Socially optimum output

1. Previously, we saw that the demand and supply curves could be understood as the representation of the private benefits and costs associated with consumption and production, where:
   1. Marginal Private Benefit (MPB): the additional benefit to the consumers from consuming an extra unit of good
   2. Marginal Private Cost (MPC): the additional cost to the producers from producing an extra unit of good.
2. These marginal private benefits and costs guide consumer and producer decisions on how much to demand and supply.
3. However, private benefits and costs don't always align with the social benefits and costs that society obtains from consuming and producing a good or service.
4. Therefore, economists make a distinction between the Marginal Private Benefits/Cost and the Marginal Social Benefits/Cost.
5. Reflecting society as a whole, the socially optimal output occurs at a production level where Marginal Social Benefit (MSB) equals the Marginal Social Cost (MSC):

$$MSB=MSC$$

where:

1. Marginal Social Benefit (MSB) is the additional benefit to the society from consuming an extra unit of good.
2. Marginal Social Cost (MSC) is the additional cost to the society from producing an extra unit of good.

In Figure 1, it can be seen that in absence of externalities:

1. The demand curve ($D$) represents both Marginal Private Benefit (MPB) and the Marginal Social Benefit (MSB) at the same time
2. The supply curve ($S$) represents both Marginal Private Cost (MPC) and the Marginal Social Cost (MSC) at the same time
3. Thus the social optimum output is reached at their intersection, at quantity $Q_{opt}$. This level of output achieves allocative efficiency.

However, Figure 1 depicts a free market where there are no externalities.

In reality, most of the times there are externalities, which alter the allocation of resources and can be:

1. Positive production externalities.
2. Positive consumption externalities.
3. Negative production externalities.
4. Negative consumption externalities.

Positive externalities of production and consumption and welfare loss

Positive Production Externalities

1. Goods and services with positive production externalities have a positive impact in society when produced.
2. This is because the Marginal Social Cost of production is lower that the Marginal Private Cost of production.

1. Figure 2 above showcases the representation of a positive production externality:
   1. The market is producing at the equilibrium set by the marginal private benefits and marginal private costs, reflected by the demand and supply curves. This market equilibrium occurs at:
      1. Quantity $Q_m$.
      2. Price $P_m$.
   2. However, there is an externality, and so the effects to society of producing good $x$ are different than the private ones.
   3. In this case, the externality is positive and of production, meaning that there is a positive spillover effect on society from the production of good $x$.
   4. This is occurs because the marginal costs to society of each unit produced are lower than the marginal private costs faced by producers.
   5. Resultantly, the MSC curve is below the MPC curve, separated by the value of the externality.
   6. As we say, the socially optimal level is determined by $MSB=MSC$, and so the intersection of the MSB and MSC curves yields:
      1. The socially optimum output quantity ($Q_{opt}$).
      2. The price $P_{opt}$.
   7. However, this social desirable quantity ($Q_{opt}$) is higher than what is being produced by the market ($Q_m$): $Q_{opt}>Q_{m}$.
2. Therefore, due to the positive production externality, the free market fails by under allocating its resources, and producing below socially optimal level.

Welfare Impact of Positive Production Externalities

1. Since there is a misallocation of resources, in the form of under allocation in this case, this means that the market fails to achieve allocative efficiency, hence there will be a welfare loss.
2. In the diagram we can observe that:
   1. At the current production level, the DWL is equal to the area $\frac{(MSB-MSC)\times(Qopt-Qm)}{2}$.
   2. If the externality is corrected, the society will gain this area as part of their welfare.
3. The externality can be corrected though:
   1. Direct Government Provision