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Doesn't the transaction cost increase with the increase of Cardano price? Is there a way to keep the transaction cost constant while raising the price of the Cardano token?

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The answers are yes, and yes, respectively.

Cardano is unique in the L1 space in that it has been designed from the start to scale with the number of unique participating nodes, rather than with the hardware capabilities of the whole constituency. For this to work, a separation of the settlement and computation layers is necessary. Until very recently, most of the developmental efforts were geared towards the backbone of the system: the Cardano Settlement Layer (CSL). In the coming months and years, much more focus will be placed on developing the Cardano Compute Layer(s), or CCL. Since the CSL is the backbone upon which all of the compute layers will rely on, it is designed to be as rigid and stable as possible, almost like a constitution. And since ADA is it's native currency with similarly rigid/fixed qualities, TX fees on the CSL will likely continue to be denominated in ADA for the foreseeable future. The CCLs however, will be a lot more flexible in their capabilities and their governance, including in their ability to accept payments in assets other than ADA.

The purpose of transaction fees (aside from preventing malicious chain bloat) is to compensate node operators for processing data. Since there currently isn't much to "process" except for basic block production/validation on the CSL, operators have no choice but to all play the same game. However, this will not be the case forever, and there will be many games the operators can play on the CCLs (i.e. oracle pools, babel fees, DEX scooping, e.t.c.). As Cardano continues to mature, node operators (currently just SPO's) will become more specialized, and the network will become a lot more distributed as a result (here's a great video by Charles explaining this). In practice, this means that all validator nodes are in competition with each other; all offering the same kinds of services, though in slightly different ways. Likewise, they will be able to specify how much and in what asset they would like to be paid.

In summary, as Cardano evolves, more and more of its total throughput will rely on the market-derived effort of all its constituent nodes, such that each node will have a greater say on what services it offers, and how to be compensated for said services. Therefore, nodes on the CCL will be able to specify that they wish to be paid in, for example, a USD-pegged stablecoin (or any other crypto-asset).

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