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Merge pull request #143 from alexanderthclark/feature/price-controls-tutorial
price controls tutorial
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‎docs/index.rst‎

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tutorials/double_auction
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tutorials/market_equilibrium
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tutorials/price_controls
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tutorials/prisoners_dilemma
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‎docs/notebooks/price_controls.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "intro",
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"metadata": {},
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"source": [
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"# Price Controls\n",
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"\n",
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"This tutorial demonstrates how to model and analyze price controls (ceilings and floors) using FreeRide.\n",
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"\n",
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"## Setup\n",
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"\n",
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"First, install FreeRide (if running in Colab):"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "install",
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"metadata": {},
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"outputs": [],
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"source": [
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"!pip install freeride"
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]
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},
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{
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"cell_type": "markdown",
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"id": "concept",
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"metadata": {},
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"source": [
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"## The Concept\n",
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"\n",
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"Price controls are government-imposed constraints on market prices:\n",
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"\n",
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"- **Price Ceiling**: A legal maximum price (e.g., rent control)\n",
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"- **Price Floor**: A legal minimum price (e.g., minimum wage)\n",
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"\n",
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"When binding, price controls create market distortions:\n",
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"- Binding ceilings (below equilibrium) create **shortages**\n",
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"- Binding floors (above equilibrium) create **surpluses**\n",
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"- Both generate **deadweight loss** by preventing mutually beneficial trades"
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]
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},
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{
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"cell_type": "markdown",
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"id": "modeling",
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"metadata": {},
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"source": [
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"## Modeling with FreeRide\n",
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"\n",
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"Let's explore how price controls affect market outcomes:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "free-market",
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"metadata": {},
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"outputs": [],
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"source": [
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"from freeride.curves import Demand, Supply\n",
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"from freeride.equilibrium import Market\n",
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"\n",
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"# Create a market\n",
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"demand = Demand.from_formula(\"P = 20 - Q\")\n",
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"supply = Supply.from_formula(\"P = 5 + 0.5*Q\")\n",
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"\n",
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"# Find free market equilibrium\n",
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"free_market = Market(demand, supply)\n",
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"print(f\"Free Market Equilibrium: P = ${free_market.p:.2f}, Q = {free_market.q:.0f}\")\n",
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"print(f\"Total Surplus: ${free_market.total_surplus:.2f}\")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "ceilings",
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"metadata": {},
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"source": [
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"## Price Ceilings\n",
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"\n",
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"A binding price ceiling creates a shortage because quantity demanded exceeds quantity supplied:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "ceiling-analysis",
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"metadata": {},
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"outputs": [],
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"source": [
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"# Apply a binding price ceiling at $8\n",
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"ceiling_market = Market(demand, supply, ceiling=8)\n",
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"\n",
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"# Calculate shortage\n",
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"q_demanded = demand.q(8)\n",
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"q_supplied = supply.q(8)\n",
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"shortage = q_demanded - q_supplied\n",
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"\n",
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"print(f\"With Price Ceiling at $8:\")\n",
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"print(f\" Quantity Supplied: {q_supplied:.0f}\")\n",
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"print(f\" Quantity Demanded: {q_demanded:.0f}\")\n",
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"print(f\" Shortage: {shortage:.0f} units\")\n",
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"print(f\" Deadweight Loss: ${ceiling_market.dwl:.2f}\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "ceiling-plot",
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"metadata": {},
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"outputs": [],
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"source": [
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"# Visualize the market with ceiling\n",
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"ceiling_market.plot(surplus=True)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "floors",
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"metadata": {},
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"source": [
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"## Price Floors\n",
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"\n",
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"A binding price floor creates a surplus because quantity supplied exceeds quantity demanded:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "floor-analysis",
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"metadata": {},
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"outputs": [],
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"source": [
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"# Apply a binding price floor at $12\n",
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"floor_market = Market(demand, supply, floor=12)\n",
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"\n",
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"# Calculate surplus\n",
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"q_demanded = demand.q(12)\n",
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"q_supplied = supply.q(12)\n",
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"surplus = q_supplied - q_demanded\n",
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"\n",
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"print(f\"With Price Floor at $12:\")\n",
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"print(f\" Quantity Demanded: {q_demanded:.0f}\")\n",
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"print(f\" Quantity Supplied: {q_supplied:.0f}\")\n",
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"print(f\" Surplus: {surplus:.0f} units\")\n",
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"print(f\" Deadweight Loss: ${floor_market.dwl:.2f}\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "floor-plot",
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"metadata": {},
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"outputs": [],
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"source": [
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"# Visualize the market with floor\n",
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"floor_market.plot(surplus=True)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "non-binding",
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"metadata": {},
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"source": [
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"## Non-Binding Controls\n",
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"\n",
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"Price controls only affect the market when they're binding:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "non-binding-analysis",
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"metadata": {},
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"outputs": [],
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"source": [
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"# Non-binding ceiling (above equilibrium)\n",
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"high_ceiling = Market(demand, supply, ceiling=15)\n",
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"print(f\"Non-binding ceiling at $15: P = ${high_ceiling.p:.2f}, Q = {high_ceiling.q:.0f}\")\n",
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"\n",
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"# Non-binding floor (below equilibrium)\n",
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"low_floor = Market(demand, supply, floor=7)\n",
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"print(f\"Non-binding floor at $7: P = ${low_floor.p:.2f}, Q = {low_floor.q:.0f}\")\n",
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"\n",
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"# Both should equal free market equilibrium\n",
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"print(f\"Free market: P = ${free_market.p:.2f}, Q = {free_market.q:.0f}\")"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.0"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

‎docs/tutorials/market_equilibrium.rst‎

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3. Explore how more/less elastic demands respond differently to supply shocks
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4. Build intuition about price sensitivity
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**Next:** Try the Prisoner's Dilemma tutorial at :doc:`prisoners_dilemma`!
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**Next:** Learn about price controls at :doc:`price_controls` or try the Prisoner's Dilemma tutorial at :doc:`prisoners_dilemma`!

