SaaS Pricing & Mechanism Design
Mussa-Rosen SaaS Versioning & Information Rent Formula
Calculate Incentive-Compatible Basic Price P_L = theta_L * q_L, High-Type Information Rent (theta_H - theta_L) * q_L, Enterprise Tier Price P_H = theta_H * q_H - Rent_H, and Total Versioning Revenue.
Price Good/Better/Best SaaS tiers without cannibalizing Enterprise accounts!
Why can’t a SaaS vendor charge Enterprise buyers 100% of their full willingness to pay theta_H * q_H when a Basic tier q_L < q_H is also on the pricing page? Michael Mussa and Sherwin Rosen (1978, Journal of Economic Theory) proved the Second-Degree Price Discrimination self-selection equations: (1) Basic Tier Participation (IR_L) sets Basic Price at P_L = theta_L * q_L (extracting full Low-Type value); (2) Because an Enterprise buyer (theta_H > theta_L) could secretly self-select into the Basic Tier and pocket surplus theta_H * q_L - P_L = (theta_H - theta_L) * q_L ("Information Rent"), Incentive Compatibility (IC_H) caps the maximum non-cannibalizing Enterprise Price at P_H = theta_H * q_H - (theta_H - theta_L) * q_L! Notice the strategic "Damaged Goods" insight: every extra feature added to Basic q_L forces a (theta_H - theta_L) discount on Enterprise P_H!
Verify on SMB_Accounts N_L = 60 (B2), Enterprise_Accounts N_H = 40 (B3), SMB_Valuation_Slope theta_L = $10/feature (B4), Enterprise_Valuation_Slope theta_H = $22/feature (B5), Basic_Tier_Scope q_L = 5 features (B6), and Enterprise_Tier_Scope q_H = 12 features (B7, zero marginal SaaS cost): Basic Price is P_L = 10 * 5 = $50.00 (E2); Enterprise Information Rent is (22 - 10) * 5 = $60.00 (E3); Maximum Incentive-Compatible Enterprise Price is P_H = 22 * 12 - 60 = $204.00 (E4—charging $205 triggers Enterprise downgrade to Basic!); and Two-Tier Menu Revenue reaches 60 * $50 + 40 * $204 = $11,160.00 (E5, beating Enterprise-Only 40 * $264 = $10,560 by +$600)! Test over-stuffed Basic tier q_L = 9: Information Rent balloons to $108, P_H drops to $156, and Menu Revenue falls to $11,640 or—when N_H = 80, N_L = 20—falls BELOW Enterprise-Only!
| Mussa-Rosen SaaS Menu Metric (60 SMB @ thL=10, 40 Ent @ thH=22; qL=5, qH=12) | Formula | Verified Output |
|---|---|---|
| Basic Tier Price P_L ($/mo) | theta_L * q_L | $50.00 / mo |
| Enterprise Information Rent ($/mo) | (theta_H - theta_L) * q_L | $60.00 / mo |
| IC-Compatible Enterprise Price P_H | theta_H * q_H - (theta_H - theta_L)*q_L | $204.00 / mo (vs $264 Full) |
| Two-Tier Versioning Revenue ($/mo) | N_L * P_L + N_H * P_H | $11,160.00 (vs $10,560 1-Tier) |
Incentive-Compatible Enterprise Tier Price Formula
Validate N_L > 0, N_H > 0, 0 < theta_L < theta_H, and 0 < q_L < q_H!
=LET(n_lo, B2, n_hi, B3, th_l, B4, th_h, B5, q_lo, B6, q_hi, B7, IF(OR(n_lo <= 0, n_hi <= 0, th_l <= 0, th_h <= th_l, q_lo <= 0, q_hi <= q_lo), "Invalid Tier Menu", ROUND(th_h * q_hi - (th_h - th_l) * q_lo, 2)))Total Two-Tier Menu Revenue Formula
Compare N_L * P_L + N_H * P_H against Enterprise-Only Revenue N_H * theta_H * q_H whenever N_H dominates the customer mix!
=IF(ISTEXT(E4), E4, ROUND(B2 * E2 + B3 * E4, 2))Try the example
Use the original values or change them to test your understanding.