Question
Can you describe what the production function for the game looks like? (How are labour, capital and resources combined? Are there constant, increasing or decreasing returns to scale?)
Answer
The production function of the game is a fixed proportions production function. Let's first state directly from the rules about the requirements of production:
"A road costs one wood and one brick.
Cities cost three grain and two ore.
Settlements cost one brick, one wood, one grain and one sheep to build.
By paying one sheep, one grain, and one ore, a player can draw a card from the top of the development deck."
Here, we see that road costs one wood and one brick. Similarly, for cities, the input requirements are fixed. This reflects that the input requirements are fixed and specific. A road cannot with built by using wood only; it would require brick as well. Therefore, it is a fixed proportion production function.
There are constant returns to scale in this game, as the fixed proportion production function means that in order to build a city you need three grain and two ore and in order to build 3 cities, you need nine grain and six ore.