Why is elasticity not constant on a straight line graph?

There are different zones of elasticity on a graph, but if we are to imagine a negatively sloped, straight line on a price v quantity graph, we find that elasticity differs based on where we look on the graph. Why is this the case, rather then elasticity being constant?

• Welcome to the site. You may find answers to this question helpful. – Adam Bailey Jul 4 at 9:49

Theoretically, the responsiveness of quantity demanded is different at different prices. Take the equation for the elasticity of demand: $$\epsilon_{D}=\frac{\Delta{Q}}{\Delta{P}}\frac{P}{Q}$$ The equation itself is non-constant as it depends on P and Q. Lets assume a linear demand curve with the simple form: $$P(Q)=6-Q$$. If we take an equal change in price, say $$\Delta{P}=1$$, and since the demand curve is linear in this case, we see it has a slope = $$-1$$ and thus the $$\Delta{Q}=1$$. If we have two situations where $$P=5$$ and $$P=4$$, then, to keep in accordance with our slope, lets say $$Q=1$$ and $$Q=2$$, respectively. The two elasticities of demand for these two prices would be $$\epsilon_{D}=5$$ and $$\epsilon_{D}=2$$ for the higher and lower price respectively.