Positive Externalities and Inefficiency:

External benefit occurs from those public goods where it is difficult, if not impossible to exclude people from benefits. Suppose, for instance, that A derives benefits from being inoculated against polio, but so do many others for whom the number of potential carriers, and hence the danger of infection, is reduced. Or by getting educated, not only A derives personal benefit but also makes it possible for others to enjoy association with a more educated community.

The following diagram represents adjustment for external benefits. The marginal private benefit of getting the vaccination is less than the marginal social or public benefit by the amount of external benefit i.e. the fact that if one person gets inoculation of polio, others are likely to get the polio even if they themselves are not vaccinated.

Here the marginal benefit of getting, polio is represented by vertical distance between the two demand curves. Here we assume that there is no external cost, so that both social cost equals private cost.

In the fig:

D_p= private demand
D_s= Social demand
S_S= supply
E_s= Ideal equilibrium
E_p=actual equilibrium
P_s= Price when social benefit schedule is reckoned with
P_p=Price when private benefit schedule is reckoned with
Q_s=Quantity produced when social benefits are taken into account
Q_p= Price when only private benefits are taken into account.

If consumers are concerned about their own private benefits, the market end up at price Pp and quantity Q_p instead of more efficient price Ps and quantity Q_s. This more efficient combination of price and quantity suggests that production should be increased as long as marginal social benefit (MSB) exceeds the marginal social cost (MSC). The ideal is that MSB should be equal to MSC. The  discussion is that an unfettered market is inefficient since at the quantity Q_p, the upshot of the marginal social benefit (FQ_p) is greater than social cost (E_pQ_p), so society as a whole would be better off if more goods had been produced. This explains why  people often buy  less education or vaccination.

With respect to public goods, it is difficult if not impossible to exclude people from benefit. The production of public goods has  beneficial externalities for all or almost all of the public.

Government should step in with collective solutions for both external benefits and costs so that the society as a whole benefits. The balance between marginal social benefits and marginal social costs should be attempted by the coordination between the two.