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Table 5.1: Bitcoin Transaction Characteristics (Source: Per day blockchain.info) Per block 848.1232877 1769.744292 0.15596529 No of transactions Estimated transaction volume (BTC) Transaction fees (BTC) 5 A Numerical Analysis of Bitcoin 122129.7534 254843.1781 22.45900183 Based on our theoretical analysis, we are now seeking to understand rencies for payments. To do so, we perform several quantitative exercises that calculate the welfare losses relative to other means of payments. We first use Bitcoin trading data to calibrate some parameters for our model. Using this calibration, we compare the currenct Bitcoin scheme and a fictitious cryptocurrency scheme that operates with an optimal reward structure with an economy that uses traditional cash instead. Then, we conduct a similar exercise by using data from US debit cards and Fedwire to see how well an optimal cryptocurrency can support such transactions. 5.1 Parameterization We assume that buyers’ utility function is u(x) = log(x+b)−logb with b ≈ 0. The length of a period is a day and the length of each trading session is 10 minutes (i.e., average block time). Setting β = 0.9999 gives an annual discount factor of 0.97. The average Bitcoin supply in 2015 was 14342502.95. Consequently, the money growth rate per day in 2015 was μ = (1 + 25/14342502.95)6×24 = 1.00025. This translates into an annual inflation rate of 9.6%. We use aggregate Bitcoin transactions to calibrate the rest of our parameters (see Table 5.1). We set σ = 0.0178 to match the average fraction of Bitcoins spent per day, and set τ = 0.15596529 /1769.744292 = 0.000088129 to match the transaction fees data. The average transaction size is τ = 1769.744292/848.1232877 = 2.086659237. Finally, we use B = 6873428.441 which is the maximum number of average-sized transactions that the existing stock of Bitcoins can support.26 26This is close to the number of blockchain wallet users which is 5439181 in 2015 (Source: blockchain.info, year-end number). the limits of using cryptocur- 28PDF Image | The Economics of Cryptocurrencies Bitcoin and Beyond
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