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 Each point on the indifference curve delivers the same level of utility.

Tradeoff = Slope Slope = ΔY/ ΔX (or dY/dX) = Marginal Rate of Substitution 1.Negative slope (linear=perfect substitutes, corner=perfect complements) 2.Convex—diminishing marginal rate of substitution—get too much of one good

Continuous Family of Curves 1.Upper right means higher utility—more of both goods or more of one with no decrease in the other has to be higher utility. 2.Entire space is covered—only portions are shown.

Utility Image: CES U(x,y) = [αx ρ + (1-α)y ρ ] (1/ ρ)

Income Constraint Optimization Income = Px X + Py Y Y = -Px / Py X + Income/Py

Marginal Rate of Substitution MRS = -slope of indifference curve = -(dy/dx) MRSxy = MU/x/MUyMarginal 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

Income and Substitution Effects A X Y Px 2Px 1 B C A: Initial Equilibrium B: Equilibrium with lower Px A->C: Substitution Effect C->B: Income Effect Substitution Effect: Same level of utility, new price. Income Effect: Lower price effectively means more money to spend on both goods.

Demand Curves A X Y Px 2Px 1 B Px 2 D