Q.A chemical factory pays Rs. 12,00,000 a year in wages, raw materials and other explicit costs, and its implicit costs (the value of the owner's own capital and premises used in the business) amount to Rs. 3,00,000. The factory also discharges untreated effluent into a nearby river, and as a result the local municipality has to spend an extra Rs. 1,50,000 a year on additional water purification. Compute the factory's private cost and its social cost of production for the year, and explain why the two differ.

Private cost is what the firm itself bears (explicit + implicit); social cost adds on the uncompensated cost the firm's pollution imposes on the municipality.

Private cost $= 12{,}00{,}000 + 3{,}00{,}000 = Rs.\,15{,}00{,}000$. Social cost $= 15{,}00{,}000 + 1{,}50{,}000 = Rs.\,16{,}50{,}000$.

Private cost is the cost the factory itself actually bears — its explicit cost plus its implicit cost:

Social cost is wider: it is the private cost PLUS any cost the factory's production imposes on third parties for which the factory pays nothing. Here, the municipality bears an extra Rs. 1,50,000 in water-purification cost purely because of the factory's untreated effluent, and the factory does not compensate the municipality for this:

The two figures differ precisely because the factory's own accounts capture only what IT pays for — its private cost — while social cost also counts the Rs. 1,50,000 the factory's pollution forces onto the wider community, a real cost of the factory's production even though it never appears in the factory's own books.

Students sometimes treat private cost and social cost as the same thing whenever a firm's own accounts are complete (i.e., include both explicit and implicit cost) — but social cost is a genuinely separate, WIDER concept that only arises when a firm's activity affects third parties who are not paid for the harm done to them; a firm with no such external effect has private cost equal to social cost.