This preview shows pages 1–8. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: HW # 01 due 3:15 today 1 Lecture 4 1minute review Consumer Problem: maximize utility subject to budget con straint Substitution Method Geometric Method/Marginal Utility per Dollar CobbDouglas Lagrangian 2 Lagrangian Method Maximize F ( x,y ) Subject to G ( x,y ) = c New variable (Lagrange multiplier) New function (Lagrangian) L ( x,y, ) = F ( x,y ) + [ G ( x,y ) c ] Solutions to original problem are critical points of L all partial derivatives = 0 3 Maximize U ( x,y ) = xy Subject to 6 x + 3 y = 120 L ( x,y, ) = xy + (6 x + 3 y 120) 4 y + 6 = 0 x + 3 = 0 6 x + 3 y 120 = 0 18  18  120 = 0 = 10 / 3 x = 10 y = 20 5 Demand function Solution to choice problem as function of income prices What happens to demand for a good when income changes? its own price changes? price(s) of other good(s) change 6 General CobbDouglas (two goods) U ( x,y ) = x a y b income = M prices = p x ,p y Lagrangian L ( x,y, ) = U ( x,y ) + (budget line) = x a y b + ( p x x + p y y M ) 7 Three equations...
View
Full
Document
 Fall '07
 McDevitt
 Utility

Click to edit the document details