Resourciv: Economic Models
Some more Resourciv updates! These are actually implemented in-game, but they have implications for how I design leading forward.
Production
I was giving myself a headache thinking about how, whether I increased the granularity of populations or kept it as unitary as it is now, I would need to deal with the most annoying part of economic games: allocating labor. Assigning peeps to individual hexes is stupid but so is giving them a list of jobs which give and take any amount of random resources; what if the numbers worked around me? There’s a nifty little formula called the Cobb-Douglas production function which handles that as well as diminishing returns: if you imagine, just because you have a bunch of cooks in the kitchen doesn’t mean you make more food, and the same if you have more kitchens than you have cooks. Labor is apparently more useful than capital since its diminishing returns (if it exceeds capital) are less so than capital (if it exceeds labor), and this is represented by their respective elasticity coefficients which are how much an increase of labor or capital results in an increase of production. There’s also a technological constant which represents the general efficiency of the operation without there being a change in labor or capital quantities invested. I’m also going to have players allocate peeps not to hexes or jobs, but to the production of specific resources; just feels the most transparent. They also won’t be allocating individual peeps or populations, but tenths of the total population.
This means you can think of a hex with a wheat farm not as producing 2 grain, but as having 2 grain-capital which is best complemented by 2 peeps (or by a number of peeps proportional to the grain-capital’s share of total capital in the settlement). Maybe that’s confusing at first, but it means less allocation-related headaches as a developer as well as a player. If I want to make more food, I can either allocate more peeps to make grain or I can make more grain farms to increase what capital my farmers are working with. I also don’t necessarily need to worry about what happens when my population grows because their allocations haven’t changed. Labor elasticity is usually around 0.7 to capital’s 0.3 (and in standard Cobb-Douglas, those two always add up to 1.0, meaning that if both labor and capital increase by the same proportion, so does production output; but that’s not necessarily true), but right now I’m using coefficients of 0.5 for each because it keeps the math simple (just take square root); we’ll see later what makes more sense.
This might be a bad idea. I still want to have a division of labor (maybe just based on who produces what) and account for products requiring any materials (which currently has an awkward approach: rather than accounting for materials as individual / specific factors of production, the materials just factor into how much total capital you have available; e.g., a smithy needs 3 ore and yields 3 metal-capital). Maybe that’s fine; I just need to figure out what it looks like in practice.
Trade Balance
I had a math problem for myself. I know how much of each resource is produced or consumed by each settlement. Assuming each settlement has equal access to export or import resources to the others, can I determine how much of each resource a particular settlement is either exporting or importing, given the potential for total surplus or deficit? That last part is important because most calculations I found assumed that the amounts being imported or exported are actual rather than potential, meaning that there could be more produced than is actually being consumed (and presumably exported). This means rather than just subtracting consumption from production, which is a real business major moment, I had to find a settlement’s share of production for a particular resource, and then multiply that by how much of the resource is actually being consumed; only then can I subtract the city’s individual consumption.
The math worked on paper so I implemented it directly into the game’s logic, but I was confused because both my test settlements had positive trade balances. Then I realized: oh shit, the state also consumes resources—and the amount was exactly 9, matching how many meeps I had and how much total food they consumed. Without the state, City A would be extracting just 1.5 value from City B; with the state, however, both cities are extracting value.
| Resource | City A | City B | State |
|---|---|---|---|
| Clay | +0.7 | –0.7 | — |
| Fish | +0.7 | +2.2 | –2.9 |
| Fruit | +1.5 | +0.8 | –2.3 |
| Grain | +1.7 | +1.2 | –2.9 |
| Spice | +1.0 | –0.1 | –0.9 |
| Wood | +0.7 | –0.7 | — |
| Total | +6.4 | +2.6 | –9.0 |
The scale is certainly off, because I can’t guarantee that the amount of food consumed by the state is accurate relative to how much is consumed by the two settlements, but you might notice the implication that a profitable military is basically a wealth factory and that it’s the state (at least early on) who enriches the population (or, at least, its wealthy strata) rather than the other way around, though that doesn’t preclude competition between the state apparatus and the property-owning class later on. I’m reminded of a couple things: Michael Heinrich’s analysis that the premodern state functions as a firm; James C. Scott’s analysis that capital logic originates in the earliest states (which are really equivalent with the ruling class, not just acting on their behalf or on behalf of the economic system itself); how David Graeber says currency originates for armies to buy food; my friend John B. telling me that modern capitalism developed as an instrument of war; and my own formula that we need not attribute social dynamics to the formal structures (e.g. the state) which may or may not enable them except, in this case, the state is an agent rather than a structure. Just fascinating. If I hook up a wealth attribute which is gradually extracted from the state into its populations, the resulting dynamic would almost certainly be of a military-industrial complex, the same which exists now and has existed since prehistory with the likes of tributary states and military expeditions.
Also note that because I know how much a settlement produces and “sells” of a resource, I can also know how much income the population makes (based on how much of the total population is allocated to producing that resource, how much income goes to owners v.s. workers, and how much is consumed v.s. wasted—all of which are either known or easy to calculate when the context is implemented). I could also use data about wasted resources to inform derived stats like resource value and unemployment, the latter informing wages for workers in capitalist contexts, and the former informing owner profits (except they will probably just “hire” less workers, so… back to the latter bucket).
What’s Next?
I’d like to crunch the numbers to figure out how I can get a majority agrarian population to start the game, and then make agriculture more efficient to boost population growth and industrial labor at different points and degrees throughout the game. I also want to figure out how best to implement elite populations, whether landlords or capitalists, since I don’t know whether they should provide some necessary resource or if they should just somehow emerge and take a slice of the population. Finally, if I go with the approach of dividing the population into tenths for allocating aggregate labor time, I need to develop an interface between that and cultural divisions—or come up with something new which lets me scale population up without worrying about allocating new labor.
Don't forget, just how tiny the elite was in antiquity. Less than a percent of the population.
ReplyDeleteto be honest i keep seeing percents around 10%! though that varies between time and place and i tend to include clergy in that count. need to keep researching though!
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