Skip to content

Discrete markets

A discrete market lists units one at a time: each buyer's willingness to pay for one more unit, and each seller's cost of one more unit. Demand and supply are step functions; the equilibrium is a whole number of units, supported by a range of prices.

Schedules

DiscreteDemand(values)
DiscreteSupply(values)
quantity_at(price)

Units bought or sold at price; a buyer or seller indifferent at the price trades.

unit_count

Number of units in the schedule.

combine(*schedules)

Merge several individual schedules into a market schedule (Market curves from individuals).

A demand schedule holds marginal willingness-to-pay values, weakly decreasing from the first unit to the last; a supply schedule holds marginal costs, weakly increasing. Values out of order raise DiscreteMarketError.

Equilibrium

solve_discrete_equilibrium(
    demand,
    supply,
    *,
    price_rule="midpoint"
)
q_starint

Units traded.

price_lowfloat

Lower end of the supporting price interval.

price_highfloat

Upper end of the supporting price interval.

pricefloat

The price chosen from the interval by price_rule.

price_ruleEquilibriumPriceRule

MIDPOINT (default), LOWER or UPPER; the strings "midpoint", "lower" and "upper" work too.

traded_valuestuple

Values of the traded units.

traded_coststuple

Costs of the traded units.

gains_from_tradetuple

Value minus cost of each traded unit.

is_unique_pricebool

Whether the interval is a single price.

Trade every unit whose value is at least its cost, and find the interval of prices at which exactly that many units are bought and sold. The result has these fields:

solve_discrete_market(demand_values, supply_values) builds both schedules from plain tuples and solves in one call. The demand values must descend and the supply values ascend so that units pair up in order.

from principle_viz import (
    DiscreteDemand,
    DiscreteSupply,
    solve_discrete_equilibrium,
)

demand = DiscreteDemand((11, 9, 7, 5, 3))
supply = DiscreteSupply((1, 3, 5, 8, 10))
eq = solve_discrete_equilibrium(demand, supply)
print(eq.q_star, eq.price_low, eq.price_high, eq.price)
# 3 5.0 7.0 6.0
print(eq.gains_from_trade)
# (10.0, 6.0, 2.0)

Three units trade at a price interval of 5 to 7, and the midpoint rule reports 6. The gains from trade total \(10 + 6 + 2 = 18\).

Consumer and producer surplus at the chosen price, in total and unit by unit (consumer_surplus_by_unit, producer_surplus_by_unit). In the example above, both are \(5 + 3 + 1 = 9\) at a price of 6.

Figure

MarketFigure.add_discrete_curves(
    demand=None,
    supply=None,
    *,
    demand_label="$D$",
    supply_label="$S$"
)
MarketFigure.add_discrete_equilibrium(result)

Draw each unit as a step \([q, q + 1)\): a filled point where the step starts (included) and an open point where it ends (excluded), joined to the next step by a dashed riser. Pass one schedule or both. The equilibrium marks \(Q^*\) and the price interval on the axes.

fig = MarketFigure(
    x_max=5.5,
    y_max=12,
    title="Discrete Demand and Supply",
)
fig.add_discrete_curves(demand, supply)
fig.add_discrete_equilibrium(eq)
fig.finalize()

The figure for this example is shown in Discrete demand and supply..

Discrete demand and supply.

Comments