Assume a coal power plant is causing an increased amount of pollution because there is a change in the amount of carbon in the coal. If the pollution causes a negative social externality that has no effect on private costs and benefits, in which of the following ways does the socially efficient equilibrium compare to the free market equilibrium? $(1$ point$)$

Optimal social quantity will equal private quantity, and social price will equal private price.

Optimal social quantity will be less than the private unregulated quantity, and social price will be less than private price.

Optimal social quantity will be less than the private unregulated quantity, and the optimal social price will be greater than the private price.

Optimal social quantity will be greater than the private unregulated quantity, and social price will be less than private price.

Optimal social quantity will be greater than the private unregulated quantity, and social price will be greater than private price.