Topic: MC2: A cryptocurrency based on a hybrid PoW/PoS system - page 38. (Read 195188 times)

% Script file for Matlab or Octave, tested with Matlab 2007b and GNU Octave 3.0.0.
%
% This script illustrates the Total Money Supply and the corresponding yearly rates of Money Supply increase
% (="inflation") of a (crypto-)currency, depending on the scheme how coins are brought into existence.
%
% Schemes considered include:
% - constant inflation rate (=exponential money supply growth)
% - linear growth of money supply (i.e. constant rate at which new coins are being generated)
% - logarithmic growth of money supply
% - Bitcoin-like coin generation with regular block reward halving
% - no growth, constant money supply

N = 248; % number of years, must be multiple of 4

timelimit=30; % how much to zoom-in after pressing , to show years 0 till "this year"


money_supply_after_1_year = 50*52500; % 52500*50 corresponds to nb of bitcoins after 1 year


%% I. Calculate the Money Supply:
%
% About the index: Index "2", i.e. money_supply_xxxx(2), denotes the amount of existing coins after the end
% of the 1st year or start of year 2.

time = [0:1:N];


%% I - (0) Constant 
money_supply_const = money_supply_after_1_year*ones(1,N+1);

%% I - (1) Linear Growth 
money_supply_linear = money_supply_after_1_year*time;

%% I - (1b) Logarithmic Growth:
% The amount of coins being mined is decreased like this:
% In the first year, coins are mined at a constant rate, and add up to Nc coins at the end of year one.
% The number of coins that are newly created in year n (n>=2) is equal to b/n * Nc,
% where b is a positive coefficient, typically between 0 and 2, but can also be greater than 2.
a = 1.0; % Nc = a*money_supply_after_1_year*ones, i.e. money supply after 1st year can be tuned by this parameter.
b = 1.8; % 0<=b<=2, or b >2 also possible
c = 1.0; % Exponent for "nb of years" variable. Greater values mean slower growth. If =0, logarithmic growth becomes linear.
money_supply_log = a*money_supply_after_1_year*ones(1,N+1);% this is the nb of coins after 1st year, i.e. money_supply_log(2)
money_supply_log(1) = 0;
for k = 3:N+1,
    n = k-1; % calculate for year "n" now:
    money_supply_log(k) = (a*money_supply_after_1_year) * b/(n)^c + money_supply_log(k-1);
end

%% I - (2) Exponential Growth (1% Inflation Per Year)
money_supply_exp1 = money_supply_after_1_year*ones(1,N+1);
money_supply_exp1(1) = money_supply_exp1(2)/1.01;
for k = 3:N+1,
    money_supply_exp1(k) = 1.01*money_supply_exp1(k-1);
end

%% I - (2b) Exponential Growth (5% Inflation Per Year)
money_supply_exp5 = money_supply_after_1_year*ones(1,N+1);
money_supply_exp5(1) = money_supply_exp5(2)/1.05;
for k = 3:N+1,
    money_supply_exp5(k) = 1.05*money_supply_exp5(k-1);
end

%% I - (3) Bitcoin-like Growth
money_supply_BTC = NaN*ones(1,N+1);
money_supply_BTC(1) = 0;
money_supply_BTC(2) = 1*money_supply_after_1_year;
money_supply_BTC(3) = 2*money_supply_after_1_year;
money_supply_BTC(4) = 3*money_supply_after_1_year;
money_supply_BTC(5) = 4*money_supply_after_1_year;
increase = 1/2*money_supply_after_1_year; % block reward halving every 4th year
for k = 6:4:N+1,
    for kk = k:k+3,
        money_supply_BTC(kk) = money_supply_BTC(kk-1) + increase;
    end
    increase = increase/2;% block reward halving every 4th year
end
money_supply_max = max(money_supply_const, money_supply_linear);
money_supply_max = max(money_supply_log,  money_supply_max);
money_supply_max = max(money_supply_exp1, money_supply_max);
money_supply_max = max(money_supply_exp5, money_supply_max);
money_supply_max = max(money_supply_BTC,  money_supply_max);

%% II. Calculate the Inflation Rate:
inflation_rate_const  = inf*ones(1,N);
inflation_rate_linear = inf*ones(1,N);
inflation_rate_log    = inf*ones(1,N);
inflation_rate_exp1   = inf*ones(1,N);
inflation_rate_exp5   = inf*ones(1,N);
inflation_rate_BTC    = inf*ones(1,N);
for k = 2:N-1,
    inflation_rate_const(k)  = money_supply_const(k+1)  / money_supply_const(k)  - 1;
    inflation_rate_linear(k) = money_supply_linear(k+1) / money_supply_linear(k) - 1;
    inflation_rate_log(k)    = money_supply_log(k+1)    / money_supply_log(k)    - 1;
    inflation_rate_exp1(k)   = money_supply_exp1(k+1)   / money_supply_exp1(k)   - 1;
    inflation_rate_exp5(k)   = money_supply_exp5(k+1)   / money_supply_exp5(k)   - 1;
    inflation_rate_BTC(k)    = money_supply_BTC(k+1)    / money_supply_BTC(k)    - 1;
end

