Social costs equal private costs when:

Social Cost= Private Cost + External Cost?
When a transaction takes place, it typically involves both private costs and external costs. Private costs are the costs that the buyer of a good or service pays the seller. This can also be described as the costs internal to the firm's production function. External costs (also called externalities), in contrast, are the costs that people other than the buyer are forced to pay as a result of the transaction. The bearers of such costs can be either particular individuals or society at large. Note that external costs are often both non-monetary and problematic to quantify for comparison with monetary values. They include things like pollution, things that society will likely have to pay for in some way or at some time in the future, but that are not included in transaction prices. Social costs are the sum of private costs and external costs.
For example, the manufacturing cost of a car (i.e., the costs of buying inputs, land tax rates for the car plant, overhead costs of running the plant and labor costs) reflects the private cost for the manufacturer (in some ways, normal profit can also be seen as a cost of production. The polluted waters or polluted air also created as part of the process of producing the car is an external cost borne by those who are affected by the pollution or who value unpolluted air or water. Because the manufacturer does not pay for this external cost (the cost of emitting undesirable waste into the commons), and does not include this cost in the price of the car , they are said to be external to the market pricing mechanism. The air pollution from driving the car is also an externality produced by the car user in the process of using his good. The driver does not compensate for the environmental damage caused by using the car.
As we know that the social cost is the sum of private cost and external cost so if external cost is zero then social cost will be equal to private cost.}