as Projections

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

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

10. 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.

11. 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

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

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

14. 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.