Inelastic demand is a term used in economics to refer to a product in which the demand does not fluctuate on the basis of price or supply. It is distinct from the vast majority of products, in which supply and demand move along a given demand curve on the basis of the price. There are certain limited products in which inelastic demand applies.
In standard economic theory, a supply and demand curve exists. According to this curve, when supply of a product goes up, the demand for the product will go down in relation to the available supply. As such, sellers will be forced to lower their prices to move their supply, thus making the demand go back up once the price is lower.
Under free market principles, the theory of supply and demand suggests that every product will ultimately be sold for its optimal price. This is sometimes referred to as pareto optimal. The basic argument that most economists make in favor of a free market system is that it is appropriate to allow the supply and demand curve decide the price, since both the seller and buyer will thus be in the best situation in which supply and demand meet.
Assume, for example, that a toaster is put on the market for $100 US Dollars (USD). Only those individuals who really want the toaster will be willing to pay that much. As a result, the supply may outpace the demand and the manufacturers will need to drop the price of the toaster.
If the toaster goes on sale for $1 USD, on the other hand, people will buy the toaster even if they don't really want or need it since the price is so low. Demand will likely outpace supply. As such, the manufacturer will raise the price. Eventually, the price will settle at the most optimal point in which suppliers can make the most profit on a given unit without reducing the demand so much that they end up making less because less people buy.
For certain products, however, demand is inelastic. Inelastic demand refers to those products in which people want the item so much, they will pay any price for it. As such, demand is not affected by price and demand does not go down. The supply and demand curve has a slope of zero and the optimal price will never be reached.
Inelastic demand does not exist for many products. A life-saving drug is one example of a product for which there would be inelastic demand. Such demand would exist for that particular product because people would pay the cost no matter how high it was and as such the manufacturer could charge whatever it liked.