flesh out example/full

examples/full/analysis/elasticity.py

@@ -1,11 +1,98 @@
 import matplotlib.figure as mplfig
 import matplotlib.pyplot as plt
 import numpy as np
+import pandas as pd
 from boredcharts import FigureRouter
 
 figures = FigureRouter()
 
 
+@figures.chart("price_vs_quantity")
+async def price_vs_quantity(margin: float) -> mplfig.Figure:
+    """plot the profitable frontier of price vs quantity for a given margin"""
+
+    # experiment results
+    results = pd.DataFrame(
+        [
+            (+0.05, -0.100),
+            (-0.03, +0.075),
+            (-0.07, +0.175),
+            (-0.10, +0.200),
+        ],
+        columns=["price", "qty"],  # pyright: ignore[reportArgumentType]
+    )
+
+    # simulation
+    n = 1000
+    price_range = (-0.14, 0.14 + 1 / n)
+    qty_range = (-0.4, 0.8 + 1 / n)
+    price_values = np.linspace(*price_range, n)
+    qty_values = np.linspace(*qty_range, n)
+
+    P, Q = np.meshgrid(price_values, qty_values)
+
+    RHS = -P * (1 / Q + 1)
+
+    fig, ax = plt.subplots(figsize=(10, 6))
+    mask = np.where(Q >= 0, margin > RHS, margin < RHS)  # pyright: ignore[reportOptionalOperand]
+    ax.contourf(P, Q, mask, levels=[0.5, 1], alpha=0.5)
+    ax.contour(P, Q, mask, levels=[0], colors="black", linewidths=0.5)
+    ax.plot(results.price, results.qty, "rx", markersize=10, markeredgewidth=2)
+
+    ax.set_title(f"Profitable region given change in price & qty for {margin=:.0%}")
+    ax.set_xlabel("Change in Price")
+    ax.set_ylabel("Change in Quantity")
+    xticks = np.arange(*price_range, 0.02)
+    yticks = np.arange(*qty_range, 0.1)
+    ax.set_xticks(xticks, [f"{x:.0%}" for x in xticks])
+    ax.set_yticks(yticks, [f"{y:.0%}" for y in yticks])
+    ax.grid(True)
+    ax.axhline(0, color="black", linewidth=0.5)
+    ax.axvline(0, color="black", linewidth=0.5)
+
+    return fig
+
+
+@figures.chart("profit_at_price_drop")
+async def profit_at_price_drop(drop: float) -> mplfig.Figure:
+    """sensitivity of profit to elasticity for a given price drop"""
+
+    base_profit = 760_000
+    n = 1000
+    elasticity_deviation_range = (-0.10, 0.10 + 1 / n)
+    elasticity_deviation = np.linspace(*elasticity_deviation_range, n)
+    # pretend we worked out this function and it's true
+    profit_values = (
+        elasticity_deviation * (10 * drop) * base_profit + base_profit * 1.05
+    )
+
+    fig, ax = plt.subplots(figsize=(5, 3))
+    ax.plot(elasticity_deviation, profit_values, linestyle="-")
+    ax.axhline(base_profit, color="black", linestyle="--")
+    ax.text(0.04, base_profit, "Current profit", va="bottom")
+    ax.fill_between(
+        elasticity_deviation_range,
+        700_000,
+        base_profit,
+        color="gray",
+        alpha=0.5,
+    )
+
+    ax.set_title(f"Profit sensitivity to elasticity for price {drop=:.0%}")
+    ax.set_xlabel("Elasticity deviation from expected (%)")
+    ax.set_ylabel("Profit ($)")
+    xticks = np.arange(*elasticity_deviation_range, 0.02)
+    ax.set_xticks(xticks, [f"{x:.0%}" for x in xticks])
+    ax.set_xlim(*elasticity_deviation_range)
+    ax.set_ylim(700000, 850000)
+    ax.yaxis.set_major_formatter("${x:,.0f}")
+    ax.axvline(0, color="black", linewidth=0.5)
+    ax.grid(True)
+    fig.tight_layout()
+
+    return fig
+
+
 @figures.chart("elasticity_vs_profit")
 async def elasticity_vs_profit(
     report_name: str, margin: float | None = None
@@ -50,15 +137,15 @@ async def elasticity_vs_profit(
             use_clabeltext=True,
         )
 
+    ax.set_title("Profitable regions given change in price & qty for various margins")
     ax.set_xlabel("Change in Price")
     ax.set_ylabel("Change in Quantity")
-    ax.set_xticks(
-        np.arange(*price_range, 0.1), [f"{x:.0%}" for x in np.arange(*price_range, 0.1)]
-    )
-    ax.set_yticks(
-        np.arange(*qty_range, 1), [f"{y:.0%}" for y in np.arange(*qty_range, 1)]
-    )
-    ax.set_title("Profitable regions given change in price & qty for set margin")
+    xticks = np.arange(*price_range, 0.1)
+    yticks = np.arange(*qty_range, 1)
+    ax.set_xticks(xticks, [f"{x:.0%}" for x in xticks])
+    ax.set_yticks(yticks, [f"{y:.0%}" for y in yticks])
+    ax.hlines(0, *price_range, color="black", linewidth=0.5)
+    ax.vlines(0, *qty_range, color="black", linewidth=0.5)
     ax.grid(True)
 
     return fig

examples/full/pages/price-elasticity.md

@@ -1,14 +1,30 @@
 August 2024
 
-## Price elasticity
+## Price decrease recommendation
 
-Here we did some more fiddly analysis and wanted to use matplotlib for whatever reason,
-no problem—it's exactly the same thing (except that these aren't interactive, just images):
+We should drop the price of our widgets by 7% because we'll sell 18% more,
+meaning we make more total profit. We observed a price elasticity of 2.5
+in the experiment cell where we dropped our price by 7%. With our current margin
+of 60%, this would increase our profit by $40,000.
 
-<pre>
-{%- raw %}
-{{ figure("elasticity_vs_profit") }}
-{% endraw -%}
-</pre>
+{{ figure("price_vs_quantity", margin=0.6, css_class="") }}
+
+We looked at other price drops of 3% and 10%. The 3% drop had the same
+elasticity as the 7% drop, which means it just wouldn't make us as much absolute
+profit. The 10% drop had a lower elasticity, meaning we'd make the same absolute
+profit as the 7% drop, but we'd have to sell more widgets to do so. I consider
+this unpreferable since it would be less capital-efficient, but if there is some
+strategic reason to flood the market with our widgets it wouldn't hurt our
+bottom line to do so:
+
+{{
+  row(
+    figure("profit_at_price_drop", drop=0.07, css_class=""),
+    figure("profit_at_price_drop", drop=0.10, css_class=""),
+  )
+}}
+
+We can generalise the elasticity relationship, but the results are kind of intuitive:
+the higher your margin, the more you can play with your pricing.
 
 {{ figure("elasticity_vs_profit") }}

pyproject.toml

@@ -8,6 +8,7 @@ dev-dependencies = [
     "ruff>=0.5.7",
     "types-markdown>=3.6.0.20240316",
     "httpx>=0.27.0",
+    "pandas-stubs>=2.2.2.240807",
 ]
 
 [tool.uv.sources]