Antitrust Economics & Merger Analysis
Upward Pricing Pressure (UPP) & GUPPI Merger Screen Formula
Calculate Gross Upward Pricing Pressure Index GUPPI_1 = D_12 * (P_2 - C_2) / P_1, Farrell-Shapiro Net UPP_1, and break-even marginal-cost efficiency E_1* in horizontal merger review.
Screen unilateral merger price incentives without arbitrary market-boundary disputes
When differentiated competitors Firm 1 (price P_1, unit cost C_1) and Firm 2 (price P_2, unit cost C_2) merge, raising P_1 recaptures fraction D_12 (the unit diversion ratio from Product 1 to Product 2) of lost sales at Product 2’s dollar margin (P_2 - C_2)! Farrell and Shapiro (2010) proved that this internalizes an opportunity cost of D_12 * (P_2 - C_2) per unit of Product 1, measured before efficiencies by Gross Upward Pricing Pressure Index GUPPI_1 = D_12 * (P_2 - C_2) / P_1, and net of cognizable marginal-cost efficiency savings E_1 * C_1 by Net UPP_1 = D_12 * (P_2 - C_2) - E_1 * C_1.
Audit a merger screen with P_1 = 100 (B2), C_1 = 60 (B3), P_2 = 120 (B4), C_2 = 75 (B5 -> partner margin 45), diversion ratio D_12 = 0.30 (B6), and claimed cost efficiency E_1 = 0.10 (B7): recaptured margin is 0.30 * 45 = 13.50/unit, GUPPI_1 = 13.50 / 100 = 0.1350 (13.50%, well above the 5%–10% antitrust scrutiny threshold!), Net UPP_1 = 13.50 - 6.00 = +7.50/unit (positive unilateral upward price pressure!), and zeroing out UPP_1 requires break-even efficiency E_1* = 13.50 / 60 = 0.2250 (22.50% unit cost cut!).
| Merger Screen Metric | Formula | Verified Output |
|---|---|---|
| Value of Diverted Sales | D_12 * (P_2 - C_2) | 13.50 per unit |
| Gross GUPPI_1 Index | D_12 * (P_2 - C_2) / P_1 | 0.1350 (13.50%) |
| Farrell-Shapiro Net UPP_1 | D_12 * (P_2 - C_2) - E_1 * C_1 | +7.50 per unit |
| Break-Even Efficiency (E_1*) | D_12 * (P_2 - C_2) / C_1 | 0.2250 (22.50% Cost Cut) |
Gross Upward Pricing Pressure Index GUPPI_1 Formula
Validate positive prices and costs (P_1 > C_1 > 0, P_2 >= C_2 >= 0) and unit diversion ratio 0 <= D_12 < 1.
=LET(p_1, B2, c_1, B3, p_2, B4, c_2, B5, d_12, B6, IF(OR(p_1 <= 0, c_1 <= 0, c_1 > p_1, p_2 <= 0, c_2 < 0, c_2 > p_2, d_12 < 0, d_12 >= 1), "Invalid Merger Input", ROUND(d_12 * (p_2 - c_2) / p_1, 4)))Farrell-Shapiro Net UPP_1 and Break-Even Efficiency Hurdle E_1* Formula
When Net UPP_1 <= 0 (i.e., E_1 >= E_1*), merger marginal-cost savings more than offset recaptured diversion cannibalization.
=LET(p_1, B2, c_1, B3, p_2, B4, c_2, B5, d_12, B6, ef_1, B7, IF(OR(p_1 <= 0, c_1 <= 0, c_1 > p_1, p_2 <= 0, c_2 < 0, c_2 > p_2, d_12 < 0, d_12 >= 1, ef_1 < 0, ef_1 >= 1), "Invalid Merger Input", ROUND(d_12 * (p_2 - c_2) - ef_1 * c_1, 4)))Try the example
Use the original values or change them to test your understanding.