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necessitates a means of payment which we assume is the cryptocurrency. The updating of this blockchain follows a PoW protocol where miners compete for the right to add a new block of balance transfers as reported by buyers into the chain for each subperiod. The mining game is identical to the one presented in Section 3. However, the reward R is not exogenous anymore, but depends on the design of the cryptocurrency (see Property (iii) in Section 2). First, the cryptocurrency can create new balances which are paid to miners that win the competition to update the blockchain. We denote the (gross) growth rate of new balances by μ ≥ 1. In addition, a fraction τ ≥ 0 of balances are paid to the successful miner as a transaction fee for including the transaction in a block. We assume that the N ̄ + 1 block winners of the night market equally share the total reward. Consequently, the block reward is given by R = Z(μ−1)+Dτ. (23) N ̄ + 1 where Z is the aggregate money balances and D is the aggregate spending in the night market. Since rewards are paid in the next period, they are discounted by β/μ taking into account inflation. 4.3 Day Market In the day market, nominal balances can be exchanged against the general good at price φ. We use z = φm to denote the real balances associated with m units of balances. All buyers, sellers and miners can produce and consume the general goods with a linear utility function. Miners can also convert general goods 1 − 1 into computing power q at any time. Since they cannot transact in the night market, miners will not hold balances across periods due to discounting. Upon receiving balances as rewards, they will simply trade them for the general good in the day market. Hence, the problem of miners is identical to the one in Section 3 simply adjusted for the discount factor β/μ ≤ β < 1. To ease exposition, we abuse notation and set ε = 0 for the seller. We use w(z) and v(z,ε) to denote respectively the day market and the night market value functions. The problem of a buyer anonymous (e.g. the KYC requirement, online wallets transactions, payments to Bitcoin exchanges, payments made by well-known merchants). Hence, double spenders can be punished either formally (e.g. legal) or informally (e.g. reputational). 22PDF Image | The Economics of Cryptocurrencies Bitcoin and Beyond
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