Platform Economics & Marketplace Pricing
Armstrong Competitive Bottleneck Platform Formula
Price asymmetric marketplaces via Mark Armstrong’s (2006) Competitive Bottleneck model: subsidize single-homing buyers P_1* = c_1 + t_1 - (alpha_2 - c_2) and monopoly-charge multi-homing sellers.
Why newspapers, app stores, and ride-hail apps subsidize single-homing consumers while taxing multi-homing sellers!
Mark Armstrong (2006) explained why asymmetric "homing" behavior dictates which side of a marketplace gets free/subsidized access and which side pays steep take rates! When Side-1 Buyers (readers, shoppers, smartphone owners) SINGLE-HOME on one platform (choosing between two Hotelling-differentiated platforms with differentiation t_1 > 0 and serving cost c_1), while Side-2 Sellers/Advertisers MULTI-HOME (joining BOTH platforms because the only way to reach Platform A’s exclusive single-homing buyers is through Platform A!), each platform holds a Competitive Bottleneck monopoly over access to its own buyers! Consequently, Platform i charges Multi-Homing Sellers their full gross cross-side value P_2* = alpha_2 * n_1 (netting (alpha_2 - c_2) per buyer), AND competes away 100% of that seller surplus to recruit extra single-homing buyers via Equilibrium Buyer Price P_1* = c_1 + t_1 - (alpha_2 - c_2)!
Verify on Buyer_Serving_Cost c_1 = 10.00 (B2), Buyer_Hotelling_Differentiation t_1 = 15.00 (B3), Seller_Gross_Value_Per_Buyer alpha_2 = 35.00 (B4), Seller_Serving_Cost_Per_Buyer c_2 = 5.00 (B5 -> Net Bottleneck Rent = 30.00/buyer), and Symmetric_Buyer_Market_Share n_1 = 0.50 (B6): Single-Homing Buyer Price drops from standalone 10 + 15 = 25.00 all the way to P_1* = 10 + 15 - 30 = -5.00 (free subscription PLUS $5 cashback/points reward!); Multi-Homing Seller Access Fee is P_2* = 35.00 * 0.50 = 17.50; and Platform Equilibrium Profit is n_1 * (P_1* - c_1 + alpha_2 - c_2) = 0.50 * (-15 + 30) = 7.50 (= n_1 * t_1)!
| Competitive Bottleneck Metric (c_1=10, t_1=15, alpha_2=35, c_2=5, n_1=0.50) | Formula | Verified Output |
|---|---|---|
| Net Seller Bottleneck Rent per Buyer | alpha_2 - c_2 = 35 - 5 | 30.00 / buyer |
| Single-Homing Buyer Price (P_1*) | c_1 + t_1 - (alpha_2 - c_2) | -5.00 (Negative Subsidy Price!) |
| Multi-Homing Seller Access Fee (P_2*) | alpha_2 * n_1 = 35 * 0.50 | 17.50 |
| Platform Equilibrium Profit | n_1 * (P_1* - c_1 + alpha_2 - c_2) | 7.50 (= 0.50 * t_1) |
Armstrong Single-Homing Buyer Equilibrium Price P_1* Formula
Validate c_1 >= 0, t_1 > 0, c_2 >= 0, and active seller participation alpha_2 >= c_2.
=LET(c_1, B2, t_1, B3, al_2, B4, c_2, B5, IF(OR(c_1 < 0, t_1 <= 0, c_2 < 0, al_2 < c_2), "Invalid Bottleneck Input", ROUND(c_1 + t_1 - (al_2 - c_2), 2)))Multi-Homing Seller Access Fee & Platform Bottleneck Profit Formula
Validate market share 0 < n_1 <= 1.
=LET(c_1, B2, t_1, B3, al_2, B4, c_2, B5, n_1, B6, IF(OR(c_1 < 0, t_1 <= 0, c_2 < 0, al_2 < c_2, n_1 <= 0, n_1 > 1), "Invalid Bottleneck Input", LET(p_1, c_1 + t_1 - (al_2 - c_2), ROUND(n_1 * ((p_1 - c_1) + (al_2 - c_2)), 2))))Try the example
Use the original values or change them to test your understanding.