Private cost refers to the expenses incurred by a firm in production of a given quantity of output. It includes payments for inputs and all explicit and implicit production expenses.
The social cost, on the other hand, is a much wider concept. It fearers to what the given volume of production costs to the society. Thus, besides the private expenses on production, social cost includes all the costs that are external to a firm and firm and not included by it as a part of cost such as atmospheric and water pollution. Thus money spent on raw materials and inputs by firm is a part of the private costs, but the smoke and acid fumes that emit from a chemical mill, the effluent polluting rivers and lakes, the impact of chemicals on workers, health and treatment expenses, etc, do not from a part of private cost. But these are an integral part of private cost are called external costs. Thus social cost includes private cost plus the external cost of producing a given output.
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