mergeron.core.guidelines_boundaries¶

Methods for defining and analyzing boundaries for Guidelines standards.

Includes function to create a canvas on which to draw boundaries for Guidelines standards.

Module Contents¶

class mergeron.core.guidelines_boundaries.MGThresholds[source]¶

Thresholds for Guidelines standards.

delta : float[source]¶

fc : float[source]¶

rec : float[source]¶

guppi : float[source]¶

dr : float[source]¶

cmcr : float[source]¶

ipr : float[source]¶

class mergeron.core.guidelines_boundaries.GuidelinesThresholds[source]¶

Guidelines thresholds by Guidelines publication year.

ΔHHI, Recapture Rate, GUPPI, Diversion ratio, CMCR, and IPR thresholds constructed from concentration standards in Guidelines published in 1992, 2010, and 2023.

pub_year : mergeron.PubYear[source]¶: Year of publication of the Guidelines.

safeharbor : MGThresholds[source]¶

Negative presumption quantified on various measures.

ΔHHI safeharbor bound, default recapture rate, GUPPI bound, diversion ratio limit, CMCR, and IPR.

presumption : MGThresholds[source]¶

Presumption of harm defined in HMG.

ΔHHI bound and corresponding default recapture rate, GUPPI bound, diversion ratio limit, CMCR, and IPR.

imputed_presumption : MGThresholds[source]¶

Presumption of harm imputed from Guidelines.

ΔHHI bound inferred from strict numbers-equivalent of (post-merger) HHI presumption, and corresponding default recapture rate, GUPPI bound, diversion ratio limit, CMCR, and IPR.

class mergeron.core.guidelines_boundaries.ConcentrationBoundary[source]¶

Concentration parameters, boundary coordinates, and area under concentration boundary.

threshold : float[source]¶

measure_name : Literal['ΔHHI', 'Combined share', 'HHI contribution, pre-merger', 'HHI contribution, post-merger'][source]¶

precision : int[source]¶

area : float[source]¶: Area under the concentration boundary.

coordinates : mergeron.ArrayDouble[source]¶: Market-share pairs as Cartesian coordinates of points on the concentration boundary.

class mergeron.core.guidelines_boundaries.DiversionBoundary[source]¶

Diversion ratio specification, boundary coordinates, and area under boundary.

Along with the default diversion ratio and recapture rate, a diversion ratio boundary specification includes the recapture form – whether fixed for both merging firms’ products (“fixed”) or consistent with share-proportionality, i.e., “inside-out”; the method of aggregating diversion ratios for the two products, and the precision for the estimate of area under the divertion ratio boundary (also defines the number of points on the boundary).

diversion_ratio : float[source]¶

recapture_rate : float[source]¶

recapture_form : mergeron.RECForm | None[source]¶

The form of the recapture rate.

When mergeron.RECForm.INOUT, the recapture rate for he product having the smaller market-share is assumed to equal the default, and the recapture rate for the product with the larger market-share is computed assuming MNL demand. Fixed recapture rates are specified as mergeron.RECForm.FIXED. (To specify that recapture rates be constructed from the generated purchase-probabilities for products in the market and for the outside good, specify mergeron.RECForm.OUTIN.)

The GUPPI boundary is a continuum of conditional diversion ratio boundaries,

\[d_{ij} \vert_{p_i, p_j, m_j} \triangleq \frac{g_i p_i}{m_j p_j} = \overline{d}\]

with \(d_{ij}\) the diversion ratio from product \(i\) to product \(j\); \(g_i\) the GUPPI for product \(i\); \(m_j\) the price-cost margin on product \(j\); \(p_i, p_j\) the prices of goods \(i, j\), respectively; and \(\overline{d}\) the diversion ratio threshold (i.e., bound).

agg_method : mergeron.UPPAggrSelector[source]¶

Method for aggregating the distinct diversion ratio measures for the two products.

Distinct diversion ratio or GUPPI measures for the two merging-firms’ products are aggregated using the method specified by the agg_method attribute, which is specified using the enum mergeron.UPPAggrSelector.

precision : int[source]¶

The number of decimal places of precision for the estimated area under the UPP boundary.

Leaving this attribute unspecified will result in the default precision, which varies based on the agg_method attribute, reflecting the limit of precision available from the underlying functions. The number of boundary points generated is also defined based on this attribute.

area : float[source]¶: Area under the diversion ratio boundary.

coordinates : mergeron.ArrayDouble[source]¶: Market-share pairs as Cartesian coordinates of points on the diversion ratio boundary.

mergeron.core.guidelines_boundaries.guppi_from_delta(_delta_bound=0.01, /, *, m_star=1.0, r_bar=DEFAULT_REC)[source]¶

Translate ∆HHI bound to GUPPI bound.

Parameters:¶

_delta_bound : float¶: Specified ∆HHI bound.
m_star : float¶: Parametric price-cost margin.
r_bar : float¶: Default recapture rate.

Returns:¶

GUPPI bound corresponding to ∆HHI bound, at given margin and recapture rate.

Return type:¶

float

mergeron.core.guidelines_boundaries.critical_diversion_share(_guppi_bound=0.075, /, *, m_star=1.0, r_bar=1.0, frac=1e-16)[source]¶

Corollary to GUPPI bound.

Parameters:¶

_guppi_bound : float¶: Specified GUPPI bound.
m_star : float¶: Parametric price-cost margin.
r_bar : float¶: Default recapture rate.

Returns:¶

Critical diversion share (diversion share bound) corresponding to the GUPPI bound for given margin and recapture rate.

Return type:¶

float

mergeron.core.guidelines_boundaries.share_from_guppi(_guppi_bound=0.065, /, *, m_star=1.0, r_bar=DEFAULT_REC)[source]¶

Symmetric-firm share for given GUPPI, margin, and recapture rate.

Parameters:¶

_guppi_bound : float¶: GUPPI bound.
m_star : float¶: Parametric price-cost margin.
r_bar : float¶: Default recapture rate.

Returns:¶

Symmetric firm market share on GUPPI boundary, for given margin and recapture rate.

Return type:¶

float