# Marginal Social Surplus

Marginal social surplus is the social surplus (sum of consumer surplus and producer surplus) provided by the last unit of a good. It's the difference between marginal social benefit and marginal social cost:

MSS = MSB - MSC

When there are no external benefits or costs, MSB and MSC are equal private marginal benefits and marginal costs and MSS becomes:

MSS = MB - MC

As an example, suppose the demand for oil and the cost of extracting it are given by the following equations:

P = 75 - Q

MC = 5 + Q

Since the demand curve shows willingness to pay or marginal benefits, the marginal social surplus curve can be found by substituting it and the MC curve into the definition of MSS:

MSS = MB - MC

MSS = (75 - Q) - (5 + Q)

MSS = 70 - 2*Q

As a check, notice that MSS = 0 when Q = 35. Inserting 35 into the demand curve gives P = W2P = MB = 40. Inserting 35 into the MC curve gives MC = 40. Thus, when MSS = 0, MB = MC. The last unit generates no social surplus because the marginal cost of producing it is just equal to the marginal benefits it provides.
URL: https://wilcoxen.maxwell.insightworks.com/pages/743.html
Peter J Wilcoxen, The Maxwell School, Syracuse University
Revised 04/12/2004