# Managerial Economics - Jerry Post.com

Managerial Economics Indifference Curves Copyright 2007 Jerry Post Utility Individuals have preferences for items These preferences are easiest to express in relative terms: How much of product x will you trade for product y? At the most basic level, utility is ordinal users only need to be able to specify whether the prefer one combination of items to another (not by how much). Indifference Curves Tradeoff between two products (or two bundles of products) that show the points where people are indifferent Example, if offered a choice of 3x or 2y, you might say that those two bundles are equivalent and you would take either one. Sample Data X Y 1 2 3 4 5

6 7 8 9 10 8 5.5 4 3 2.5 2 1.75 1.5 1.25 1.1 Y 9 8 7 6 5 4 3 2 1 0 1 2

3 4 5 6 7 8 9 10 Each point on the indifference curve delivers the same level of utility. Tradeoff = Slope Y 9 8 7 6 5 4 3 2 1 0

1 2 3 4 5 6 7 8 9 10 Slope = Y/ X (or dY/dX) = Marginal Rate of Substitution 1. Negative slope (linear=perfect substitutes, corner=perfect complements) 2. Convexdiminishing marginal rate of substitutionget too much of one good Continuous Family of Curves 10 9 8 7 6 5

4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 1. Upper right means higher utilitymore of both goods or more of one with no decrease in the other has to be higher utility. 2. Entire space is coveredonly portions are shown. Utility Image: CES 10

8-10 6-8 8 6 4 S9 S7 2 S5 S3 U(x,y) = [x + (1-)y ](1/ ) 9 7 5 3 1 0 S1

4-6 2-4 0-2 Income Constraint Optimization Income Py Px 50 10 5 9 X Y 1 8 2 5.5 3 4 4 3 5 2.5 6 2 7 1.75 8 1.5 9 1.25 10 1.1

Slope -2.5 -1.5 -1 -0.5 -0.5 -0.25 -0.25 -0.25 -0.15 Expense YI 85 65 55 50 50 50 52.5 55 57.5 61 Income = Px X + Py Y Y = -Px / Py X + Income/Py 8 4.5 4

3.5 3 2.5 2 1.5 1 0.5 0 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7

8 9 10 Marginal Rate of Substitution MRS = -slope of indifference curve = -(dy/dx) MRSxy = MU/x/MUy Marginal Utility U = F(x, y) dU = (U/ x)dx + (U/ y)dy On an indifference curve, dU=0 by definition - (U/ x)dx = (U/ y)dy -MUx dx = MUy dy MUx/MUy = -dy/dx Slope of budget line is Px/Py, so MUx/MUy = Px/Py (opportunity cost = price) Or MUx/Px = MUy/Py Price Decrease 16 14 12 10 8 6 4 2 0

1 2 3 4 5 6 7 8 9 10 Income and Substitution Effects A: Initial Equilibrium B: Equilibrium with lower Px A->C: Substitution Effect C->B: Income Effect Y Substitution Effect: Same level of utility, new price. Income Effect: Lower price effectively means

more money to spend on both goods. B A C Px 1 Px 2 X Y Demand Curves B A Px 1 Px 2 Px 1 Px 2 D X

## Recently Viewed Presentations

• Demo Thank You MicroArray Data Analysis Candice Quadros & Amol Kothari Neural Network for classification Harnessing the power of a neural network for classifying samples. Neural Network for classification Reduce the no. of genes : We have to reduce the...
• Interspersion is mixing lots of different stages within an area. The best way of measuring the amount of interspersion is to use the interspersion index principle. This involves counting the number of times a habitat changes from east to west...
• Picture 1 pt. Name 1 pt. Birth date 1 pt. Birth place 1 pt. Death date 1 pt. What important events were going on during their life 2 pts. Their educational background 1 pt. Two interesting facts about them 2...
• Chapter 37. Care of Patients with Cardiac Problems. Heart Failure. ... The most reliable criteria for diagnosing endocarditis include positive blood cultures, a new regurgitant murmur, and evidence of endocardial involvement by echocardiography.
• ACL Data Resources and Tools for Title VI. Presented by . Kristen (Krissy) Hudgins, ACL's Office of Performance and Evaluation. May 22, 2019. Good morning, my name is Kristen Hudgins and I work at ACL in the Office of Performance...
• HYPERBOLA. The accompanying drawing shows ground contours at ten-metre vertical intervals on a map. In the space provided draw a vertical section (profile) on the line DE. ... Dividing the line into three equal parts will locate heights of 20m...
• Student Login Link. Socrative Website. Socrative How-To. Create a New Quiz. Launching and sharing a quiz #6 Kahoot. Kahoot Example. Team Mode. Individual Mode. Kahoot Website. Kahoot How-To #7 Nearpod. Nearpod Example. ... Digital Tools for Formative Assessment
• To assess the need for multilevel modeling, we first ran a multilevel logit model to obtain the district level variance, likelihood ratio test, and intraclass correlation (ICC). The likelihood ratio test compares the goodness of fit of hierarchical model to...