mergeron.perks.guidelines_boundary_functions_extra¶
Specialized methods for defining and analyzing boundaries for Guidelines standards.
These methods (functions) provide rely on scipy of sympy for core computations, and may provide improved precision than core functions, but tend to have poor performance
Module Contents¶
-
mergeron.perks.guidelines_boundary_functions_extra.dh_area_quad(_dh_val=
0.01, /)[source]¶ Area under the ΔHHI boundary.
When the given ΔHHI bound matches a Guidelines safeharbor, the area under the boundary is half the intrinsic clearance rate for the ΔHHI safeharbor.
-
mergeron.perks.guidelines_boundary_functions_extra.hhi_delta_boundary_qdtr(_dh_val=
0.01, /)[source]¶ Generate the list of share combination on the ΔHHI boundary.
Share combinations for the share-weighted average share-ratio boundary.
Diversion share, \(\overline{d} / \overline{r}\) or \(\overline{g} / (m^* \cdot \overline{r})\).
Recapture rate.
Whether “own-share” or “cross-product-share” (or None for simple, unweighted average)
Whether recapture rate is share-proportional (“inside-out”) or has fixed value for both merging firms (“fixed”).
Array of share-pairs, area under boundary.
Share combinations for the share-ratio boundaries using various aggregators.
Reimplements the arithmetic-averages and distance estimations from function, diversion_share_boundary_wtd_avg but uses the Minkowski-distance function, scipy.spatial.distance.minkowski for all aggregators. This reimplementation is useful for testing the output of diversion_share_boundary_wtd_avg but runs considerably slower.
Diversion share, \(\overline{d} / \overline{r}\) or \(\overline{g} / (m^* \cdot \overline{r})\).
Recapture rate.
Whether “arithmetic mean” or “distance”.
Whether “own-share” or “cross-product-share”.
Whether recapture rate is share-proportional (“inside-out”) or has fixed value for both merging firms (“fixed”).
Number of decimal places for rounding returned shares and area.
Array of share-pairs, area under boundary.
Share combinations along the simple average diversion-ratio boundary.
Notes
An analytical expression for the exact average boundary is derived and plotted from the y-intercept to the ray of symmetry as follows:
from sympy import latex, plot as symplot, solve, symbols s_1, s_2 = symbols("s_1 s_2") g_val, r_val, m_val = 0.06, 0.80, 0.30 d_hat = g_val / (r_val * m_val) # recapture_form = "inside-out" sag = solve( (s_2 / (1 - s_1)) + (s_1 / (1 - (r_val * s_2 + (1 - r_val) * s_1))) - 2 * d_hat, s_2 )[0] symplot( sag, (s_1, 0., d_hat / (1 + d_hat)), ylabel=s_2 ) # recapture_form = "fixed" sag = solve((s_2/(1 - s_1)) + (s_1/(1 - s_2)) - 2 * d_hat, s_2)[0] symplot( sag, (s_1, 0., d_hat / (1 + d_hat)), ylabel=s_2 )Diversion share, \(\overline{d} / \overline{r}\) or \(\overline{g} / (m^* \cdot \overline{r})\).
Recapture rate.
Whether recapture rate is share-proportional (“inside-out”) or has fixed value for both merging firms (“fixed”).
Number of decimal places for rounding returned shares.
Array of share-pairs, area under boundary, area under boundary.