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Chapter Six

Chapter Six. Demand. Income Changes. A plot of quantity demanded against income is called an Engel curve . Income Changes. Fixed p 1 and p 2 . y’ < y’’ < y’’’. Income offer curve. y. x 2 ’’’. y’’’. Engel curve; good 1. x 2 ’’. y’’. x 2 ’. y’. x 1 ’. x 1 ’’’. x 1 ’. x 1 ’’’.

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Chapter Six

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  1. Chapter Six Demand

  2. Income Changes • A plot of quantity demanded against income is called an Engel curve.

  3. Income Changes Fixed p1 and p2. y’ < y’’ < y’’’ Incomeoffer curve y x2’’’ y’’’ Engelcurve; good 1 x2’’ y’’ x2’ y’ x1’ x1’’’ x1’ x1’’’ x1* x1’’ x1’’

  4. Income Changes and Cobb-Douglas Preferences • An example of computing the equations of Engel curves; the Cobb-Douglas case. • The ordinary demand equations are

  5. Income Changes and Cobb-Douglas Preferences Rearranged to isolate y, these are: Engel curve for good 1 Engel curve for good 2

  6. Income Changes and Cobb-Douglas Preferences y Engel curvefor good 1 x1* y Engel curvefor good 2 x2*

  7. Income Changes and Perfectly-Complementary Preferences • Another example of computing the equations of Engel curves; the perfectly-complementary case. • The ordinary demand equations are

  8. Income Changes and Perfectly-Complementary Preferences Rearranged to isolate y, these are: Engel curve for good 1 Engel curve for good 2

  9. Income Changes Fixed p1 and p2. x2 y’ < y’’ < y’’’ y x2’’’ y’’’ Engelcurve; good 1 x2’’ y’’ x2’ y’ x1’ x1’’’ x1’’’ x1’ x1* x1 x1’’ x1’’

  10. Quasi-linear Indifference Curves x2 Each curve is a vertically shifted copy of the others. Each curve intersectsboth axes. x1

  11. ~ x1 Income Changes; Quasilinear Utility x2 Engelcurve forgood 1 y x1* ~ x1 x1

  12. ~ x1 Income Changes; Quasilinear Utility Engelcurve forgood 2 y x2 x2* x1

  13. Income Effects • A good for which quantity demanded rises as income increases is called normal. • Therefore when a good is normal its Engel curve must be positively sloped.

  14. Income Effects • A good for which quantity demanded falls as income increases is called inferior. • Therefore when a good is income inferior its Engel curve must be negatively sloped.

  15. Income Changes; Goods1 & 2 Normal Engelcurve; good 2 y y’’’ y’’ y’ Incomeoffer curve x2’’’ x2’ x2* y x2’’ x2’’’ y’’’ Engelcurve; good 1 x2’’ y’’ x2’ y’ x1’ x1’’’ x1’ x1’’’ x1* x1’’ x1’’

  16. Income Changes; Good 2 Is Normal, Good 1 Becomes Income Inferior x2 Incomeoffer curve x1

  17. Income Changes; Good 2 Is Normal, Good 1 Becomes Income Inferior m x2 Engel curvefor good 2 x2* m Engel curvefor good 1 x1* x1

  18. Ordinary Goods • A good is called ordinary if the quantity demanded always increases as its own-price decreases.

  19. Ordinary Goods Fixed p2 and y. Downward-sloping demand curve x2 p1 p1 price offer curve Û Good 1 isordinary x1* x1

  20. p1 Own-Price Changes Ordinarydemand curvefor commodity 1 Fixed p2 and y. p1’’’ p1’’ p1’ x1* x1*(p1’) x1*(p1’’’) x1*(p1’’) x1*(p1’’’) x1*(p1’) x1*(p1’’)

  21. p1 Own-Price Changes Ordinarydemand curvefor commodity 1 Fixed p2 and y. p1’’’ p1’’ p1 price offer curve p1’ x1* x1*(p1’) x1*(p1’’’) x1*(p1’’) x1*(p1’’’) x1*(p1’) x1*(p1’’)

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

  23. Own-Price Changes • What does a p1 price-offer curve look like for a perfect-complements utility function? Then the ordinary demand functionsfor commodities 1 and 2 are

  24. Own-Price Changes With p2 and y fixed, higher p1 causessmaller x1* and x2*.

  25. p1 Own-Price Changes Ordinarydemand curvefor commodity 1 is Fixed p2 and y. p1’’’ x2 p1’’ y/p2 p1’ x1* x1

  26. Own-Price Changes • What does a p1 price-offer curve look like for a perfect-substitutes utility function? Then the ordinary demand functionsfor commodities 1 and 2 are

  27. Own-Price Changes and

  28. p1 Own-Price Changes Ordinarydemand curvefor commodity 1 Fixed p2 and y. Fixed p2 and y. p1’’’ x2 p2 = p1’’ p1 price offer curve p1’ x1* x1

  29. Giffen Goods • If, for some values of its own-price, the quantity demanded of a good rises as its own-price increases then the good is called Giffen.

  30. Giffen Goods Demand curve has a positively sloped part Fixed p2 and y. x2 p1 p1 price offer curve Û Good 1 isGiffen x1* x1

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