Show that the equilibrium price decreases when the number of firms increases

Question

Consider a competitive market with the demand function X(p). There are m number of identical firms, and the supply function of a particular firm is y(p). We assume that X'(p) < 0 and y'(p) > 0. Show that the equilibrium price decreases when the number of firms increases.

Answer 1

If X'(p) < 0 and y'(p) > 0, this means tht demand is downward sloping and supply is upward sloping. This is the standard setup of the supply/demand graph. An increase in the number of firms in the market means that supply will increase, causing the supply curve to shift to the right. The new spply curve intersects demand at a point with a higher quantity and a lower price.