Perfect complements u We know u Focus on one good (x1) u How the demand is affected by a change a) in “own” price b) in income c) in price of other commodity u One variable at the time!
Own-Price Changes u We focus on good 1 u We hold p 2 and m constant. u We change p 1 u The change represented by: - Price offer curve - Demand curve
Own-Price Change p 1 x1x1 x2x2 Fix p 2 =1 and m=12. Vary p 1 =1, p 1 ’=3, p 1 ’’=4 (5,7) (3,3) (2.5,3) p 1 price offer curve x1*x1* p1p1 Demand curve for commodity 1
Own-Price Changes u The curve containing all the utility- maximizing bundles traced out as p 1 changes, with p 2 and m constant, is the p 1 - price offer curve. u The plot of optimal choice of x 1 against p 1 is the demand curve for commodity 1.
Ordinary and Giffen Goods u A good is called ordinary if the quantity always increases as the price decreases. u If, for some values of the price, the quantity demanded rises as the price increases, then the good is called Giffen.
Two examples We find price offer and demand curve for u Cobb-Douglas preferences u Perfect complements u In both cases we keep fixed
Summary: u Price offer curve - Cobb-Douglas – flat line - Perfect Complements – optimal proportion line u Demand curve - Cobb-Douglas – downward slopping - Perfect Complements – downward slopping Conclusion: both ordinary goods u Preferences generating Giffen good?
Giffen Good x1x1 x2x2 p 1 price offer curve x1*x1* Demand curve has a positively sloped part Good 1 is Giffen p1p1
Income Changes u We still focus on good 1 u We hold p 1 and p 2 constant. u We change m u The change represented by: - Income offer curve - Engel curve
x1x1 x2x2 Fix p 1 =1, p 2 =1 Vary m=12, m’=6, m’’=4 (5,7) (3,3) (2,2) income offer curve x1*x1* m Engel curve for commodity 1 Income Changes
Goods u A good for which quantity demanded rises with income is called normal. (positive slope of Engel curve) u 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 u Cobb-Douglas preferences u Perfect complements u In both cases we assume
Summary: u Income offer curve - Cobb-Douglas – ray from origin - Perfect Complements – optimal proportion line u Engel curve - Cobb-Douglas – upward slopping - Perfect Complements – upward slopping Conclusion: both normal goods u Preferences generating inferior good: textbook.
Cross-Price Effects u If an increase in p 2 –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?