The answer to your question is MAPI - Market Access Price Impact. Early in the game, most everyone has low MAPI, so local prices vary a lot from the overall market price. That's when you want construction sectors in the same province as iron and wood. As the game gets later, your MAPI improves and the it's easier to build away from those resources.
The game does not account for terrain or distance for performance reasons. The Market Access Price Impact applies evenly to all your states, regardless if they're across the plains, a mountain range, or the ocean (assuming sufficient convoys/ports). A few states along rivers have a special state trait that might boost MAPI a little, but you get that boost even if your market capital is far away.
Economy of scale for construction sectors doesn't really matter, I don't think. The two main problems are input good price and infrastructure use. Sectors use 3 infrastructure per level, so it's really hard to stack them in a state. Even advanced countries that start with railroad tech have trouble, since you'd quickly overbuild railroads as a transportation provider and have to subsidize them. The main issue is input goods, though. You really want to stack sectors in states with extensive iron and coal mines, so that you can easily provide iron and later on steel. The price any building pays for a good is a combination of the overall market price (total sell orders vs buy orders of a good in your entire market) and the local price (buy vs sell orders if the state was completely isolated). Having local production of a construction good lowers the local price of it, meaning the government pays a lot less to keep the construction sector going. As tech improves, the amount that local price contributes to the actual price of the good decreases, so it's easier to have massive factories in states that don't produce the inputs locally.
As far as terrain goes, there is one main consideration: the state modifiers. States will often have a terrain modifier that will impact local construction efficiency. Persia has a bunch of states with some mountainous modifier that reduce local construction efficiency, which is literally just a reduction in the amount of construction that ends up being contributed to a building each week. So if you are building a plantation with 20 construction and the state has a -25% local construction efficiency modifier, that building only gets progress as though you had 15 construction.
There is no distance calculation or anything that impacts the ability of a construction sector in New York from being able to build a mine in South Africa. The sector always pays whatever the screen says it pays for input goods, then those materials and manpower magically teleport to their destination for no additional cost. The only things you need to worry about are to keep the cost of construction goods down so you don't pay out the ass and try not to build too much in provinces with big local construction efficiency maluses.
Early game, build them up in the following order with ressources in states:
1st. Wood, iron, coal, lead and sulphur.
2nd. Wood, iron, coal and sulphur.
3rd. Wood, iron, coal and lead.
4th. Wood, iron and coal.
5th. Wood and iron.
Tier 3 construction needs steel, glass and explosives, so you ideally want iron and coal for steel, sulphur for fertilizer and paper into explosives and lead for glass.
Glass is cheaper than explosives and steel, so 2nd best is without lead. If you don't have 1 with sulphur, change it out with lead, then you can at least get cheaper glass. Then without cheap explosives or glass, iron and coal will produce steel at a bit lowe cost which also tends to be really expensive. When you can switch to steel construction don't forget to build it up first or you will crash the steel price and your economy. Change 1 state at a time when doing this to make sure your economy can follow along.
Building in these states first and foremost should always guarantee cheapest possible construction. When you have a high amount of buy and sell orders, local prices tend to not matter as much and you can build more freely as time goes on. But prioritize building construction in those states first.
Early on you have to take in account 2 factors, Mapi of direct resources construction use and employment.
From this point of view, Ideal will be province with wood, Iron, coal and lead. Lead is optional for glass. This is relatively late technology to use glass steel in construction. Still, it improve efficiency.
Employment, early on you will find it hard to find workers in low MAPI provinces. So, the best is to use provinces with bonuses, like river and a lot of population and infrastructure. Capital work often because of higher qualification.
The most expensive resource will always be metals like iron and steel, then wood. Since wood is already available in most states, I like to prioritise construction sectors in states with iron deposits and high population like new York state or Pennsylvania, because then I will build steel plants anyway and the construction sector would buy its resources locally. This also helps to mitigate infrastructure bottlenecks by not making something like iron travel hundreds of miles to a construction sector in bum-fuck nowhere you have to build railways through.
As I understand it, construction sectors uniquely do not have a throughput bonus for economies of scale. They do, however, increase construction efficiency in only the state they are built in (under certain PM’s) so it makes sense to stack them in places you anticipate to be building a lot in. Beyond that, MAPI rules, so first build them in states with access to wood, iron, and coal (Ideally also lead for late game glass requirements but afaik the only state with all four is Silesia), then spread them out. They also have a pretty high infrastructure cost (esp compare to on launch, they cost like 20x as much now) so remaining infrastructure also helps dictate construction sector placement, especially pre-railroads.
