Pigouvian Subsidy Definition & Examples
A Pigouvian subsidy (also called Pigovian subsidy after Arthur Cecil Pigou introduced the concept) is sometimes applied to those markets that have positive externalities attached to them. The idea is to encourage more production and consumption in order to reach a more efficient outcome that fully utilizes the potential gains that the free market will leave on the table.
A subsidy is just one of several options that a government could take in order to reach a more socially efficient quantity of production in the market, but it is usually one of the most effective options. Other options include marketing and promotion, or direct controls such as mandating extra production, or possibly even nationalizing the particular industry in order to provide the desired quantity of goods or services directly to the public.
A subsidy is usually the simplest and most efficient means of moving the free market to the desired equilibrium point, and a graph can easily illustrate how it works.
Pigouvian Subsidy Graph
Starting with the free market supply and demand curves in the graph below i.e., the red S=MPC and black MPB curves (where MPC means marginal private cost, and MPB means marginal private benefit), we can see that these intersect at a quantity of q and a price of p. However, the marginal private benefit curve (which is simply another name for the demand curve when there are externalities present) does not represent the full benefits to society.
The full benefits are represented by the blue MSB curve (which stands for marginal social benefit), and the efficient equilibrium point in the market occurs at its intersection with the red supply curve S=MPC i.e.,where the marginal social benefit equals the marginal social cost.
As can be seen in the graph, this results in an efficient equilibrium price of p* at an efficient output level of q*, and the net gains to society from this are illustrated by the green area above the supply curve and below the MSB curve.
Why is this green area indicative of the extra gains to society? Because for each extra unit of output from the original level of q, up to the optimal level of q*, we can clearly see that the marginal social benefits are higher than the costs (represented by the red supply curve).
However, at an output rate of q*, the black marginal private benefit curve shows that private individuals will only pay a price of p', which means that a Pigouvian subsidy will need to pick up the shortfall, and be equal to p* - p'.
Pigouvian Subsidy Formula
From the graph above we can derive the Pigouvian subsidy formula that will yield the most surplus for society. The overall cost of the subsidy can be written as:
Cost = q*(p* - p')
Both producers and consumers will benefit, with an extra consumer surplus equal to the top part of the green area, and extra producer surplus equal to the bottom part of the green area.
Consumers clearly benefit because because the price that they pay has fallen whilst their consumption has increased. Firms also clearly benefit because the price that they receive has risen and their sales have increased.
Only the taxpayer loses out, because taxes will need to rise in order to pay for the subsidy. However, whilst the extra tax burden is not illustrated (because it gets complicated by the extra tax receipts generated from the businesses whose profits are now higher), the green area in the diagram does illustrate the overall net benefit after costs are accounted for.