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maxB σ[δN(ε)εu(x(ε))−x(ε)]dFε(ε)−βR(N ̄+1) (38) μ,τ,R μ subject to (d(ε),x(ε),N(ε)) is an optimal offer for any (μ,τ,R) (39) B(μ−1+στ) x(ε)dFε(ε)≥βR(N ̄+1) (40) 1−τ μ This is akin to a Ramsey Problem in the optimal tax literature where the planner takes into account that individuals make optimal decisions taking the policy (μ,τ) as given. The first constraint requires that the allocations satisfy the first-order conditions from the buyer’s decision problem. The last constraint is the budget constraint for the planner to deliver rewards R to miners for the N ̄ + 1 blocks.25 Given that only DS-proof contracts are offered, we now show that the optimal cryptocurrency system takes a simple form, summarized by the following proposition. Proposition 8. The optimal reward structure is to set transaction fees to zero and only relies on seignorage; i.e., τ = 0 and μ > 1. Positive rewards are required to induce mining activities. Since both transaction fees and inflation distort buyers’ incentives to consume in the night market, the optimal designer needs to set (μ,τ) to minimize the total distortion as a result of mining and the loss of trade surplus. Given a level of reward R, lowering transaction fees for trades, but increasing inflation can generate more surplus from trades. The reason is that the inflation tax is shared by all buyers while transaction fees are paid only by the buyers that have a chance to trade. These buyers when facing the fee are precisely the ones who have a high valuation of balances. This implies that levying reward costs upfront in terms of inflation allows distortions to be smoothed out across all buyers upfront. 25Note the N ̄ could also be a system parameter in our model. We simply impose here that N ̄ is just sufficiently large to allow for the optimal DS proof contract given ε ̄. 27PDF Image | The Economics of Cryptocurrencies Bitcoin and Beyond
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