The economics of Bitcoin transaction fees

We study the economics of Bitcoin transaction fees in a simple static partial equilibrium model with the specificity that the system security is directly linked to the total computational power of miners. We show that any situation with a fixed fee is equivalent to another situation with a limited block size. In both cases, we give the optimal value of the transaction fee or of the block size. We also show that making the block size a non binding constraint and, in the same time, letting the fee be fixed as the outcome of a decentralized competitive market cannot guarantee the very existence of Bitcoin in the long-term.