Econ Lab · Markets

Positive externalities

We usually meet externalities as a problem. A factory pollutes, a neighbour blasts music, and the market makes too much of the thing nobody wants nearby. But not every spillover is a harm. Some are gifts.

A flu shot protects you. It also lowers the chance that you pass the flu to the person next to you on the train. Slide the spillover up and watch the market fall short of what is best.

024680100200300400
Vaccinations\text{Vaccinations}
Value ($)\text{Value (\$)}
deadweight loss\text{deadweight loss}
private benefit\text{private benefit}
social benefit\text{social benefit}
cost\text{cost}
Qmarket=200Q_{\text{market}} = 200
Qsocial=238Q_{\text{social}} = 238

Not every spillover is a harm. Some are gifts. When your flu shot also shields everyone near you, the benefit to society is larger than the benefit you personally count.

A small spillover. Each shot hands others about 1.51.5 dollars of protection, but buyers count only their own. So they stop at 200200 vaccinations when 238238 would be best, and the shaded triangle is the gains left on the table, worth about 2828 dollars. The gap is real but modest. A subsidy of 1.51.5 dollars a shot, equal to the spillover, gets buyers to count the full benefit and closes it.

Move the slider to set how much each shot protects others. The shaded triangle is the gain the market leaves on the table.

Two kinds of benefit

When you decide whether to get the shot, you weigh what it is worth to you. That is the private benefit. Society gets more, because your shot also shields the people you would have infected. Add the spillover to your private value and you get the social benefit.

MSB=MPB+b\text{MSB} = \text{MPB} + b

The dashed social-benefit line sits a height bb above the private one. The bigger the spillover, the further apart they sit.

Where the market stops

Buyers keep getting shots as long as their own benefit beats the cost. The market settles where private benefit meets cost.

8−Q50=Q50  ⇒  Qmarket=2008 - \tfrac{Q}{50} = \tfrac{Q}{50} \;\Rightarrow\; Q_{\text{market}} = 200

That number never moves, because the spillover changes what is good for society, not what is good for the individual buyer.

Where society would stop

If we counted the full benefit, we would keep going until social benefit met cost. Solving with the spillover in gives a higher target.

8−Q50+b=Q50  ⇒  Qsocial=25(8+b)8 - \tfrac{Q}{50} + b = \tfrac{Q}{50} \;\Rightarrow\; Q_{\text{social}} = 25(8 + b)

The gap between the two points is the under-vaccination. The shaded triangle measures the value of the shots that should happen and do not.

Closing the gap

A subsidy equal to the spillover does the trick. Pay each buyer bb for getting the shot and their private benefit line lifts up to meet the social one. The market now stops exactly at the social optimum, and the triangle vanishes. The mirror image of a pollution tax: when a thing helps bystanders, you pay people to do more of it rather than charging them to do less.

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