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A.6 Proof of Proposition 8 Proposition A.5. The optimal reward structure sets transaction fees to zero and only relies on seignorage; i.e., τ = 0 and μ > 1. The idea of the proof is as follows. If fees are not zero, one can design a new policy that (i) relies on less costs for mining and (ii) makes all buyers better off. The policy change will combine three changes. First, it reduces transaction fees to zero. Second, it will increase the seignorage rate to compensate for the loss in the expected tax rates from fees. Third, it will generate a revenue for miners given these changes that does not change the choice set for any individual bilateral transaction. We then proceed as follows. First, we show that the policy change is feasible and that it improves the planner’s objective provided that the transaction size and confirmation lags weakly increase in all bilateral meetings. Then, we show that buyers have an incentive to only change their optimal offer in that way. The proof relies on the fact that the planner can generate more revenue than the amount of rewards paid out to miners. This implies that the planner can have extra revenue available in the centralized market after the policy change. We then show further that, if the extra revenue is positive, the planner can make everyone (weakly) better off by reducing seignorage to lower revenue. This implies that it is optimal to collect seignorage just enough to finance mining costs. A.6.1 Preliminaries The social planner’s problem is given by maxB σ[δN(ε)εu(x(ε))−x(ε)]dFε(ε)−βR(N ̄+1) (A.19) (A.20) (A.21) μ,τ,R μ subject to (d(ε),x(ε),N(ε)) is an optimal offer for any (μ,τ,R) B(μ−1+στ) x(ε)dFε(ε)≥βR(N ̄+1) 1−τ μ Note that we have assumed that the sufficient condition for No-DS offers is satisfied. Hence, all 49PDF Image | The Economics of Cryptocurrencies Bitcoin and Beyond
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