Locational Marginal Pricing when different prices and when the same?

Question

I am kinda confused about this YouTube video.

So the LMP with no constraints is the same in both nodes. For me it was the same because I used those offers from node 1 also in node 2 and we chose the highest offer because also those companies who wanted to sell it for 35$ will not say no if you buy it from them for 42 dollars and we do this because it is the easiest way to calculate the price so everyone is happy.

Now later in the video (from 1:48-2:37 min) the price is different in each node because of the transmission constraint. Why? I mean I still just used the third package with 38$ per MWh because it is cheaper for node 2, why would I still let node 1 pay for that?

Answer 1

okay meanwhile I got the answer to this:

the main idea behind LMP is to reduce the marginal cost of the WHOLE system.... therefore it is cheapier if you select those offers that way....

calculations:

38 * 600 + 48 * 600 = 51600

if we would do it as I thought makes more sense:

36 * 400 + 48 * 800 = 52800

as you can see even though the price seems to be more fair for node 1 now in total the costs increased from 51600 dollars to 52800 dollars