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Specialist Economic Equivalency - Merchants vs Scientists

In the wake of the Epic 12 report by pindicator, a discussion arose about the economic production of specialists. Like most players in the Epic, pindicator had Delhi as a huge commerce city with lots of science buildings. He noted that it seemed more efficient to run Merchant specialists in other cities, in order to keep the science slider percentage high to leverage Delhi's science productivity.

The questions are, is that intuition right? And how can we quantify it?

The short answer to the former is yes. Gold and beakers do not exist in a 1-to-1 equivalency in Civ 4. There most certainly is a difference between merchant and scientist specialists.

For purposes of this discussion, we make a few simplifying abstractions. Strictly speaking, the game economy does not directly convert between gold and beakers. We convert future commerce or specialist production to either gold or beakers, but I'll speak as if they are currently equivalent. Second, the in-game research slider only operates in 10% increments, while I assume a slider that can adjust in increments of arbitrary precision. This is correct if you consider the aggregate operation of the slider over time. For example, if you want to run 78% research, you can run 70% for two turns and 80% for eight turns.

For every empire, there exists a conversion factor between gold and research beakers. This conversion factor is essentially the ratio of the average empire-wide multiplier for each type of production. As a simple example, suppose you have a single city, with +0% gold and +100% science, producing 60 commerce per turn. You can convert that 60 commerce to 60/0 gold/beakers, or 59/2, or 40/40, or 1/118, or 0/120. For this empire, 1 gold = 2 beakers.

You can derive this ratio in-game. Look at the F2 economic advisor screen and click your slider one step. Disregarding roundoff artifacts, the change you see in each of your gold production and science production is your national ratio.

This ratio applies across your entire civ's production. Suppose we need 20 gold per turn to pay our civ's expenses, so that Delhi is producing 20/80 gold/beakers. Now suppose you have a second city that's producing nothing except for one specialist with no multipliers. If you make that specialist a scientist, that's +3 research, making the national production 20/83. But if we hire a merchant instead, we can bump our science slider so that Delhi is producing 17/86 gold/beakers with the merchant making up the rest of the cash shortfall. Our merchant is actually indirectly generating 6 beakers!

This principle is continuous - any gold that you generate anywhere in this empire is as good as generating 2 beakers. This simple example acts as a proof of concept of the original question.

Now, how does this play out in practice? For most actual civilizations, the conversion factor is fairly close to 1:1, so any economy you produce is equally valuable, and that's good enough for the casual player or the AI. Even in this hypothetical scenario, you're likely to regress that ratio closer to 1:1 going forward, as your capital fills in the missing cash multiplier buildings.

However, that 1:1 generality is usually at least slightly and sometimes considerably skewed towards beakers. There are several reasons for this.

So if you have an Academy (or several), and Oxford in a city producing a substantial share of your total commerce, then the equivalency ratio skews drastically in favor of beakers. So gold produced elsewhere becomes more dear. We have two different currencies; one has undergone inflation and one has not. The one that hasn't (gold) is more scarce. So when you can equivalently produce either of them (by choosing which specialist to hire), producing gold is more valuable.

This skew towards beakers is a subtle reason that the monk economy works so well. Gold generated by a shrine typically enables beaker production in excess of the face value of the gold itself.

Finally, the equivalency of gold and beakers only applies as long as you are able to fluidly convert one to the other via the slider. The chief case where this breaks down is in an OCC, where you can't run deficit research (you don't have any expenses), so gold cannot be applied towards research, so your specialists should always be scientists. This is intuitively obvious.

Now that we've established the existence of the equivalency ratio and shown a simple example, let's work through a specific quantitative example.

A note on notation: A city's economic multiplier can be expressed in several ways. Consider a city with only a library for +25% science, and nothing else. A scientist in this city will produce 3.75 beakers, which can be expressed as 3 * (1 + 25%), or 3 + 25%, or 3 * 125%, or 3 * 1.25. These are all equivalent and I use each notation interchangeably.

