A common definition of the law of demand is given in the article The Economics of Demand:
- "The law of demand states that ceteribus paribus (latin for 'assuming all else is held constant'), the quantity demand for a good rise as the price falls. In other words, the quantity demanded and the price is inversely related."
The law of demand implies a downward sloping demand curve, with quantity demanded to increase as price decreases. There are theoretical cases where the law of demand does not hold, such as Giffen goods, but empirical examples of such goods are few and far between. As such, the law of demand is a useful generalization for how the vast majority of goods and services behave.
Intuitively, the law of demand makes a lot of sense- if individuals' consumption is determined by some sort of cost-benefit analysis, a reduction in cost (i.e. price) should lower a number of benefits a good or service needs to bring a consumer in order to be worth purchasing. This, in turn, implies that price reductions increase the number of goods for which consumption is worth the price paid, so demand increases.