Industrial Organization & Pricing Strategy
Coase Durable-Good Monopoly: Leasing vs Spot Sale Formula
Quantify Ronald Coase’s (1972) durable-good time-inconsistency profit loss by comparing 2-period commitment leasing (1 + delta)*(a^2 / 4) against spot selling a^2 * (2 + delta)^2 / (4 * (4 + delta)).
Why Xerox and IBM leased machines: a durable seller’s worst competitor is its own future self!
Ronald Coase (1972) and Jeremy Bulow (1982) proved a striking paradox: a monopolist selling a long-lived durable good (enterprise software licenses, aircraft, luxury hardware) WITHOUT price-commitment power competes against its own future clearance discounts! Under 2-period per-period valuation v in [0, a], zero unit cost, and discount factor delta in [0, 1], a Leasing / Commitment firm rents at a / 2 each period for PV profit Pi_lease* = (1 + delta) * (a^2 / 4). A Spot Seller, however, inevitably cuts Period 2 price to p_2* = x_1 / 2 on unsold buyers [0, x_1], so strategic Period 1 buyers refuse to pay full price — forcing Period 1 price down to p_1* = a * (2 + delta)^2 / (2 * (4 + delta)) and shrinking PV profit to Pi_spot* = (a^2 * (2 + delta)^2) / (4 * (4 + delta))!
Verify with choke per-period value a = 100 (B2) and patient discount factor delta = 1.00 (B3): Leasing / Most-Favored-Customer Commitment earns Pi_lease* = 2 * 2,500 = 5,000.00 (selling/leasing at PV 100.00 to the top 50% of buyers), whereas No-Commitment Spot Selling sets p_1* = 100 * 9 / 10 = 90.00, p_2* = 30.00, and earns Pi_spot* = 4,500.00 — losing an exact 500.00 (10.00% Coase time-inconsistency penalty!) purely from inability to commit not to discount in Period 2!
| Durable-Good Regime (a = 100, delta = 1.00) | Prices (Period 1 / Period 2) | Present-Value Profit |
|---|---|---|
| Leasing / Price Commitment | Rental 50 + 50 (PV = 100.00) | 5,000.00 |
| No-Commitment Spot Sales | p_1* = 90.00, then p_2* = 30.00 | 4,500.00 (-10.00% Loss!) |
| Myopic / Impatient Limit (delta = 0) | p_1* = 50.00 (Single Period) | 2,500.00 (Identical) |
Subgame-Perfect Spot-Selling Durable Monopolist PV Profit Formula
Validate choke demand a > 0 and discount factor 0 <= delta <= 1.
=LET(a_mx, B2, del_d, B3, IF(OR(a_mx <= 0, del_d < 0, del_d > 1), "Invalid Coase Input", ROUND(((a_mx^2) * ((2 + del_d)^2)) / (4 * (4 + del_d)), 4)))Leasing / Best-Price Commitment Profit Advantage (Pi_lease* - Pi_spot*) Formula
Measure the exact dollar value of contractual leasing, buyback guarantees, or Most-Favored-Customer clauses that restore full commitment.
=LET(a_mx, B2, del_d, B3, IF(OR(a_mx <= 0, del_d < 0, del_d > 1), "Invalid Coase Input", LET(pi_ls, (1 + del_d) * (a_mx^2) / 4, pi_sp, ((a_mx^2) * ((2 + del_d)^2)) / (4 * (4 + del_d)), ROUND(pi_ls - pi_sp, 4))))Try the example
Use the original values or change them to test your understanding.