‎docs/tutorials/price_controls.rst‎

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Price Controls
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==============
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.. raw:: html
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<div style="margin-bottom: 1rem;">
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<a href="https://colab.research.google.com/github/alexanderthclark/FreeRide/blob/main/docs/notebooks/price_controls.ipynb" target="_blank">
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<img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab" style="margin-right: 10px;"/>
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</a>
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<a href="../notebooks/price_controls.ipynb" download>
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<img src="https://img.shields.io/badge/Download-Notebook-blue?style=flat&logo=jupyter" alt="Download Notebook"/>
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</a>
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</div>
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The Concept
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-----------
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Price controls are government-imposed constraints on market prices:
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- **Price Ceiling**: A legal maximum price (e.g., rent control)
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- **Price Floor**: A legal minimum price (e.g., minimum wage)
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When binding, price controls create market distortions:
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- Binding ceilings (below equilibrium) create **shortages**
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- Binding floors (above equilibrium) create **surpluses**
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- Both generate **deadweight loss** by preventing mutually beneficial trades
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Modeling with FreeRide
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----------------------
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Let's explore how price controls affect market outcomes:
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.. code-block:: python
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from freeride.curves import Demand, Supply
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from freeride.equilibrium import Market
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# Create a market
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demand = Demand.from_formula("P = 20 - Q")
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supply = Supply.from_formula("P = 5 + 0.5*Q")
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# Find free market equilibrium
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free_market = Market(demand, supply)
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print(f"Free Market Equilibrium: P = ${free_market.p:.2f}, Q = {free_market.q:.0f}")
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print(f"Total Surplus: ${free_market.total_surplus:.2f}")
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**Expected Output:**
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.. code-block:: text
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Free Market Equilibrium: P = $10.00, Q = 10
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Total Surplus: $125.00
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Price Ceilings
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--------------
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A binding price ceiling creates a shortage because quantity demanded exceeds quantity supplied:
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.. code-block:: python
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# Apply a binding price ceiling at $8
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ceiling_market = Market(demand, supply, ceiling=8)
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# Calculate shortage
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q_demanded = demand.q(8)
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q_supplied = supply.q(8)
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shortage = q_demanded - q_supplied
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print(f"With Price Ceiling at $8:")
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print(f" Quantity Supplied: {q_supplied:.0f}")
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print(f" Quantity Demanded: {q_demanded:.0f}")
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print(f" Shortage: {shortage:.0f} units")
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print(f" Deadweight Loss: ${ceiling_market.dwl:.2f}")
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# Visualize the market with ceiling
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ceiling_market.plot(surplus=True)
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**Expected Output:**
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.. code-block:: text
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With Price Ceiling at $8:
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Quantity Supplied: 6
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Quantity Demanded: 12
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Shortage: 6 units
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Deadweight Loss: $8.00
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The plot shows the binding ceiling creating a wedge between quantity supplied and demanded,
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with the red area representing deadweight loss.
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Price Floors
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------------
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A binding price floor creates a surplus because quantity supplied exceeds quantity demanded:
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.. code-block:: python
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# Apply a binding price floor at $12
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floor_market = Market(demand, supply, floor=12)
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# Calculate surplus
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q_demanded = demand.q(12)
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q_supplied = supply.q(12)
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surplus = q_supplied - q_demanded
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print(f"With Price Floor at $12:")
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print(f" Quantity Demanded: {q_demanded:.0f}")
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print(f" Quantity Supplied: {q_supplied:.0f}")
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print(f" Surplus: {surplus:.0f} units")
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print(f" Deadweight Loss: ${floor_market.dwl:.2f}")
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# Visualize the market with floor
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floor_market.plot(surplus=True)
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**Expected Output:**
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.. code-block:: text
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With Price Floor at $12:
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Quantity Demanded: 8
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Quantity Supplied: 14
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Surplus: 6 units
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Deadweight Loss: $8.00
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The plot shows the binding floor creating excess supply, with producers unable to sell all
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they wish at the floor price.
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Non-Binding Controls
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--------------------
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Price controls only affect the market when they're binding:
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.. code-block:: python
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# Non-binding ceiling (above equilibrium)
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high_ceiling = Market(demand, supply, ceiling=15)
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print(f"Non-binding ceiling at $15: P = ${high_ceiling.p:.2f}, Q = {high_ceiling.q:.0f}")
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# Non-binding floor (below equilibrium)
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low_floor = Market(demand, supply, floor=7)
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print(f"Non-binding floor at $7: P = ${low_floor.p:.2f}, Q = {low_floor.q:.0f}")
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# Both should equal free market equilibrium
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print(f"Free market: P = ${free_market.p:.2f}, Q = {free_market.q:.0f}")
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**Expected Output:**
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.. code-block:: text
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Non-binding ceiling at $15: P = $10.00, Q = 10
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Non-binding floor at $7: P = $10.00, Q = 10
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Free market: P = $10.00, Q = 10

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