# Slope vs elasticity of demand function - Is it the same thing?

Do the slope of a linear demand function and the elastisicy of demand coincide when we use specific preferences for pricing. As a paradigm, if we consider the case of CARA normal preferences, by solving the proble of the represenative conumer, we know that the demand function is a linear one. In this case the slope and the elasticity of the demand function coincide, but is this the case in general?

• No, the elasticity varies along linear demand curves. Because the slope of such demand curves is constant, it cannot always be equal. Nov 19, 2020 at 10:54

No, slope of a demand function is $$\frac{\partial q(p)}{\partial p}$$ elasticity of demand is $$\frac{\partial q(p)}{\partial p} \frac{p}{q(p)}$$. So they cannot be same except in some special cases.
• @HungerLearn what do you mean by 2 paradigms? This is one paradigm + math. For example, if $q(p)=100$ then $\partial q(p)/ \partial p= 0$ and at the same time also $\partial q(p)/ \partial p *p/q(p)=0$. Or if $q(p) = p$ then $\partial q(p)/ \partial p= 1$ and $\partial q(p)/ \partial p *p/q(p)=1$ Nov 19, 2020 at 11:13