So far, we have mostly talk about negative externalities. But what about

positive externalities? The logic is exactly the same. Let us show it$.$

Imagine an apple$-$bee externality in which a beekeeper is located next to

a$20-$acre apple orchard. Each hive of bees is capable of pollinating $14$ acre

of apple trees, thereby raising the value of apple output by $$25.$

$($a$)$ Suppose the market value of the honey from one hive is $$50$ and that

the beekeeper$$s marginal costs are given by

MC $=30+0$:$5$Q

where Q is the number of hives employed. In the absence of any bar$-$

gaining, how many hives will the beekeeper have and what portion of

the apple orchard will be pollinated? Assume the beekeeper operates

in a perfectly competitive market $($i$.$e$.,$ she is a price taker$).$

$($b$)$ What is the maximum amount per hive the orchard owner would pay

as a subsidy to the beekeeper to prompt her to install extra hives?

Will the owner have to pay this much to prompt the beekeeper to

use enough hives to pollinate the entire orchard?