Price controls

A price ceiling below the equilibrium price, or a floor above it, binds: the market does not clear, and the quantity traded is the smaller of the quantities demanded and supplied at the controlled price.

PriceControlScenario(control_type, control_price)
PriceControlType.CEILING | PriceControlType.FLOOR

A CEILING or FLOOR at control_price, from principle_viz.core.controls.

evaluate_price_control(
    demand,
    supply,
    scenario
)

is_bindingbool

Whether the control changes the outcome.

traded_quantityfloat

Quantity actually traded.

consumer_pricefloat

Price buyers pay: the controlled price when binding, otherwise the equilibrium price.

producer_pricefloat

Price sellers receive: the controlled price when binding, otherwise the equilibrium price.

shortagefloat

Excess demand under a ceiling (zero otherwise).

surplusfloat

Excess supply under a floor (zero otherwise).

baseline_equilibriumEquilibriumResult

The uncontrolled market.

The controlled market, as a PriceControlResult:

from principle_viz import evaluate_price_control
from principle_viz.core.controls import (
    PriceControlScenario,
    PriceControlType,
)

scenario = PriceControlScenario(PriceControlType.CEILING, 4.0)
ceiling = evaluate_price_control(demand, supply, scenario)
print(
    ceiling.is_binding,
    ceiling.traded_quantity,
    ceiling.shortage,
)
# True 2.0 4.0

A ceiling above the equilibrium price (for example 7) leaves is_binding False.

MarketFigure.add_price_control(
    result,
    *,
    gap_brace="line"
)

Draw the control line, named "Price ceiling" or "Price floor", with \(p_c\) on the price axis. A binding control also marks \(Q_d\) and \(Q_s\) and braces the gap: "Shortage" below a ceiling, "Surplus" above a floor. gap_brace="axis" braces it under the quantity axis instead (see A binding price ceiling. and A binding price floor.).

outcome_from_control() turns the result into a market outcome for the welfare functions of Welfare (see Welfare under a price ceiling of 3.5.):

from principle_viz.welfare.surplus import (
    compare_surplus,
    outcome_from_control,
    outcome_from_equilibrium,
)

eq = solve_equilibrium(demand, supply)
baseline = outcome_from_equilibrium(eq)
controlled = outcome_from_control(ceiling)
delta = compare_surplus(demand, supply, baseline, controlled)
fig.add_price_control(ceiling)
fig.add_welfare(delta.policy)

Under a price ceiling, the deadweight loss is the surplus of the units that are no longer traded, and part of the remaining surplus transfers from sellers to buyers.

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