Goldenhill Apiary keeps bees to produce and sell jars of honey. While foraging for nectar, the bees also pollinate the apple trees at the neighbouring Orchard Vale farm, increasing Orchard Vale's fruit yields. This pollination benefit is not paid for by Orchard Vale and is not r…

Answer: ((a)) Goldenhill Apiary only takes account of its own marginal private cost (MPC) of keeping bees and producing honey when deciding how much to produce, but the bees also pollinate Orchard Vale's apple trees, creating a marginal external benefit (MEB) that the apiary is not paid for,… ((b)) (i) The free-market output is 3 thousand jars of honey per month, where MPB equals MPC; (ii) the socially optimal output is 5 thousand jars per month, where MSB equals MSC; since the free-market output is below the socially optimal output, the free market under-provides honey pr… ((c)) At the free-market output of 3 thousand jars, MEB = MPC − MSC = 43 − 19 = $24 per jar; since this gap falls in a straight line from $24 at the free-market output (3 thousand jars) to $0 at the socially optimal output (5 thousand jars), the deadweight welfare loss is the triangul… ((d)) A specific subsidy of $24 per jar, equal to the constant marginal external benefit, would lower Goldenhill Apiary's effective marginal cost from MPC to MPC minus the subsidy, which equals MSC, so the profit-maximising firm would now choose to produce where MPB equals MSC, i.e. a…. Part (a): Why this is a positive externality of production Goldenhill Apiary decides how much honey to produce by weighing up its own private costs of keeping bees against the price it can charge. It is not paid anything extra for the fact…

A Level Economics 9708: Positive Externalities of Production and Subsidies

Output (thousand jars of honey per month)	Price = MPB = MSB ($ per jar)	MPC ($ per jar)	MEB ($ per jar)	MSC = MPC − MEB ($ per jar)
0	61	25	24	1
1	55	31	24	7
2	49	37	24	13
3	43	43	24	19
4	37	49	24	25
5	31	55	24	31
6	25	61	24	37

Output (thousand jars of honey per month)

Price = MPB = MSB ($ per jar)

MPC ($ per jar)

MEB ($ per jar)

MSC = MPC − MEB ($ per jar)

Part (a): Why this is a positive externality of production

Goldenhill Apiary decides how much honey to produce by weighing up its own private costs of keeping bees against the price it can charge. It is not paid anything extra for the fact that its bees also pollinate crops in the local area. But as the bees forage for nectar, they also pollinate the apple trees at Orchard Vale, boosting Orchard Vale’s fruit yields at no cost to Orchard Vale.

This means: $MSC = MPC - MEB$

where $MEB > 0$ is the marginal external benefit of the pollination. Because Goldenhill Apiary’s production decisions are guided only by $MPC$ , not the lower $MSC$ , it produces less than is socially desirable. This uncompensated third-party benefit is exactly what defines a positive externality of production.

Part (b): Free-market output and socially optimal output

Free-market output: Goldenhill Apiary maximises profit where the price it receives (equal to $MPB$ , since honey buyers pay based on their own private benefit) equals its marginal private cost, $MPB = MPC$ . Reading the table, at an output of 3 thousand jars, $MPB = MSB = 43$ and $MPC = 43$ , both equal $43 per jar. So the free-market output is 3 thousand jars per month.

Socially optimal output: allocative efficiency requires marginal social benefit to equal marginal social cost, $MSB = MSC$ . At an output of 5 thousand jars, $MSB = 31$ and $MSC = 31$ , both equal $31 per jar. So the socially optimal output is 5 thousand jars per month.

Because the free-market output (3 thousand jars) is below the socially optimal output (5 thousand jars), the positive externality causes the market to under-provide honey production, and, with it, the pollination service Orchard Vale relies on.

Part (c): External benefit and deadweight welfare loss

At the free-market output of 3 thousand jars per month: $MEB = MPC - MSC = 43 - 19 = 24$

So the marginal external benefit is $24 per jar at this output (matching the constant MEB column in the table).

Between the free-market output (3 thousand jars) and the socially optimal output (5 thousand jars), the gap between $MSC$ and $MSB$ narrows from $24 per jar (at 3 thousand jars, where $MPB - MSC = 43 - 19 = 24$ ) down to $0 (at 5 thousand jars, where $MSB = MSC = 31$ ). Since both $MSB$ and $MSC$ change at a constant rate with output, this gap shrinks in a straight line, so the deadweight welfare loss is the area of a triangle: $DWL = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times (5-3) \times 24 = 24$

Because output is measured in thousand jars, this deadweight welfare loss of $24$ represents $24 thousand ($24,000) per month. The value of the pollination (and honey) foregone because too little honey is produced between the free-market and socially optimal quantities.

Part (d): A corrective subsidy

A specific subsidy of $24 per jar, set equal to the constant marginal external benefit, would reduce Goldenhill Apiary’s effective marginal cost for every jar produced to: $MPC - \text{subsidy} = MPC - MEB = MSC$

Facing this lower effective marginal cost, the profit-maximising apiary would now choose its output where $MPB = MPC - \text{subsidy}$ , which, because $MPC - \text{subsidy} = MSC$ , is exactly where $MPB = MSC$ , i.e. at the socially optimal output of 5 thousand jars per month. The subsidy “internalises” the externality by rewarding Goldenhill Apiary for the full social value of its production.

Final answers

(a) MSC is lower than MPC because of the uncompensated marginal external benefit (the pollination) received by Orchard Vale
(b) Free-market output = 3 thousand jars/month; socially optimal output = 5 thousand jars/month; the free market under-provides honey and pollination
(c) MEB at the free-market output = $24 per jar; deadweight welfare loss = $24 thousand ($24,000) per month
(d) A specific subsidy of $24 per jar (equal to the MEB) would move output to the socially optimal level