Price Controls
==============
.. raw:: html
The Concept
-----------
Price controls are government-imposed constraints on market prices:
- **Price Ceiling**: A legal maximum price (e.g., rent control)
- **Price Floor**: A legal minimum price (e.g., minimum wage)
When binding, price controls create market distortions:
- Binding ceilings (below equilibrium) create **shortages**
- Binding floors (above equilibrium) create **surpluses**
- Both generate **deadweight loss** by preventing mutually beneficial trades
Modeling with FreeRide
----------------------
Let's explore how price controls affect market outcomes:
.. code-block:: python
from freeride.curves import Demand, Supply
from freeride.equilibrium import Market
# Create a market
demand = Demand.from_formula("P = 20 - Q")
supply = Supply.from_formula("P = 5 + 0.5*Q")
# Find free market equilibrium
free_market = Market(demand, supply)
print(f"Free Market Equilibrium: P = ${free_market.p:.2f}, Q = {free_market.q:.0f}")
print(f"Total Surplus: ${free_market.total_surplus:.2f}")
**Expected Output:**
.. code-block:: text
Free Market Equilibrium: P = $10.00, Q = 10
Total Surplus: $125.00
Price Ceilings
--------------
A binding price ceiling creates a shortage because quantity demanded exceeds quantity supplied:
.. code-block:: python
# Apply a binding price ceiling at $8
ceiling_market = Market(demand, supply, ceiling=8)
# Calculate shortage
q_demanded = demand.q(8)
q_supplied = supply.q(8)
shortage = q_demanded - q_supplied
print(f"With Price Ceiling at $8:")
print(f" Quantity Supplied: {q_supplied:.0f}")
print(f" Quantity Demanded: {q_demanded:.0f}")
print(f" Shortage: {shortage:.0f} units")
print(f" Deadweight Loss: ${ceiling_market.dwl:.2f}")
# Visualize the market with ceiling
ceiling_market.plot(surplus=True)
**Expected Output:**
.. code-block:: text
With Price Ceiling at $8:
Quantity Supplied: 6
Quantity Demanded: 12
Shortage: 6 units
Deadweight Loss: $8.00
The plot shows the binding ceiling creating a wedge between quantity supplied and demanded,
with the red area representing deadweight loss.
Price Floors
------------
A binding price floor creates a surplus because quantity supplied exceeds quantity demanded:
.. code-block:: python
# Apply a binding price floor at $12
floor_market = Market(demand, supply, floor=12)
# Calculate surplus
q_demanded = demand.q(12)
q_supplied = supply.q(12)
surplus = q_supplied - q_demanded
print(f"With Price Floor at $12:")
print(f" Quantity Demanded: {q_demanded:.0f}")
print(f" Quantity Supplied: {q_supplied:.0f}")
print(f" Surplus: {surplus:.0f} units")
print(f" Deadweight Loss: ${floor_market.dwl:.2f}")
# Visualize the market with floor
floor_market.plot(surplus=True)
**Expected Output:**
.. code-block:: text
With Price Floor at $12:
Quantity Demanded: 8
Quantity Supplied: 14
Surplus: 6 units
Deadweight Loss: $8.00
The plot shows the binding floor creating excess supply, with producers unable to sell all
they wish at the floor price.
Non-Binding Controls
--------------------
Price controls only affect the market when they're binding:
.. code-block:: python
# Non-binding ceiling (above equilibrium)
high_ceiling = Market(demand, supply, ceiling=15)
print(f"Non-binding ceiling at $15: P = ${high_ceiling.p:.2f}, Q = {high_ceiling.q:.0f}")
# Non-binding floor (below equilibrium)
low_floor = Market(demand, supply, floor=7)
print(f"Non-binding floor at $7: P = ${low_floor.p:.2f}, Q = {low_floor.q:.0f}")
# Both should equal free market equilibrium
print(f"Free market: P = ${free_market.p:.2f}, Q = {free_market.q:.0f}")
**Expected Output:**
.. code-block:: text
Non-binding ceiling at $15: P = $10.00, Q = 10
Non-binding floor at $7: P = $10.00, Q = 10
Free market: P = $10.00, Q = 10
