L06 Demand

Review Model of choice parameters Example 1: Cobb Douglass

Perfect Complements

Perfect Substitutes:Problem x2 x1

Magic Formula (Substitutes)

Comparative statics 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.

Ordinary and Giffen goods p1 x1*

Cobb-Douglas example We find price offer and demand curve for Cobb-Douglas preferences We keep fixed

Cobb-Douglass example Data , variable

Quiz For Cobb-Douglass Price offer curve flat Demand downwar-slopping Q1: For Cobb-Douglas preferences commodities are ordinary goods are Giffen goods Depends on the parameters I do not know

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)

Cobb-Douglas example We find income offer and Engel curve for Cobb-Douglas preferences In both cases we assume

Cobb-Douglass example Data , variable

Quiz For Cobb-Douglass Income offer curve- ray from origin Egnel curve upward-slopping Q1: For Cobb-Douglas preferences commodities are normal goods are inferior goods Depends on the parameters I do not know

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