How does Einsteins explanation of the photons explain the effect of varying intensity of light in the Photoelectric effect?

The Photoelectric Effect - when a material emits electrons from its surface as it's exposed to incident light. It might be expected that an increase in light intensity would increase the KE of the emitted electrons but this is actually not the case, classically this can not be explained but Einstein showed this could be understood using an idea that light is quantised in bundles called photons, where the energy of said electron is given by: E=hf. This allows us to understand that each time an electron is emitted from the surface of the material all of its energy has come from a single photon. From this we can say that an increase of light intensity will increase the amount of photons incident on the surface per unit time thus increasing the amount of emitted electrons per unit time but each electron has absorbed the same amount of energy from the individual photons.