# Chapter Six Demand. Income Changes u A plot of quantity demanded against income is called an Engel curve.

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Chapter Six Demand

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

Income Changes Fixed p 1 and p 2. y’ < y’’ < y’’’ x 1 ’’’ x 1 ’’ x1’x1’ x 2 ’’’ x 2 ’’ x2’x2’ Income offer curve x1*x1* y x 1 ’’’ x 1 ’’ x1’x1’ y’ y’’ y’’’ Engel curve; good 1

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

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

Income Changes and Cobb- Douglas Preferences y y x1*x1* x2*x2* Engel curve for good 1 Engel curve for good 2

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

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

Income Changes x1x1 x2x2 y’ < y’’ < y’’’ x 1 ’’ x1’x1’ x 2 ’’’ x 2 ’’ x2’x2’ x 1 ’’’ x1*x1* y y’ y’’ y’’’ Engel curve; good 1 x 1 ’’’ x 1 ’’ x1’x1’ Fixed p 1 and p 2.

Quasi-linear Indifference Curves x2x2 x1x1 Each curve is a vertically shifted copy of the others. Each curve intersects both axes.

Income Changes; Quasilinear Utility x2x2 x1x1 x1x1 ~ x1*x1* y x1x1 ~ Engel curve for good 1

Income Changes; Quasilinear Utility x2x2 x1x1 x1x1 ~ x2*x2* y Engel curve for good 2

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

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

Income Changes; Goods 1 & 2 Normal x 1 ’’’ x 1 ’’ x1’x1’ x 2 ’’’ x 2 ’’ x2’x2’ Income offer curve x1*x1* x2*x2* y y x 1 ’’’ x 1 ’’ x1’x1’ x 2 ’’’ x 2 ’’ x2’x2’ y’ y’’ y’’’ y’ y’’ y’’’ Engel curve; good 2 Engel curve; good 1

Income Changes; Good 2 Is Normal, Good 1 Becomes Income Inferior x2x2 x1x1 Income offer curve

Income Changes; Good 2 Is Normal, Good 1 Becomes Income Inferior x2x2 x1x1 x1*x1* x2*x2* m m Engel curve for good 2 Engel curve for good 1

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

Ordinary Goods Fixed p 2 and y. x1x1 x2x2 p 1 price offer curve x1*x1* Downward-sloping demand curve Good 1 is ordinary  p1p1

x 1 *(p 1 ’’’) x 1 *(p 1 ’) x 1 *(p 1 ’’) p1p1 x 1 *(p 1 ’) x 1 *(p 1 ’’’) x 1 *(p 1 ’’) p1’p1’ p 1 ’’ p 1 ’’’ x1*x1* Own-Price Changes Ordinary demand curve for commodity 1 Fixed p 2 and y.

x 1 *(p 1 ’’’) x 1 *(p 1 ’) x 1 *(p 1 ’’) p1p1 x 1 *(p 1 ’) x 1 *(p 1 ’’’) x 1 *(p 1 ’’) p1’p1’ p 1 ’’ p 1 ’’’ x1*x1* Own-Price Changes Ordinary demand curve for commodity 1 p 1 price offer curve Fixed p 2 and y.

Own-Price Changes u The curve containing all the utility- maximizing bundles traced out as p 1 changes, with p 2 and y constant, is the p 1 - price offer curve. u The plot of the x 1 -coordinate of the p 1 - price offer curve against p 1 is the ordinary demand curve for commodity 1.

Own-Price Changes u What does a p 1 price-offer curve look like for a perfect-complements utility function? Then the ordinary demand functions for commodities 1 and 2 are

Own-Price Changes With p 2 and y fixed, higher p 1 causes smaller x 1 * and x 2 *.

p1p1 x1*x1* Ordinary demand curve for commodity 1 is Fixed p 2 and y. Own-Price Changes x1x1 x2x2 p1’p1’ p 1 ’’ p 1 ’’’ y/p 2

Own-Price Changes u What does a p 1 price-offer curve look like for a perfect-substitutes utility function? Then the ordinary demand functions for commodities 1 and 2 are

Own-Price Changes and

Fixed p 2 and y. Own-Price Changes x2x2 x1x1 p1p1 x1*x1* Fixed p 2 and y. p1’p1’ p 2 = p 1 ’’ p 1 ’’’ p 1 price offer curve Ordinary demand curve for commodity 1

Giffen Goods u 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.

Giffen Goods Fixed p 2 and y. x1x1 x2x2 p 1 price offer curve x1*x1* Demand curve has a positively sloped part Good 1 is Giffen  p1p1

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