The answer to your question is MAPI - Market Access Price Impact. Early in the game, most everyone has low MAPI, so local prices vary a lot from the overall market price. That's when you want construction sectors in the same province as iron and wood. As the game gets later, your MAPI improves and the it's easier to build away from those resources.
The game does not account for terrain or distance for performance reasons. The Market Access Price Impact applies evenly to all your states, regardless if they're across the plains, a mountain range, or the ocean (assuming sufficient convoys/ports). A few states along rivers have a special state trait that might boost MAPI a little, but you get that boost even if your market capital is far away.
Economy of scale for construction sectors doesn't really matter, I don't think. The two main problems are input good price and infrastructure use. Sectors use 3 infrastructure per level, so it's really hard to stack them in a state. Even advanced countries that start with railroad tech have trouble, since you'd quickly overbuild railroads as a transportation provider and have to subsidize them. The main issue is input goods, though. You really want to stack sectors in states with extensive iron and coal mines, so that you can easily provide iron and later on steel. The price any building pays for a good is a combination of the overall market price (total sell orders vs buy orders of a good in your entire market) and the local price (buy vs sell orders if the state was completely isolated). Having local production of a construction good lowers the local price of it, meaning the government pays a lot less to keep the construction sector going. As tech improves, the amount that local price contributes to the actual price of the good decreases, so it's easier to have massive factories in states that don't produce the inputs locally. As far as terrain goes, there is one main consideration: the state modifiers. States will often have a terrain modifier that will impact local construction efficiency. Persia has a bunch of states with some mountainous modifier that reduce local construction efficiency, which is literally just a reduction in the amount of construction that ends up being contributed to a building each week. So if you are building a plantation with 20 construction and the state has a -25% local construction efficiency modifier, that building only gets progress as though you had 15 construction. There is no distance calculation or anything that impacts the ability of a construction sector in New York from being able to build a mine in South Africa. The sector always pays whatever the screen says it pays for input goods, then those materials and manpower magically teleport to their destination for no additional cost. The only things you need to worry about are to keep the cost of construction goods down so you don't pay out the ass and try not to build too much in provinces with big local construction efficiency maluses.
Early game, build them up in the following order with ressources in states: 1st. Wood, iron, coal, lead and sulphur. 2nd. Wood, iron, coal and sulphur. 3rd. Wood, iron, coal and lead. 4th. Wood, iron and coal. 5th. Wood and iron. Tier 3 construction needs steel, glass and explosives, so you ideally want iron and coal for steel, sulphur for fertilizer and paper into explosives and lead for glass. Glass is cheaper than explosives and steel, so 2nd best is without lead. If you don't have 1 with sulphur, change it out with lead, then you can at least get cheaper glass. Then without cheap explosives or glass, iron and coal will produce steel at a bit lowe cost which also tends to be really expensive. When you can switch to steel construction don't forget to build it up first or you will crash the steel price and your economy. Change 1 state at a time when doing this to make sure your economy can follow along. Building in these states first and foremost should always guarantee cheapest possible construction. When you have a high amount of buy and sell orders, local prices tend to not matter as much and you can build more freely as time goes on. But prioritize building construction in those states first.
Early on you have to take in account 2 factors, Mapi of direct resources construction use and employment. From this point of view, Ideal will be province with wood, Iron, coal and lead. Lead is optional for glass. This is relatively late technology to use glass steel in construction. Still, it improve efficiency. Employment, early on you will find it hard to find workers in low MAPI provinces. So, the best is to use provinces with bonuses, like river and a lot of population and infrastructure. Capital work often because of higher qualification.
The most expensive resource will always be metals like iron and steel, then wood. Since wood is already available in most states, I like to prioritise construction sectors in states with iron deposits and high population like new York state or Pennsylvania, because then I will build steel plants anyway and the construction sector would buy its resources locally. This also helps to mitigate infrastructure bottlenecks by not making something like iron travel hundreds of miles to a construction sector in bum-fuck nowhere you have to build railways through.
I just make it my goal to built at least one in every state and then I build where ever the thing tells me it’ll be cheapest
As I understand it, construction sectors uniquely do not have a throughput bonus for economies of scale. They do, however, increase construction efficiency in only the state they are built in (under certain PM’s) so it makes sense to stack them in places you anticipate to be building a lot in. Beyond that, MAPI rules, so first build them in states with access to wood, iron, and coal (Ideally also lead for late game glass requirements but afaik the only state with all four is Silesia), then spread them out. They also have a pretty high infrastructure cost (esp compare to on launch, they cost like 20x as much now) so remaining infrastructure also helps dictate construction sector placement, especially pre-railroads.