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L06

L06. Demand. Review: Cobb-Douglass. Utility (2 forms) Indifference curve map SoH : Magic formulas: Solution always interior. Extreme p: Perfect Complements. Utility Indifference curve map SoH : Magic formulas:

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L06

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  1. L06 Demand

  2. Review: Cobb-Douglass • Utility (2 forms) • Indifference curve map • SoH: Magic formulas: • Solution always interior

  3. Extreme p: Perfect Complements • Utility • Indifference curve map • SoH: Magic formulas: • Solution always interior

  4. Extreme p: Perfect Substitutes • Utility • Indifference curve map • Magic formulas: • Bang-Bang Solution (typically corners)

  5. 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!

  6. 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

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

  8. 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.

  9. Ordinary and Giffen goods p1 x1*

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

  11. Cobb-Douglass example Data , variable

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

  13. 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

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

  15. 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)

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

  17. Cobb-Douglass example Data , variable

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

  19. 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.

  20. Cobb Douglas example Gross complements of substitutes?

  21. Perfect Complements example Gross complements

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