Two brokerage regimes

Under "0.03% or ₹20, whichever is lower" brokerage, derive the intraday break-even move in basis points as a function of the order value $N = PQ$ for $N$ below and above $\text{₹}20/0.0003$. Show that it is continuous at the boundary, constant below it and decreasing above it, and find its limit as $N \to \infty$. Check your formula against m01_costs_tax.breakeven_move for $N = \text{₹}30{,}000$, ₹1 lakh and ₹50 lakh at $P = \text{₹}1{,}500$.