Exceptions to the law of demand

The law of demand does not always apply. We could have a case where at a higher price, more of the quantity of the commodity is demanded and hence an upsloping demand curve. The upsloping demand curve expresses a positive relationship between price and quantity demanded.
 
Standard microeconomic assumptions cannot be used to prove that the demand curve is downward sloping. However, despite years of
searching, no generally agreed upon example of a good that has an
upward-sloping demand curve (also known as a Giffen good) has been found. Non-economists sometimes think that certain goods would have such a curve.
 
For example, some people will buy a luxury car because it is expensive.
 
In this case the good demanded is actually prestige, and not a car, so
when the price of the luxury car decreases, it is actually changing the
amount of prestige so the demand is not decreasing since it is a different good (see Veblen good). Even with downward-sloping demand curves, it is possible that an increase in income may lead to a decrease in demand for a particular good, probably due to the existence of more attractive alternatives which become affordable: a good with this property is known as an inferior good.