Chapter 6
Comparative Statistics
Comparative statics
Once we have derived demand functions, we want to study how the quantity demanded changes with income, own price and price of the other good.
This is called comparative statics
Income Effect
normal goods
-> quantity demanded increases with income
inferior good -> quantity demanded decreases with income
luxury goods
if the demand for it increases more than proportionally with income
necessary goods
if demand for it increases less than proportionally with income
homothetic preference
if the demand for it increases by the same proportion as income
Homothetic preference can also be interpreted as a preference for the ratio of the two goods. A all income levels (holding prices fixed), the consumer will demand x1 and x2 in the same proportions
Own price effect
ordinary goods
if quantity demanded of good 1 decreases with p1, it is an ordinary good
giffen good
if quantity demanded of good 2 increases in p1, it is a giffen good
Other price effects
Substitute
Good 1 is a substitute for good 2 if 
Complement
Good 1 is a complement for good 2 if
Income effect: Engel curve
Engel curve: a useful visualisation of income effects
The Engel curve for a good depicts how quantity demanded changes with income
Inferior good -> quantity falls with income
normal good -> quantity rises with income
(necessary goods, luxury goods, or the homothetic preference)
Price effects: Demand curve
demand curve -> x1(p1,p2,m)
inverse demand -> p1(x1)