To calculate the national aggregate multiplier for beakers and for gold, average each city's multiplier weighted by its commerce production (including trade routes and Bureaucracy). It simplifies things to also include 100% for each city's base production in this step (so a city with only a library would be 125%.) Consider this example:

Delhi 60 150% 335% Oxford, Academy, library, university, observatory, monastery, bank
CityB 30 200% 150% library, university, bank, market, grocer
CityC 10 100% 100% No multiplier buildings

Our national gold multiplier is (60 * 150% + 30 * 200% + 10 * 100%) / (60 + 30 + 10) = 160%. This isn't the sum of our multiplier buildings, or the straight average of each city; it's the weighted average of each city. Notice that the overall ratio is close to Delhi's (because Delhi is our commerce gorilla), but CityB pulls it above that to a greater extent than CityC pulls it down, because CityB has more weight than CityC.

Likewise, our national science average multiplier is (60 * 335% + 30 * 150% + 10 * 100%) / (60 + 30 + 10) = 256%. Our national value ratio of gold:beakers is 160:256, or exactly 1:1.6.

Suppose CityC wants to hire a specialist. This is pretty straightforward. There's no multipliers in the city, so you can produce either gold or science here on a one-to-one basis. But we should hire a merchant. Why? Because hiring a scientist will produce a flat 3 research. But the 3 gold produced by a merchant will instead enable us (via raising the science slider) to produce 3 * 1.6 = 4.8 beakers elsewhere in our empire.

Now suppose CityB wants to hire a specialist. Mr Scientist would give us 3 + 50% = 4.5 beakers. Mr Merchant would give us 3 + 100% = 6 gold, and that 6 gold translates to 6 * 1.6 = 9.6 beakers elsewhere in the empire. Both intuitively and mathematically, it's very clear-cut for the merchant.

Suppose Delhi itself wants to hire a specialist. Intuitively, we'd say a scientist with that high multiplier, and we'd be right. Mr Scientist produces 3 + 235% = 10.05 beakers. Mr Merchant produces 3 * 1.5 = 4.5 gold, which translates only to 4.5 * 1.6 = 7.2 beakers of increased science slider, less than the scientist.

Now here's a tricky example. Suppose we had a City D (producing no commerce so as not to affect the national value ratio.) And suppose this city has a library for 125% science production, and no gold multiplier buildings. Mr Scientist produces 3 * 1.25 = 3.75 beakers. But Mr Merchant produces his 3 gold which translates into 3 * 1.6 = 4.8 beakers via the slider!

How can this be? A city with a higher science multiplier than gold still came out ahead by hiring a merchant? The answer is that each city's production is not absolute, but is relative to our national gold:science ratio. If a city's own gold:science ratio (1:1.25 for City D here) is lower than the national gold:science ratio (1:1.6) here, it should hire a merchant. If a city's own gold:science ratio is higher than the national gold:science ratio (for Delhi, compare its 1:2.17 to national 1:1.6), it should hire scientists.

As proof, consider the breakeven crossover point, which would be in a city with exactly 1:1.6 ratio. This could be 100% cash and 160% science, or 125%:200% gold:science, or 150%:240%. Let's use that middle one. Mr Scientist produces 3 * 200% = 6 beakers. Mr Merchant produces 3 * 125% = 3.75 gold, which equals 3.75 * 1.6 = 6.00 slider-beakers. Exactly the same.

The practical impact is as pindicator surmised. Most empires will have at least a slight skew towards beaker production from the slider, so merchants should be favored over scientists. However, this only applies so long as the city hiring the specialist doesn't have a science multiplier exceeding its gold multiplier by more than your national science multiplier exceeds your national gold multiplier.

Also, there can come a time in the industrial age where the situation reverses. There's a period when 100% cash multiplier is available for each city (grocer, market, bank) but only 75% science multiplier (library, observatory, university, but not yet laboratory.) And if Wall Street is equally productive as Oxford, you could have the national gold multiplier exceed the science multiplier, for a beaker:gold ratio actually lower than 1:1. If this happens, then the correct tactic is to push the cash slider higher and compensate by hiring scientist specialists instead.

There will be a quiz on this tomorrow. dubious.gif 15x16 Class dismissed. cool.gif 15x15