How Economics Can help with Trading Pieces

Ah yes, economics, depending on how well you listened to 9th grade, it is very familiar, or very vague. The examples shown are here to help with piece activity, and trading with the power of economics.

Example 1: White has just moved his rook to e1 to completely trap the knight on e5. What should Black do?

Rxe8 is mandatory or else back rank mate is coming up, and Black solidly wins this endgame with 3 more pieces than White.

This is why the trade matters, though we still had one rook up from White, they lost 100% of their rooks while we just lost only 50% of our rooks. Don't lose or "sell" something that you have very little of, for something equal or worse in return!

Example #2

Should White trade or retreat?

Here, White retreating is a good idea, as trading would result in a lot of activity for Black's dark squared bishop; and trading bishops for Black was very bad, as it resulted in White's king's rook in an open file, allowing rapid development of White's pieces. Just like in economics, always look at the bigger picture, will the trade result in a larger advantage positionally?

So that you now know how to trade, the TL;DR here is don't trade if you're behind material, but if the material is equal, trade only for a positional advantage, and you're behind, don't trade at all!