calc_omax_pmax: Calculate Omax and Pmax for Demand Curves

In beezdemand: Behavioral Economic Easy Demand

Calculate Omax and Pmax for Demand Curves

Description

Calculates the maximum expenditure (Omax) and the price at maximum expenditure (Pmax) for the exponential demand model used in the two-part hurdle model.

Usage

calc_omax_pmax(Q0, k, alpha, price_range = NULL)

Arguments

Q0	Intensity parameter (consumption at price 0).
k	Scaling parameter for the exponential decay.
alpha	Elasticity parameter (rate of decay).
price_range	Numeric vector of length 2 specifying the price range to search for Pmax. Default is NULL, which uses an adaptive range based on alpha (approximately 0 to 10/alpha).

Details

For the demand function:

Q(p) = Q_0 \cdot \exp(k \cdot (\exp(-\alpha \cdot p) - 1))

Expenditure is E(p) = p * Q(p). Omax is the maximum of E(p) and Pmax is the price at which this maximum occurs. These are found numerically.

The search range is automatically adjusted based on alpha to ensure the maximum is found. For small alpha values, Pmax can be quite large.

Value

A named list with:

Pmax

Price at maximum expenditure

Omax

Maximum expenditure (price * quantity)

Qmax

Quantity at Pmax

See Also

calc_group_metrics, fit_demand_hurdle

Examples

# Calculate for group-level parameters
calc_omax_pmax(Q0 = 10, k = 2, alpha = 0.5)

# With k >= e (~2.718), a local maximum exists
calc_omax_pmax(Q0 = 10, k = 3, alpha = 0.5)

beezdemand documentation built on March 3, 2026, 9:07 a.m.