Lecture 4 - Lecture 4 Utility Maximization I For whosoever...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Lecture 4 Utility Maximization I For whosoever will save his life shall lose it: and whosoever will lose his life for my sake shall find it. Matthew 16:25 The Economics Outline 1. Budget Constraint 2. Utility Maximization (graph) 3. Corner Solutions 4. Marshallian Demand The Mathematics Outline 1. Constrained Maximization 2. Lagrangian Multiplier If you faced no constraints and if the nonsatiation axiom was not violated at any positive consumption values, then it would not be possible to maximize utility as you could always consume one more unit and increase utility. However, we all face constraints and in consumer theory we quantify the main constraint as an income constraint or budget constraint-- we are constrained in what we consume by how much we can afford. The Budget Constraint I = Income P x = Price of good x P y = Price of good y x = Quantity of good x y = Quantity of good y Budget Constraint: I y P x P y x + We can graph the budget constraint by first solving for y as follows: x P P P I P x P I y y x y y x = Dr. Steven Waters Econ 380 Page 1 of 7 L4: Utility Maximization I The budget constraint then looks like this: Maximizing Utility with an Income Constraint We can demonstrate maximizing utility with a budget constraint graphically as follows: In this figure, the budget constraint (as identified by the straight line) shows the consumption bundles that the individual can purchase. By looking at the tangency point between the indifference curve and the budget constraint, point A, we find the maximum utility that the individual can attain given the budget constraint. Dr. Steven Waters Econ 380 Page 2 of 7 L4: Utility Maximization I From the above discussion of the budget constraint and from our previous discussion about the MRS, we know: 1. Slope of the budget constraint = y x P P 2. Slope of the indifference curve = 2....
View Full Document

This note was uploaded on 11/30/2011 for the course STAT 380 taught by Professor Stevens during the Spring '11 term at Brigham Young University, Hawaii.

Page1 / 7

Lecture 4 - Lecture 4 Utility Maximization I For whosoever...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online