As we already know, equilibrium price and equilibrium quantity in a given market are determined by the intersection of the supply and demand curves. Depending on the elasticities of supply and demand, the equilibrium price and quantity can behave differently with shifts in supply and demand. We can see one example of how this works if we imagine a supply curve shifting in and out along a single demand curve. If demand is very elastic, then shifts in the supply curve will result in large changes in quantity demanded and small changes in price at the equilibrium point.
If demand is very inelastic, however, shifts in the supply curve will result in large changes in price and small changes in quantity at the equilibrium point.
Imagine, for example, that due to war or other events overseas, the supply of oil to the U.S. shifts inward, and therefore the domestic supply of gasoline does, too. Because American consumers are not willing to significantly cut their gasoline consumption in the short run (meaning they are very inelastic in the short run) a shift in the supply curve affects the price much more than the quantity. A powerful general rule can be gleaned from this example: if one curve (whether supply or demand) is inelastic, shifts in the complementary curve (whether demand or supply) affect price more than quantity; on the flip side, if one curve is elastic, shifts in the other curve affect quantity more than price.
Practically speaking, the government often has to take such effects into consideration before making policy changes. For example, if the government's goal is to limit imports in order to promote domestic industry, it must first consider whether its policy will have the desired effect. If demand for imports is inelastic, an increased tariff on imports will only result in increased prices without a significant drop in quantity of imports consumed, which does not benefit domestic producers and only results in angry domestic consumers.