Mithril for Timber
The Lord of the Rings: The Rings of Power: S1, E7 “The Eye”
Comparative Advantage and Trade: Gains from Trade
Earlier in the first season, the elves Elrond and Celebrimbor began forming plans to build a new tower for forging. But to finish it by Spring, they require more resources than currently available in Eregion.
Elrond: “Have you considered seeking partners outside the confines of our own race?”
Celebrimbor: “How far outside?”
Elrond’s idea is to bring a proposal to the dwarves of Khazad-Dûm. Celebrimbor is skeptical despite his admiration of the dwarves’ industrial might.
Celebrimbor: “An alliance with the dwarves would be the diplomatic achievement of the age.”
His skepticism is warranted, it turns out. Elrond has an uphill climb to convince his old friend, Prince Durin, to treat with him. Once Prince Durin agrees that the Elves need the mithril, Elrond must convince King Durin. Elrond approaches with an offer.
Elrond: “We ask for something sacred from this mountain. And so, we offer something sacred in return. In exchange for access to your mithril mines, the Elves are prepared to furnish this city with game, grain, and timber from the elder forests of Eriador for the next five centuries.”
King Durin has no desire to provide mithril to the Elves as a charity case. It must be in the dwarves’ best interest for him to accept. Is this offer really in the best interest of the dwarves?
Suppose the following are true to simplify the story:
- The Elves of Eregion and the dwarves of Khazad-Dûm produce and consume two goods: timber (by the cord) and mithril (by the ounce).
- The resources of each realm are defined by its number of workers. Suppose Khazad-Dûm and Eregion each have 30,000 workers.
- Each realm produces timber and mithril as follows:
- In Eregion, it takes the work of 20 elves to produce a cord of timber and 200 elves to produce an ounce of mithril.1
- In Khazad-Dûm, it takes the work of 60 dwarves to produce a cord of timber and 5 dwarves to produce an ounce of mithril.2
- The elves propose a trade that amounts to providing a cord of timber for every ounce of mithril they receive.
A trade alliance would allow each realm to specialize, producing only one of the two goods and trading for the other. Massive gains arise if each realm specializes based on comparative advantage. A realm has comparative advantage if it can produce a good at lower opportunity cost.
Timber:
- In Eregion, each additional cord of timber requires 20 more elves. Those elves are no longer producing mithril, leading to 0.1 fewer ounces of mithril.
- In Khazad-Dûm, each additional cord of timber requires 60 dwarves. Those dwarves are no longer producing mithril, leading to 12 fewer ounces of mithril.
- Because Eregion’s opportunity cost is lower, the elves have the comparative advantage in producing timber.
Mithril:
- In Eregion, each additional ounce of mithril requires 200 more elves. Those elves are no longer producing timber, leading to 10 fewer cords of timber.
- In Khazad-Dûm, each additional ounce of mithril requires 5 dwarves. Those dwarves are no longer producing timber, leading to 0.083 fewer cords of timber.
- Because Khazad-Dûm’s opportunity cost is lower, the dwarves have the comparative advantage in producing mithril.
If King Durin accepts, the dwarves can specialize in mithril extraction, knowing that timber will be provided by the elves. And the elves can specialize in timber production, since the dwarves will provide the much-needed mithril.
This arrangement clearly suits the elves. Elrond made the offer, and he’s plenty wise. We can visualize this using a production possibilities frontier (PPF), which shows all combinations of timber and mithril Eregion can produce on its own. Keep in mind that consumption is what Eregion is really after. Production is a means to an end. The real measure of prosperity is consumption possibilities. What can the elves possibly consume? It depends on whether trade occurs.
Without an alliance, Eregion would be left choosing a production (and consumption) combination on its PPF. Any amount of mithril it’s able to come up with requires large sacrifices in timber. But an alliance with the dwarves eases the sacrifice. Instead of giving up 10 cords of timber for every ounce of mithril (through the reassigning of elven workers), Eregion only gives up 1 cord (through trade with the dwarves).3 Trading allows the elves to consume combinations of timber and mithril that were previously unimaginable.
What about the dwarves? King Durin is difficult to sway, but the same logic applies.
When Khazad-Dûm is left to its own production methods, every cord of timber produced costs 12 ounces of mithril. And the dwarves need timber! But if they accept Elrond’s proposal, they can forgo sending dwarves out into the forests and send them to the mines instead, where their talents are best used. Then they trade for timber from the elves, giving up only an ounce of mithril for every cord of timber.
Just like for the elves, trade creates massive gains. The dwarves can now consume combinations of mithril and timber that were previously impossible. More generous trade terms would be even better, but their gains are already massive at the suggested price.4 What makes this possible? The two races, dwarves and elves, have very different skills and abilities to access their natural resources. If Elrond had approached the elves of Lórien instead, the possible gains from trade would likely be much smaller. Through specialization and trade, differences between groups create prosperity.
Unfortunately, King Durin rejects Elrond’s proposal.5 Perhaps he could use an economics lesson or two.
“Lice-bearded, uncaring, old fool!”
1 Given the scarcity, a more accurate model might assume each ounce of mithril requires 10,000 elves or perhaps even infinitely many. This change would only strengthen the conclusions.
2 These values reflect both the skills of elves and dwarves but also the ease with which each realm could access these natural resources. We are also assuming here that opportunity costs are constant. The first cord of timber the dwarves produce sets them back the same amount of mithril as the 100th cord.
3 This logic reveals what terms of trade the elves would find acceptable. If they can trade for mithril by giving up less than 10 cords for each ounce, gains in consumption are possible. So, the elves would gain even if the price was 9 cords of timber for each ounce of mithril.
4 What is the minimum compensation such that the dwarves still gain from trade? If left to their own production, each cord of timber costs the dwarves 12 ounces of mithril. If the terms of trade were 11 ounces of mithril for each cord of timber, the dwarves would still gain.
5 Why? It could be a negotiating tactic for more generous trade terms. But it seems more cautious than that, as King Durin argues that mithril mining is unsafe. However, Prince Durin later mines for it himself and safely discovers massive stores of mithril. Even then, King Durin is unmoved.
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1 Given the scarcity, a more accurate model might assume each ounce of mithril requires 10,000 elves or perhaps even infinitely many. This change would only strengthen the conclusions.
2 These values reflect both the skills of elves and dwarves but also the ease with which each realm could access these natural resources. We are also assuming here that opportunity costs are constant. The first cord of timber the dwarves produce sets them back the same amount of mithril as the 100th cord.
3 This logic reveals what terms of trade the elves would find acceptable. If they can trade for mithril by giving up less than 10 cords for each ounce, gains in consumption are possible. So, the elves would gain even if the price was 9 cords of timber for each ounce of mithril.
4 What is the minimum compensation such that the dwarves still gain from trade? If left to their own production, each cord of timber costs the dwarves 12 ounces of mithril. If the terms of trade were 11 ounces of mithril for each cord of timber, the dwarves would still gain.
5 Why? It could be a negotiating tactic for more generous trade terms. But it seems more cautious than that, as King Durin argues that mithril mining is unsafe. However, Prince Durin later mines for it himself and safely discovers massive stores of mithril. Even then, King Durin is unmoved.