L04 Choice

Big picture Behavioral Postulate: A decisionmaker chooses its most preferred alternative from the set of affordable alternatives. Budget set = affordable alternatives To model choice we must have decisionmaker’s preferences.

MRS and Utility Function MRS is a slope of the indifference curve at x x2 x1 Q: Can we recover MRS from U(x)?

Utility and Marginal Utility

MRS and Marginal Utility Yes, but we have to find marginal utilities for both goods first (MU) MU: How much utility we gain by adding an extra unit of good i

Example V(x1,x2) = ln(x1)+ln(x2)

Example V(x1,x2) = x1x2

Cobb-Douglass utility Cobb Douglass utility function Log function Conclusion: preferences are Cobb-Douglass

Quiz Assume At bundle (2,4) , on the margin A: x1 is more precious than x2 B: x1 is less precious than x2 C: They are equally precious D: Insufficient information to determine

Problem: We know preferences (utility function) and We want to know optimal choice

Choice $ $ $ $ $ $ $ $ $ $

Different prices How can we modify our argument if Marginal utility of a dollar We should equalize MU of a $!

Choice $ $ $ $ $ $ $ $ $ $

Problem (thinking on the margin!) Two secrets of happiness: 1. Spend your total income 2. Equalize marginal utility of a $ Rearranging:

Choice: Calculation

Choice: geometric interpretation x2 x1

Quiz Optimal choice is A: bundle (10,10) B: bundle (5,5) C: bundle (7,3) D: bundle (13,7)