ECON 100A Lecture Notes - Lecture 14: Expenditure Function, Substitute Good
Document Summary
Q2 1- : u (q1,q2) = q1, q1 = i / p1, q2 = (1 ) i / p2. Perfect substitutes: u (q1, q2) = q1 + q2. Q1 = 0 if p1 > p2. What is the lowest possible expenditure level e that maintains a particular of utility u (bar) Min q1, q2 e = p1q1 + p2q2 s. t. Constraint maximization (1. ) vs minimizing expenditure (2. : 1, 2. The solution is the expenditure function e = e (p1, p2, u(bar)) Example: what is the expenditure function for cobb douglas, min p1q1 + p2q2 s. t. q1. = p1q1 + p2q2 + (u(bar) - q1: f. o. c. / q1 = p1 - q1. / q2 = p2 - (1- ) q1. / = u (bar) - q1. P1 / p2 = / (1 ) * q2 / q1. P1q1 = / (1- ) * p2q2.
