According to the International Monetary Fund, "there are differences between private costs and the costs to the society as a whole". In a situation where there are positive social costs, it means that the first of the Fundamental theorems of welfare economics failed in that relying merely on private markets for price and quantity lead to an inefficient outcome. Market failures or situations in which consumption, investment, and production decisions made by individuals or firms result in indirect costs i.e. have an effect on parties external to the transaction are one of the most common reasons for government intervention. In economics, these indirect costs which lead to inefficiencies in the market and result in a difference between the private costs and the social costs are called externalities. Thus, social costs are the costs pertaining to the transaction costs to the society as a whole. Generally, social costs are easier to think about in marginal terms i.e. marginal social cost. Marginal social cost refers to the total costs that the society pays for the production of an extra unit of the good or service in question. Mathematically, this can be represented by Marginal Social Cost (MSC) = Marginal Private Cost (MPC) + Marginal External Costs (MEC).
Social costs can be of two types -- Negative Production Externality and Positive Production Externality. Negative Production Externality refers to a situation in which marginal damages are social costs to society that result in Marginal Social Cost being greater than the Marginal Private Cost i.e. MSC > MPC. Intuitively, this refers to a situation in which the production of the firm reduces the well-being of the people in the society who are not compensated for the same. For example, steel production results in a negative externality because of the marginal damages pertaining to pollution and negative environmental effects. Steelmaking results in indirect costs as a result of emission of pollutants, lower air quality, etc. For example, these indirect costs might include the health of a homeowner near the production unit and higher healthcare costs which have not been factored into the free market price and quantity. Given that the producer does not bear the burden of these costs, they are not passed down to the end user thus creating a situation where MSC > MPC.
This example can be better elucidated with a diagram. Profit-maximizing organizations in a free market will set output at QMarket where marginal private costs (MPC) is equal to marginal benefit (MB). Intuitively, this is the point on the diagram where the private supply curve (MPC) and consumer demand curve (MB) intersect i.e. where consumer demand meets firm supply. This results in a competitive market equilibrium price of pMarket.
In the presence of a negative production externality, the private marginal cost increases i.e. shifted upwards to the left by marginal damages to yield the marginal social curve. The star in the diagram, or the point where the new supply curve (inclusive of marginal damages to society) and the consumer demand intersect, represents the socially optimum quantity Qoptimum and price. At this social optimum, the price paid by the consumer is p*consumer and the price received by the producers is p*producer.
High positive social costs, in the form of marginal damages, lead to an over-production. In the diagram, there is overproduction at QMarket - Qoptimum with an associated deadweight loss of the shaded triangle. One of the public sector remedies for internalizing externalities is a corrective tax. According to neoclassical economist Arthur Pigou, in order to correct this market failure (or externality) the government should levy a tax which equals to marginal damages per unit. This would effectively increase the firm's private marginal so that SMC = PMC.