# Marginal Social Benefit

Marginal social benefit is equal to the private marginal benefit a good provides plus any external benefits it creates. In other words, MSB gives the total marginal benefit of the good to society as a whole. In mathematical notation:

MSB = MBprivate + MBexternality

It is used for evaluating efficiency in the presence of positive externalites.

When calculating MSB, be sure to add the individual marginal benefits "vertically". That is, be sure that you are adding up the marginal benefits produced by each unit of the good. In mathematical terms:

MSB(Q) = MBprivate(Q) + MBexternality(Q)

As an example, suppose a company is thinking about buying and redeveloping part of an old abandoned industrial site near the center of a city. Such areas are called "brownfields" and are a big problem for many cities because they are unsightly and may be polluted. Redeveloping them often produces big external benefits. Suppose in this case the marginal benefit the firm gets is given by the function:

MBp(Q) = 2000 - 5Q

where Q is the number of acres redeveloped. In addition, redeveloping gives the city \$100 of external benefits per acre:

MBe(Q) = 100

The MSB of redevelopment are given by:

MSB(Q) = MBp(Q) + MBe(Q) = (2000 - 5Q) + 100 = 2100 - 5Q

URL: https://wilcoxen.maxwell.insightworks.com/pages/125.html
Peter J Wilcoxen, The Maxwell School, Syracuse University
Revised 08/17/2016