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offers satisfy the no-DS constraint μ x(ε) ≤R(N(ε)+1)N(ε). β1−τ Note also that the revenue constraint (A.21) is a weak inequality. This implies that the planner is allowed to achieve a (non-negative) surplus by choosing any particular policy. It is understood that this surplus could be distributed in the centralized market to anyone – miner, sellers or buyers – as a lump-sum transfer without affecting the total surplus as there is no wealth effect due to agents’ quasi-linear preferences. Importantly, the planner makes thus a distinction between the revenue raised and the rewards paid to miners. Hence, we define a policy to be (μ,τ,R). A.6.2 A welfare-improving policy change Suppose that τ0 > 0, μ0 ≥ 1 and R0 is a feasible policy. Consider the following policy change τ1 = τ0 − ξ μ1 = μ0 + σξ R = R 1 − τ0 μ1 1 0 1 − τ1 μ0 (A.22) (A.23) (A.24) Note that the rewards R1 that flow to miners are also adjusted in the policy change. Also note that τ0 ≥ ξ > 0 is arbitrary and, thus, we can set it to τ0.32 We denote the optimal choice for each policy by x∗i (ε) and show first that this policy change is feasible if the transaction size increases in all bilateral meetings. Lemma A.6. The policy change is feasible if x∗1(ε) ≥ x∗0(ε). Proof. The No-DS for the old policy is given by μ1 x(ε) ≤ R1(N(ε) + 1)N(ε) (A.25) β 1−τ1 Using the definition of R1, it is immediate that – by construction – the constraints are identical for all given n ∈ {1,...,N ̄ − 1}, no matter what the value of ε ∈ (0,τ0] is. Hence, the set of feasible choices for bilateral meetings remains unchanged. 32COMMENT: It will become clear later that raising seignorage is not an issue. See Laffer curve. 50PDF Image | The Economics of Cryptocurrencies Bitcoin and Beyond
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