# Externality and Output

In a positive externality, can government just set the price to the socially efficient price instead of a subsidy to correct an externality?

• Then this is below the market price, so less of the externality will be produced. They should pay a subsidy instead. Nov 16 '20 at 18:59

In principle in both positive and negative externality scenario government could just set price to the socially efficient price.

However, outside of static textbook example this is non-starter. The socially efficient price even in presence of externalities (positive or negative) is not constant and it will fluctuate across time. Hence government would have to always change the price it sets. This is problematic since estimating what the socially optimal price is in every instance and in real time is virtually impossible.

Consequently, it is considered more convenient to simply issue subsidy equal to the value of positive externality. In such way no matter how the socially optimal price fluctuates across time as long as the value of positive externality remains constant government does not need to change it across time. Value of positive externality that activity does without doubt fluctuates less frequently than prices so government wound need to reevaluate the subsidy just occasionally.

For a government to address a positive externality by setting the price of a good to its socially efficient price would raise several difficulties. The diagram below relates to the case of a good subject to a positive production externality so that marginal social cost MSC is less than marginal private cost MPC (but no consumption externality, so marginal social benefit MSB equals marginal private benefit MPB).

The MPB and MPC curves correspond to demand and supply, so in the absence of government intervention the market will clear at price $$P_0$$ and quantity $$Q_0$$. The socially efficient price however is $$P_E$$, where MSB equals MSC. Consider now what will happen if the government tries to set the price at that point:

1. The government's knowledge of the location of the MSB and MSC curves at any time may be imperfect, so it may not set the price at the correct (socially efficient) level.
2. Circumstances will probably change over time, shifting the MSB and MSC curves, so that as 1muflon1 points out the socially efficient price will change over time and it will be difficult for the government to respond in real time.
3. Suppose however that the government does succeed in setting the price at $$P_E$$. Producers, acting in accord with their private interests, will produce not at the socially efficient quentity but where the MPC curve reaches price $$P_E$$, at $$Q^*$$. Thus the effect of setting the price at $$P_E$$ and taking no other action will be the opposite of what was intended: production will be less than at the free market price, and therefore the external social benefit will be less. Consumer welfare will also be less, since the output available to consumers will be reduced from $$Q_0$$ to $$Q^*$$. Moreover, since quantity demanded at $$P_E$$ exceeds quantity supplied, the market will not clear and some form of rationing will be needed to determine which demands will be met and which will not.
4. The last point leads to a further difficulty. Given the need for rationing, there will be strong incentives for producers to try to sell at a higher price than $$P_E$$, and therefore a challenge for the government in enforcing that price.

To address difficulties 3 and 4, a government could combine setting the price at $$P_E$$ with establishing publicly-managed production to make up the difference between $$Q^*$$ and $$Q_E$$. But this brings costs and difficulties of its own.

In the case of a consumption externality, difficulty 3 takes a different form. The problem then is that the socially efficient price exceeds the free market price, resulting in a reduction in quantity demanded by consumers and consequently a reduction in the external social benefit from their consumption.