Suppose we have a very elastic supply curve and a very inelastic demand curve. Further suppose there is a decrease in input prices which shifts the supply curve outward. By taking an extreme representation (vertical demand curve and horizontal supply curve), I can see that it will be mainly price that is affected: the equilibrium price decreases while equilibrium quantity hardly changes.
How can I show this more intuitively or mathematically?
Edit: Just thought about this. I don't think the elasticity of the supply curve matters. Only the elasticity of the curve that isn't shifting does. Is this the answer?