diff --git a/efficient_fees/service_stake.ipynb b/efficient_fees/service_stake.ipynb
new file mode 100644
index 0000000..136b857
--- /dev/null
+++ b/efficient_fees/service_stake.ipynb
@@ -0,0 +1,139 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 116,
+   "id": "eca38ae3-3df1-40f9-9a4b-ddc539559aba",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from dataclasses import dataclass\n",
+    "\n",
+    "@dataclass\n",
+    "class ServiceNetwork:\n",
+    "    total_nmo_stake: int = 0\n",
+    "    total_lp_supply: int = 0\n",
+    "    \n",
+    "    def stake(self, nmo):\n",
+    "        if self.total_nmo_stake == 0:\n",
+    "            # this is the only staker in the network\n",
+    "            self.total_nmo_stake = nmo\n",
+    "            self.total_lp_supply = 1.0\n",
+    "            return self.total_lp_supply\n",
+    "        \n",
+    "        lp_tokens = nmo / self.total_nmo_stake * self.total_lp_supply\n",
+    "        self.total_nmo_stake += nmo\n",
+    "        self.total_lp_supply += lp_tokens\n",
+    "        return lp_tokens\n",
+    "\n",
+    "    def unstake(self, lp_tokens):\n",
+    "        nmo = self.query_stake(lp_tokens)\n",
+    "        self.total_nmo_stake -= nmo\n",
+    "        self.total_lp_supply -= lp_tokens\n",
+    "        return nmo\n",
+    "\n",
+    "    def query_stake(self, lp_tokens):\n",
+    "        nmo = lp_tokens / self.total_lp_supply * self.total_nmo_stake    \n",
+    "        return nmo\n",
+    "    \n",
+    "    def reward(self, r_nmo):\n",
+    "        self.total_nmo_stake += r_nmo\n",
+    "\n",
+    "def print_lp_positions(sn, lpers):\n",
+    "    print(f\"{\"actor\":^7}|{\"lp\":^5}|{\"nmo\":^7}\")\n",
+    "    print(\"-------+-----+-------\")\n",
+    "    for actor, lp in lpers.items():\n",
+    "        print(f\"{actor:7}|{lp:5.2f}|{sn.query_stake(lp):7.2f}\")\n",
+    "\n",
+    "    print(\"-------+-----+-------\")\n",
+    "    print(\"{actor:7}|{lp:5.2f}|{nmo:7.2f}\".format(actor=\"total\", lp=sum(lpers.values()), nmo=sum(sn.query_stake(lp) for lp in lpers.values())))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 119,
+   "id": "0b58cd02-3427-4388-992b-8347cb2a601a",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      " actor | lp  |  nmo  \n",
+      "-------+-----+-------\n",
+      "alice  | 1.00|  10.00\n",
+      "bob    | 1.00|  10.00\n",
+      "charlie| 3.00|  30.00\n",
+      "-------+-----+-------\n",
+      "total  | 5.00|  50.00\n",
+      "\n",
+      "network is rewarded by 5 NMO\n",
+      "\n",
+      " actor | lp  |  nmo  \n",
+      "-------+-----+-------\n",
+      "alice  | 1.00|  11.00\n",
+      "bob    | 1.00|  11.00\n",
+      "charlie| 3.00|  33.00\n",
+      "-------+-----+-------\n",
+      "total  | 5.00|  55.00\n",
+      "\n",
+      "new stakers after network rewards get fewer LP tokens\n",
+      "\n",
+      " actor | lp  |  nmo  \n",
+      "-------+-----+-------\n",
+      "alice  | 1.00|  11.00\n",
+      "bob    | 1.00|  11.00\n",
+      "charlie| 3.00|  33.00\n",
+      "dan    | 0.91|  10.00\n",
+      "-------+-----+-------\n",
+      "total  | 5.91|  65.00\n"
+     ]
+    }
+   ],
+   "source": [
+    "sn = ServiceNetwork()\n",
+    "\n",
+    "stakers = {\"alice\": 10, \"bob\": 10, \"charlie\": 30}\n",
+    "\n",
+    "lpers = {actor: sn.stake(nmo) for actor, nmo in stakers.items()}\n",
+    "\n",
+    "print_lp_positions(sn, lpers)\n",
+    "\n",
+    "print(\"\")\n",
+    "print(\"network is rewarded by 5 NMO\")\n",
+    "sn.reward(5)\n",
+    "print(\"\")\n",
+    "\n",
+    "print_lp_positions(sn, lpers)\n",
+    "\n",
+    "print(\"\")\n",
+    "print(\"new stakers after network rewards get fewer LP tokens\")\n",
+    "print(\"\")\n",
+    "stakers[\"dan\"] = 10\n",
+    "lpers[\"dan\"] = sn.stake(stakers[\"dan\"])\n",
+    "print_lp_positions(sn, lpers)\n"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.12.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/efficient_fees/shell.nix b/efficient_fees/shell.nix
new file mode 100644
index 0000000..8d96840
--- /dev/null
+++ b/efficient_fees/shell.nix
@@ -0,0 +1,23 @@
+{ pkgs ? import <nixpkgs> {} }:
+
+pkgs.mkShell {
+  buildInputs = with pkgs; [
+    # Defines a python + set of packages.
+    (python3.withPackages (ps: with ps; with python3Packages; [
+      jupyter
+      ipython
+
+      # Uncomment the following lines to make them available in the shell.
+      # pandas
+      numpy
+      matplotlib
+      scipy
+      sympy
+      pyvis
+      networkx
+    ]))
+  ];
+
+  # Automatically run jupyter when entering the shell.
+  shellHook = "jupyter notebook";
+}