Lecture 3 MGMT © 2011 Houman Younessi Rational Choice – Consumer behavior 50 Bread Potatoes I1 I2 A B Indifference Curves A’ Welcome to Carbland

Lecture 3 MGMT © 2011 Houman Younessi 50 Bread Potatoes B A Indifference Curves must not intersect A’

Lecture 3 MGMT © 2011 Houman Younessi Style MPG H R S Style MPG H R S High marginal rate of substitution of MPG for style Low marginal rate of substitution of MPG for style Marginal Rate of Substitution

Lecture 3 MGMT © 2011 Houman Younessi Marginal Rate of Substitution The marginal rate of substitution of good X for Y is defined as the number of units of good Y that must be given up if the consumer, after receiving the extra unit of good X is to remain indifferent The absolute value of the slope of the indifference curve is the marginal rate of substitution

Lecture 3 MGMT © 2011 Houman Younessi Utility MPG Style Houman’s indifference curves Which one provides the greatest utility? Utility measures the level of satisfaction attached to a given market basket

Lecture 3 MGMT © 2011 Houman Younessi Budget Line 50 Bread Potatoes $40 Budget lines $20 Budget lines Slope of the budget line

Lecture 3 MGMT © 2011 Houman Younessi Equilibrium Market Basket 50 Bread Potatoes I2 I1 I3 H H= Equilibrium market basket for $40 budget line and bread price $0.80 and potato price of $10

Lecture 3 MGMT © 2011 Houman Younessi 50 Bread Potatoes I2 I1 H K Effect of Price Change

Lecture 3 MGMT © 2011 Houman Younessi Deriving an Individual’s Demand Curve We said at the price of $0.80 for bread, demand was 25 loaves (equilibrium) At $1.60 a loaf, demand was 12.5 loaves (again equilibrium) We have two points on the demand line, so we can plot it!! Price Quantity demanded Demand for bread $0.40 $0.80 $1.20 $1.60 $

Lecture 3 MGMT © 2011 Houman Younessi Deriving Market Demand Curve Market demand curve is the horizontal sum of all the individual demand curves. In other words, to find the total quantity demanded, we add up all the individual quantities demanded by each and every consumer in the market at that price. Price Quantity

Lecture 3 MGMT © 2011 Houman Younessi Deriving Market Demand Curve An Empirical Approach Based on directly obtaining demand information through consumer interviews and market experiments Let us start with a simplified case of only one factor influencing the quantity demanded in the market. Let us say Price. Through various means we obtain the following data regarding demand at various prices Price ($) Quantity (tons)

Lecture 3 MGMT © 2011 Houman Younessi P=a+bQ

Lecture 3 MGMT © 2011 Houman Younessi Method of Least Square Y1 Y’1 Y2 Y’2 Y3 Y’3 Y4 Y’4 Must minimize: In general we must minimize: But: Substituting, we get: Which we must minimize We know that the expression above would be a minimum if:

Lecture 3 MGMT © 2011 Houman Younessi Therefore we have: Solving simultaneously and letting and be the mean values of all X and Y respectively, we have: alternatively

Lecture 3 MGMT © 2011 Houman Younessi Using the data in the table below: Price ($)=Y Quantity (tons)= XX2X2 Y2Y2 XY Total Mean X11 Mean Y So: Price ($)Y'

Lecture 3 MGMT © 2011 Houman Younessi r 2 =1.00 r 2 =0.30 r 2 =0.90 r 2 =0.00 Coefficient of Determination

Lecture 3 MGMT © 2011 Houman Younessi Coefficient of Determination Without proof: Note also that: is known as the correlation coefficient and is an important statistical entity

Lecture 3 MGMT © 2011 Houman Younessi Multiple Regression When the relationship is dependent on more than one independent variable, multiple regression is used. For example when we wish to estimate the parameters for: Q= aP+bI+cS+dA where P is the average price of laptops in 2007 I is the per capita disposable income in 2007 S is the average price of typical software packages in 2007 A is the average expenditure on advertising in 2007 The approach and interpretation remains the same but the analysis and the formula is far more complex than to be presented here. Fortunately most statistical software packages handle multiple regression easily.

Lecture 3 MGMT © 2011 Houman Younessi Non-linear Regression The models whose parameters have been estimated so far, have all be linear. How would we estimate the parameters of a model that is not linear? For example: We do so by employing a mathematical “trick” called linearization.

Lecture 3 MGMT © 2011 Houman Younessi Linearization This is best done by example:

Lecture 3 MGMT © 2011 Houman Younessi Trend Analysis More about the value of Y How do we get “more” reliable values of Y? By looking and analyzing the TRENDS that Y has followed in the past A trend is a relatively smooth, long term movement of a variable There are usually four components to a trend: -Regular trend -Seasonal variation -Cyclical variation -Irregularity

Lecture 3 MGMT © 2011 Houman Younessi Trend Analysis Correcting for Seasonal and Cyclical Variation

Lecture 3 MGMT © 2011 Houman Younessi Trend Analysis Correcting for Irregularity