Economics

% Saving: 200 a month at 5 % a year, compounded monthly, for 30 years
r = 0.05/12; n = 0:360;
saved = 200 * ((1 + r).^n - 1) / r;
paidIn = 200 * n;

% Borrowing: 300 000 over 30 years at 4 % — the annuity formula gives a fixed monthly payment
P = 300000; i = 0.04/12; N = 360;
pay = P * i / (1 - (1 + i)^-N);
balance = P * (1 + i).^n - pay * ((1 + i).^n - 1) / i;
interest = i * balance(1:end-1);              % interest part of each payment

subplot(2, 1, 1)
area(n/12, saved), hold on, plot(n/12, paidIn, 'k--', 'LineWidth', 1.5), hold off
title(sprintf('Saving 200/month at 5%%: %.0f after 30 years (%.0f paid in)', saved(end), paidIn(end)))
xlabel('years'), legend('balance', 'paid in')
subplot(2, 1, 2)
area(n(2:end)/12, [interest; pay - interest]')
title(sprintf('Mortgage: %.2f per month, %.0f interest in total', pay, sum(interest)))
xlabel('years'), legend('interest', 'repayment')

% Linear demand and supply (an illustrative textbook market)
q = linspace(0, 100, 200);
demand = 120 - 1.0*q;                 % what buyers will pay for quantity q
supply = 20 + 0.6*q;                  % what sellers need for quantity q
tax = 16;                             % per unit, paid by sellers

q0 = fzero(@(x) (120 - x) - (20 + 0.6*x), 50);          % equilibrium without tax
qt = fzero(@(x) (120 - x) - (20 + tax + 0.6*x), 50);    % with tax
pb = 120 - qt; ps = pb - tax;                          % price buyers pay / sellers keep

plot(q, demand, q, supply, q, supply + tax, '--', 'LineWidth', 1.8), hold on
fill([0 qt qt 0], [ps ps pb pb], 'g', 'FaceAlpha', 0.25)                  % tax revenue
fill([qt q0 qt], [pb 120 - q0 ps], 'r', 'FaceAlpha', 0.35)                % deadweight loss
plot(q0, 120 - q0, 'ko', 'MarkerSize', 7), hold off
legend('demand', 'supply', 'supply + tax', 'tax revenue', 'deadweight loss')
xlabel('quantity'), ylabel('price'), ylim([0 130])
title(sprintf('Tax %d: quantity %.1f → %.1f, revenue %.0f, loss %.0f', tax, q0, qt, tax*qt, tax*(q0 - qt)/2))

% Capital per worker k grows by saving and shrinks by depreciation and population growth:
%   dk/dt = s k^α − (δ + n) k        output per worker y = k^α
alpha = 0.33; delta = 0.05; n = 0.01;
rates = [0.15 0.25 0.35];
for s = rates
  [t, k] = ode45(@(t, k) s*k.^alpha - (delta + n)*k, [0 150], 1);
  plot(t, k.^alpha, 'LineWidth', 2), hold on
  kstar = (s / (delta + n))^(1/(1 - alpha));
  yline(kstar^alpha, ':')
end
hold off
legend('s = 15 %', '', 's = 25 %', '', 's = 35 %', '')
xlabel('years'), ylabel('output per worker')
title('Higher saving → higher steady state, not faster long-run growth')

% Simulated incomes (not real data): log-normal distributions with different spreads
rng(2)
spreads = [0.4 0.7 1.0];
for sg = spreads
  income = sort(exp(10 + sg*randn(1, 5000)));
  L = [0, cumsum(income) / sum(income)];
  p = linspace(0, 1, numel(L));
  G = 1 - 2*trapz(p, L);                     % Gini = area between equality line and curve × 2
  plot(p, L, 'LineWidth', 2, 'DisplayName', sprintf('σ = %.1f, Gini = %.2f', sg, G)), hold on
end
plot([0 1], [0 1], 'k--', 'DisplayName', 'perfect equality'), hold off
legend show, axis square
xlabel('share of people (poorest first)'), ylabel('share of total income')
title('Lorenz curves of simulated incomes')

% Live data from the World Bank API (needs an internet connection)
d = webread('https://api.worldbank.org/v2/country/NLD;USA;JPN/indicator/FP.CPI.TOTL.ZG?format=json&per_page=300&date=1970:2024');
rows = d{2};                                   % d{1} describes the request, d{2} holds the records
names = {'Netherlands', 'United States', 'Japan'};
for c = 1:numel(names)
  yr = []; val = [];
  for k = 1:numel(rows)
    r = rows{k};
    if strcmp(r.country.value, names{c}) && ~isempty(r.value)
      yr(end+1) = str2double(r.date); val(end+1) = r.value;
    end
  end
  [yr, idx] = sort(yr);
  plot(yr, val(idx), 'LineWidth', 1.8), hold on
end
yline(2, ':', '2 % target'), hold off
legend(names{:}), xlabel('year'), ylabel('consumer prices, % per year')
title('Inflation (World Bank, FP.CPI.TOTL.ZG)')