We use microeconomic theory to describe the inner workings of Constant Function Market Makers (CFMMs). We show that standard results from consumer theory apply in this new context, endowing us with powerful tools to characterize the optimal design of CFMMs. We employ them to analyze the externalities that traders and liquidity providers exert on each other when interacting through a CFMM. Liquidity providers reduce the execution costs by flattening the bonding curve on which trades are executed. Arbitrageurs impose an adverse selection cost on liquidity providers by unfavorably rebalancing their portfolio. We show that the strengths of these two externalities are pinned down by the curvature of the bonding curve and are inversely related to each other, thereby identifying the fundamental economic tradeoff that market designers have to address.

We propose a model that uses the exchange rate of Bitcoin against the US dollar to predict the computing power of Bitcoin?s network. We show that free entry places an upper bound on mining revenues and explain how it can be identified. Calibrating the model?s parameters allows us to accurately forecast the evolution of the network computing power over time. We find that a significant share of mining rewards was invested in mining equipment and that the seigniorage income of miners was limited.