Industrial Organization & Pricing Strategy
Bulow-Coase Durable Monopoly Selling vs Leasing Formula
Quantify Ronald Coase’s (1972) and Jeremy Bulow’s (1982) two-period durable-goods monopoly price erosion and compare subgame-perfect outright selling profit against credible leasing.
Why Xerox, IBM, and SaaS vendors lease instead of selling perpetual ownership!
Ronald Coase (1972) conjectured — and Jeremy Bulow (1982) proved analytically — that a durable-goods monopolist who sells outright competes against its OWN future self! Under two-period single-period rental demand p(Q) = a - b * Q (zero marginal production cost, discount factor delta in [0, 1]), a monopolist that LEASES (or sells cloud SaaS subscriptions) commits to Q_Lease = a / (2*b) per period and earns full Monopoly PV Profit Pi_Lease = (1 + delta) * (a^2 / (4 * b))! By contrast, if the monopolist SELLS durable units Q_1 in Period 1, it cannot resist cutting Period-2 price to P_2 = (a - b * Q_1) / 2 to harvest remaining buyers! Rational Period-1 buyers foresee that Period-2 price cut, depressing Period-1 Selling Quantity to Q_1_Sell = (2 * a) / (b * (4 + delta)), Period-1 Price to P_1_Sell = (a * (2 + delta)^2) / (2 * (4 + delta)), and Subgame-Perfect Selling PV Profit to Pi_Sell = ((a^2) / (4 * b)) * (((2 + delta)^2) / (4 + delta)) < Pi_Lease!
Verify on Rental_Demand_Intercept a = 100 (B2), Demand_Slope b = 1 (B3), and Discount_Factor delta = 1.00 (B4): Credible Leasing PV Profit is (1 + 1) * (10,000 / 4) = 5,000.00 (charging 50/period, equivalent to $100 two-period value); Outright Selling Period-1 Quantity is (2 * 100) / (4 + 1) = 40.00 units at P_1 = 90.00 (followed by P_2 = 30.00!), yielding Subgame-Perfect Selling PV Profit = 2,500 * (9 / 5) = 4,500.00 — losing 500.00 (10.00% of monopoly value) purely from lack of commitment!
| Durable Monopoly Regime (a = 100, b = 1, delta = 1.0) | Formula | Verified Output |
|---|---|---|
| Credible Leasing / Subscription PV Profit | (1 + delta) * (a^2 / (4 * b)) | 5,000.00 (Full Commitment) |
| Outright Sale Period-1 Price (P_1_Sell) | a * (2 + delta)^2 / (2 * (4 + delta)) | 90.00 (vs 100 Committed Sale) |
| Subgame-Perfect Outright Selling PV Profit | (a^2 / (4 * b)) * ((2 + delta)^2 / (4 + delta)) | 4,500.00 |
| Coase Commitment Value of Leasing | Pi_Lease - Pi_Sell | 500.00 (10.00% Gain from Leasing!) |
Credible Two-Period Leasing vs Subgame-Perfect Selling PV Profit Formula
Validate demand parameters a > 0, b > 0, and discount factor 0 <= delta <= 1.
=LET(a_in, B2, b_sl, B3, dl_f, B4, IF(OR(a_in <= 0, b_sl <= 0, dl_f < 0, dl_f > 1), "Invalid Durable Input", ROUND(((a_in ^ 2) / (4 * b_sl)) * (((2 + dl_f) ^ 2) / (4 + dl_f)), 2)))Coase Time-Inconsistency Profit Erosion % Formula
Notice that when delta = 0 (no Period 2), (2^2 / 4) = 1 so Pi_Sell = Pi_Lease = 2,500.00 and Coase erosion vanishes to 0.00%!
=LET(dl_f, B4, IF(OR(B2 <= 0, B3 <= 0, dl_f < 0, dl_f > 1), "Invalid Durable Input", ROUND(1 - (((2 + dl_f) ^ 2) / ((1 + dl_f) * (4 + dl_f))), 4)))Try the example
Use the original values or change them to test your understanding.