% Special correction for exponential inflation rates:
inflation_rate_const(1) = inflation_rate_const(2);
inflation_rate_exp1(1)  = inflation_rate_exp1(2);
inflation_rate_exp5(1)  = inflation_rate_exp5(2);

%% III. Plot Results:
figure
subplot(2,2,1);
plot(time, money_supply_exp5,'r-.','linewidth',2); hold on;
plot(time, money_supply_exp1,'r-','linewidth',2); hold on;
plot(time, money_supply_linear,'b-','linewidth',2);
plot(time, money_supply_log,'c--','linewidth',2);
plot(time, money_supply_BTC,'m-','linewidth',2);
plot(time, money_supply_const,'g-','linewidth',2);
grid on;
title('Total Money Supply');
xlabel('Time in Years')
ylabel('Total Money Supply (Coins in Existence)')
legend('Inflation 5% p.a.','Inflation 1% p.a.','Constant Linear Increase',['Logarithmic Increase, a=',num2str(a),', b=',num2str(b)],'BTC-like Increase','No Money Increase','location','northwest');

subplot(2,2,2);
semilogy(time, money_supply_exp5,'r-.','linewidth',2); hold on;
semilogy(time, money_supply_exp1,'r-','linewidth',2); hold on;
semilogy(time, money_supply_linear,'b-','linewidth',2);
%semilogy(time, money_supply_log,'c--','linewidth',2);
semilogy([0.25, 0.5, time(2:end)], [[0.25, 0.5]*money_supply_log(2),money_supply_log(2:end)],'c--','linewidth',2);
% semilogy(time, money_supply_BTC,'m-','linewidth',2);
semilogy([0.25, 0.5, time(2:end)], [[0.25, 0.5]*money_supply_BTC(2),money_supply_BTC(2:end)],'m-','linewidth',2);
semilogy(time, money_supply_const,'g-','linewidth',2);
grid on;
title('Total Money Supply (Logarithmic Scale)');
xlabel('Time in Years')
ylabel('Total Money Supply (Coins in Existence)')

subplot(2,2,3);
plot(time(1:end), 100*[inflation_rate_exp5(1),inflation_rate_exp5],'r-.','linewidth',2); hold on;
plot(time(1:end), 100*[inflation_rate_exp1(1),inflation_rate_exp1],'r-','linewidth',2); hold on;
plot(time(2:end), 100*inflation_rate_linear,'b-','linewidth',2);
plot(time(2:end), 100*inflation_rate_log,'c--','linewidth',2);
plot(time(2:end), 100*inflation_rate_BTC,'m-','linewidth',2);
plot(time(1:end), 100*[inflation_rate_const(1),inflation_rate_const],'g-','linewidth',2);
grid on;
title('Yearly "Inflation" Rate of Total Money Supply');
xlabel('Time in Years')
ylabel('Yearly Increase of Money Supply in Percent')
legend('Inflation 5% p.a.','Inflation 1% p.a.','Constant Linear Increase',['Logarithmic Increase, a=',num2str(a),', b=',num2str(b)],'BTC-like Increase','No Money Increase','location','northeast');

subplot(2,2,4);
semilogy(time(1:end), 100*[inflation_rate_exp5(1),inflation_rate_exp5],'r-.','linewidth',2); hold on;
semilogy(time(1:end), 100*[inflation_rate_exp1(1),inflation_rate_exp1],'r-','linewidth',2); hold on;
semilogy(time(2:end), 100*inflation_rate_linear,'b-','linewidth',2);
semilogy(time(2:end), 100*inflation_rate_log,'c--','linewidth',2);
semilogy(time(2:end), 100*inflation_rate_BTC,'m-','linewidth',2);
semilogy(time(1:end), 100*[inflation_rate_const(1),inflation_rate_const],'g-','linewidth',2);
grid on;
title('Yearly "Inflation" Rate of Total Money Supply (Logarithmic Scale)');
xlabel('Time in Years')
ylabel('Yearly Increase of Money Supply in Percent')
legend('Inflation 5% p.a.','Inflation 1% p.a.','Constant Linear Increase',['Logarithmic Increase, a=',num2str(a),', b=',num2str(b)],'BTC-like Increase','No Money Increase','location','southeast');
a=axis;
axis([a(1), a(2), 1e-3, 1e2]);


disp('--> Press  to zoom in...')
pause
for k=1:4,
    subplot(2,2,k);
    a=axis;
    if k < 3,
        a4=money_supply_max(timelimit);
    elseif k == 3,
        a4=30;
    else
        a4=a(4);
    end
    axis([a(1), timelimit, a(3), a4]);
end