If a price-demand equation is solved for p, then price is expressed as p = g(x) and x becomes the independent variable. In this case, it can be shown that the elasticity of demand is given by E(x) = - [g(x) / xg'(x)]. Use the given price-demand equation to find the values of x for which demand is elastic and for which demand is inelastic.

Question

If a price-demand equation is solved for p, then price is expressed as p = g(x) and x becomes the independent variable. In this case, it can be shown that the elasticity of demand is given by E(x) = - [g(x) / xg'(x)]. Use the given price-demand equation to find the values of x for which demand is elastic and for which demand is inelastic.
p = g(x) = 12960 - 0.1x^2

I am really stuck on this question and don't know how to start, could someone please show me?

Steve · Answer

you have to remember that inelastic means that E(x) > 0 (I think) E(x) = -[(12960-.1x^2)/(-.2x^2)] = 64800/x^2 - .5 E(x) > 0 means x < 360 That sound familiar? Or am I way off base here?