Various figures showing the UK tax bands including how the personal allowance removal affects marginal tax. Graphs with personal allowance removal added are classed as “with cliff edge”.
National Insurance is not included at the moment.
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# Take Home and Tax %
Various figures showing the UK tax bands including how the personal allowance removal affects marginal tax. Graphs with personal allowance removal added are classed as "with cliff edge".
National Insurance is not included at the moment.
```{python}
# Setup Calculations
import matplotlib.pyplot as plt
import numpy as np
def pound_format(x, pos):
return "£{:.0f}k".format(x/1000)
plt.rcParams['svg.fonttype'] = 'none'
thresholds = [0, 12570, 50271, 125140]
rates = [0, 0.2, 0.4, 0.45]
earnings = np.linspace(0,200000, 1000)
tax = np.zeros_like(earnings)
for t,r in zip(thresholds, rates):
tax[earnings>=t] = r
# Take Home Based On Tax
approximate_takehome_per_interval = np.diff(earnings[1:])[0]*(1-tax[1:])
approximate_takehome = np.cumsum(approximate_takehome_per_interval)
# Approximating Take Home After PA Removal
# Removal modelled as if it is an expansion of the sub £125140 band, which it in all effects will be.
threshold = np.full_like(earnings, 12570)
removal = (earnings-100000)/2
personal_allowance_removal = np.maximum(np.minimum(removal, threshold)*rates[2],np.zeros_like(earnings))
personal_allowance_diff = np.diff(personal_allowance_removal)
#
marginal_tax = tax[1:]+abs(personal_allowance_diff/np.diff(earnings[1:])[0])
with_pa_removal = approximate_takehome - personal_allowance_removal[1:]
```
```{python}
import matplotlib.pyplot as plt
ax1 = plt.axes()
ax1.plot(earnings, tax*100, label="No Cliff Edge")
ax1.set_xlabel("Earnings (£)")
ax1.xaxis.set_major_formatter(pound_format)
ax1.set_ylabel("Marginal Tax Rate");
plt.plot(earnings[1:], marginal_tax*100, linestyle='--', label='Cliff Edge')
plt.legend()
plt.grid()
ax1.set_xlim((0,200000))
```
```{python}
ax1 = plt.axes()
ax1.plot(earnings[1:], approximate_takehome, label="No Cliff Edge")
ax1.plot(earnings[1:], with_pa_removal, label="Cliff Edge")
ax1.set_ylabel("Take Home (£)")
ax1.xaxis.set_major_formatter(pound_format)
ax1.yaxis.set_major_formatter(pound_format)
ax1.set_xlim((0,200000))
ax1.set_xlabel("Earnings (£)")
ax1.legend()
ax1.grid()
```
```{python}
#| label: fig-takehome
#| fig-cap: Take home %, and inversely tax % of income given a salary.
ax1 = plt.axes()
ax1.plot(earnings[1:], with_pa_removal/earnings[1:]*100, label="Take Home")
ax1.set_ylabel("Take Home %", color='tab:blue')
ax1.tick_params(axis='y', colors='tab:blue')
ax1.xaxis.set_major_formatter(pound_format)
ax2 = ax1.twinx()
ax2.plot(earnings[1:], (1-with_pa_removal/earnings[1:])*100, color='tab:red')
ax2.set_ylabel("Tax %", color='tab:red')
ax2.tick_params(axis='y', colors='tab:red')
ax1.grid()
ax2.set_ylim((-2.5,42.5))
ax1.set_xlim((0,200000))
ax1.set_ylim(57.5,102.5)
```