L06 Demand

Review Model of choice parameters Example 1: Cobb Douglass

Perfect Complements

Perfect complements We know Focus on one good (x1) How the demand is affected by a change a) in “own” price b) in income c) in price of other commodity One variable at the time!

Own-Price Changes We focus on good 1 We hold p2 and m constant. We change p1 The change represented by: Price offer curve Demand curve

Own-Price Change p1 Vary p1=1, p1’=3, p1’’=4 Fix p2=1 and m=12. x2 Demand curve for commodity 1 p1 price offer curve p1 (5,7) (2.5,3) (3,3) x1* x1

Own-Price Changes The curve containing all the utility-maximizing bundles traced out as p1 changes, with p2 and m constant, is the p1- price offer curve. The plot of optimal choice of x1 against p1 is the demand curve for commodity 1.

Own-Price Changes The curve containing all the utility-maximizing bundles traced out as p1 changes, with p2 and m constant, is the p1- price offer curve. The plot of optimal choice of x1 against p1 is the demand curve for commodity 1.

Ordinary and Giffen goods p1 x1*

Two examples We find price offer and demand curve for Cobb-Douglas preferences Perfect complements In both cases we keep fixed

Cobb-Douglass example Data , variable

Perfect Complements Data , variable

Summary: Price offer curve - Cobb-Douglas – flat line - Perfect Complements – optimal proportion line Demand curve - Cobb-Douglas – downward slopping - Perfect Complements – downward slopping Conclusion: both ordinary goods Preferences generating Giffen good?

Giffen Good Demand curve has a positively sloped part p1 price offer x2 p1 price offer curve p1 Û Good 1 is Giffen x1 x1*

Income Changes We still focus on good 1 We hold p1 and p2 constant. We change m The change represented by: Income offer curve Engel curve

Income Changes Fix p1=1, p2=1 Vary m=12, m’=6, m’’=4 x2 Engel curve for commodity 1 income offer curve m (5,7) (3,3) (2,2) x1* x1

Goods A good for which quantity demanded rises with income is called normal. (positive slope of Engel curve) A good for which quantity demanded falls as income increases is called income inferior. (negative slope of Engel curve)

Two examples We find income offer and Engel curve for Cobb-Douglas preferences Perfect complements In both cases we assume

Cobb-Douglass example Data , variable

Perfect Complements Data , variable

Summary: Income offer curve - Cobb-Douglas – ray from origin - Perfect Complements – optimal proportion line Engel curve - Cobb-Douglas – upward slopping - Perfect Complements – upward slopping Conclusion: both normal goods Preferences generating inferior good: textbook.

Cross-Price Effects If an increase in p2 increases demand for commodity 1 then commodity 1 is a gross substitute for commodity 2. reduces demand for commodity 1 then commodity 1 is a gross complement for commodity 2.

Cobb Douglas example Gross complements of substitutes?

Perfect Complements example Gross complements