Say you make plastic cups. The plastic for one cup costs $1. The machine to make the plastic cups costs $50 and the mould for the cups is another $50.
If you were to make 1 cup, that cup would’ve cost you $101 to make, because your total cost is $101 and it got you 1 cup.
Now say you make 100 cups. You would pay $100 in plastic, but the $100 for the mould and machine stays the same regardless of how many cups you make.
Now your cost per cup made is $2, because while you still pay $1 per cup, you are able to spread the $100 cost of the machine across the 100 cups.
This is economies of scale at a basic level.
Now say that you can buy another mould for your plastic cup maker so that you can also make plastic trays and this add-on is also $50.
You have now spent $150 to be able to make plastic cups and plastic trays.
If you now were to make 1 cup and 1 tray, you will have spent $2 in plastic and $150 for the machine. Your cost per unit is $76.
One of your competitors however only makes cups and another only makes trays. Because they both need to have their own $50 machines and $50, making the same number of cups and trays would be more expensive for them. It would cost them $202 to make the same number of cups and trays. The cost per unit in that case is $101.
This is economies of scope at a basic level.
This can get a lot more complicated. For example you might be able to negotiate a better plastic price as you are buying twice as much as your competitors. Your machine will also be used twice as much, so it will have to be serviced twice as often which might impact your ability to keep up production. Similarly the downtime from swapping out moulds might impact your production rate. The cool thing is that you can exactly calculate if having two machines for example would be more cost effective than having a single machine with two moulds, etc.
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