function [it_pounds, it_pct, nic_pounds, nic_pct, total_pounds, total_pct, takehome_pounds] = tax(gross, tax_rates, tax_widths, claw_start, claw_rate, nic_rates, nic_widths, plot_all)
%TAX: Compute the pounds and percentage cost of taxable pay of income tax
%and National Insurance. (Or just tax in places without NI).
%
%[it_pounds it_pct nic_pounds nic_pct total_pounds total_pct takehome_pounds] = tax(gross, tax_rates, tax_widths, nic_rates, nic_widths, plot_all)
%
%Inputs:
%   GROSS:      Vector of taxable pay amounts to compute all outputs for.
%   TAX_RATES:  Percentages of tax rates matching entries in tax_widths.
%   TAX_WIDTHS: Width in pounds of each tax band, ended by Inf. NOT the
%   income levels at which they begin to apply. For example, for 2007-08:
%
%   Personal allowance, or 0% band          = £5225.
%   10% band = First £2230 taxable          = £2230 in width.
%   22% band = £2230 - £34600 taxable       = £32370 in width.
%   40% band = £34600 - (unlimited) taxable = £Inf in width.
%
%   Therefore, tax_rates and tax_widths are set up as follows:
%
%   TAX_RATES  = [ 0    10    22   40];
%   TAX_WIDTHS = [5225 2230 32370 Inf];
%
%   CLAW_START: Value of GROSS at which the clawback of personal allowance
%   starts.
%   CLAW_RATE: A 2-vector, [PER STEP], where PER is the clawback for each
%   increment in GROSS of STEP. E.g. a clawback of £1 for every £2 of GROSS
%   is expressed as CLAW_RATE = [1 2].
%
%   NIC_RATES:  As TAX_RATES. (Omit if no NIC-equivalent needed).
%   NIC_WIDTHS: As TAX_WIDTHS. (Omit if no NIC-equivalent needed).
%   PLOT_ALL :  Single boolean true/false whether to draw the output plot.
%
%Outputs:
%   These all have obvious names, and each produce a vector with entries
%   corresponding to the entries of input GROSS.

for g = 1:length(gross)
    it_pounds(g)       = tax_calc(gross(g), tax_rates, tax_widths, claw_start, claw_rate);
    it_pct(g)          = 100*it_pounds(g)/gross(g);

    nic_pounds(g)      = tax_calc(gross(g), nic_rates, nic_widths);
    nic_pct(g)         = 100*nic_pounds(g)/gross(g);

    total_pounds(g)    = it_pounds(g) + nic_pounds(g);
    total_pct(g)       = 100*total_pounds(g)/gross(g);
    
    takehome_pounds(g) = gross(g) - total_pounds(g);
end

if exist('plot_all', 'var') && plot_all

    %Plots for amounts in pounds
    figure;
    plot(gross, it_pounds, 'b', gross, nic_pounds, 'r', gross, total_pounds, 'm', gross, takehome_pounds, 'g');
    set(get(gca, 'Children'), 'LineWidth',2);
    set(gca, 'XMinorTick', 'off', 'YMinorTick', 'on');
    legend('Income tax', 'National insurance', 'Combined', 'Take home');
    xlabel('Annual taxable pay, GBP');
    ylabel('Annual amount, GBP');
    grid on;
    
    %Plots for percentages
    figure;
    plot(gross, it_pct, 'b', gross, nic_pct, 'r', gross, total_pct, 'm');
    set(get(gca, 'Children'), 'LineWidth',2);
    set(gca, 'XMinorTick', 'off', 'YMinorTick', 'on');
    legend('Income tax', 'National insurance', 'Combined');
    xlabel('Annual taxable pay, GBP');
    ylabel('Percentage of taxable pay');
    grid on;
end

%%%%Calculation engine%%%%
function total_tax = tax_calc(gross, rates, widths, claw_start, claw_rate)

tax_band    = 1;
income_left = gross;
total_tax   = 0;

%Clawback if necessary
if exist('claw_start', 'var') && exist('claw_rate', 'var')
    widths(1) = clawback(gross, claw_start, claw_rate, widths(1));
end

while tax_band <= length(widths) && income_left > 0
    taxable_this_band = min([widths(tax_band) income_left]);
    total_tax         = total_tax + taxable_this_band*rates(tax_band)/100;
    income_left       = income_left - taxable_this_band;
    tax_band          = tax_band + 1;
end

function new_limit = clawback(gross, claw_start, claw_rate, initial_limit)
%GROSS:      Vector of taxable pay amounts to compute all outputs for.
%CLAW_START: Values of GROSS at which the clawback starts
%CLAW_RATE: A 2-vector, [PER STEP], where PER is the clawback for each
%increment in GROSS of STEP. E.g. a clawback of £1 for every £2 of GROSS
%is expressed as CLAW_RATE = [1 2].
%INITIAL_LIMIT: The un-clawedback value to begin with.
%
%NEW_LIMIT is the clawed-back value of INITIAL_LIMIT.

claw_length = max(gross - claw_start, 0);
claw        = claw_rate(1) * floor(claw_length/claw_rate(2));
new_limit   = max(initial_limit - claw, 0);
</source>

;For the 2010-11 tax year:
<source lang="matlab">
tax_rates  = [0 20 40 50];
tax_widths = [6475 37400 112600 Inf];
claw_start = 100000;
claw_rate  = [1 2];
nic_rates  = [0 11 1];
nic_widths = [110*52 (844-110)*52 Inf];