Very elastic supply + very inelastic demand 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?
Consider the inverse functions

$$Q^d = A-bP$$

$$Q^s = C + dP$$

to have the situation described by the OP, we will have that $b$ is "very small" while $d$ is "very large".

Equilibrium price and quantity are

$$P^* = \frac {A-C}{d+b} = \frac {A}{d+b}-\frac {C}{d+b}$$

$$Q^* = A- b\frac {A-C}{d+b} = A- b\frac {A}{d+b}+b\frac {C}{d+b}$$

The change described by the OP amounts to $\Delta C &gt; 0$. Then

$$\Delta P^*|_{\Delta C} = -\frac {1}{d+b}\Delta C $$

while

$$\Delta Q^*|_{\Delta C} = \frac {b}{d+b}\Delta C$$

Comparing the two in absolute terms, we get

$$\frac {|\Delta P^*|}{\Delta Q^*} = \frac 1 b$$

... from which we conclude:

1) To have equilibrium price be relatively more affected than equilibrium quantity when the supply curve shifts outwards, we need the marginal effect of price on quantity demanded ($b$) to be smaller than unity

2) The above does not depend on how elastic or inelastic is the supply curve.