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.

• The Academy multiplies beakers but there is no comparable building for cash multiplication.
• Research buildings usually come sooner than cash buildings:
  • An efficient empire usually runs a high science slider, so it's correct to prioritize research buildings over gold.
  • Culture production makes the library and university more attractive.
  • The design of the tech tree (Liberalism slingshot) leads to Education and Astronomy almost always being higher priority than Guilds and Banking.
• The relation between Oxford University and Wall Street has an effect too:
  • Oxford comes earlier than Wall Street.
  • Oxford invariably goes in your highest commerce city, while Wall Street usually goes in your shrine city. So Oxford contributes more to the aggregate civ-wide multiplier than Wall Street does, because it operates on more base commerce.

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:

City	Commerce	Gold	Science
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. Class dismissed.