Environmental & Natural Resource Economics
Gordon-Schaefer Fishery MSY, MEY & Open-Access Formula
Compare biological Maximum Sustainable Yield (E_MSY = r/(2*q)), Open-Access Bionomic rent dissipation (E_OA), and conservationist Maximum Economic Yield (E_MEY = E_OA / 2).
Prove H. Scott Gordon’s (1954) conservation surprise: economic MEY preserves MORE fish than biological MSY!
In H. Scott Gordon (1954) and Milner Schaefer’s (1957) renewable-fishery model, fish biomass X grows logistically as G(X) = r * X * (1 - X / K) and fleet effort E harvests H = q * E * X (price p, unit effort cost c, viability p * q * K > c). Steady-state stock is X(E) = K * (1 - q * E / r). Comparing three regimes exposes the Tragedy of the Commons AND a delightful surprise: (1) Biological Maximum Sustainable Yield sets E_MSY = r / (2 * q) and X_MSY = K / 2; (2) Unregulated Open Access expands boats until Total Revenue = Total Cost (zero economic rent!), pushing effort up to E_OA = (r / q) * (1 - c / (p * q * K)) and depleting stock to X_OA = c / (p * q); (3) Optimal Sole-Owner / ITQ Quota Maximum Economic Yield sets E_MEY = E_OA / 2 — deploying FEWER boats and preserving a LARGER fish stock X_MEY = (K + X_OA) / 2 > K / 2 than biological MSY!
Check by hand with Growth_r = 0.40 (B2), Carrying_Capacity_K = 1,000 tons (B3), Catchability_q = 0.001 (B4), Price_p = 10 (B5), and Boat_Cost_c = 2 (B6): MSY deploys E_MSY = 200 boat-days (X_MSY = 500 tons, Rent = 600.00); Open Access floods the sea with E_OA = 320 boat-days (depleting X_OA = 200 tons, Rent = 0.00!); and MEY deploys E_MEY = 160 boat-days, maintaining X_MEY = 600 tons (> 500!) and earning maximum sustainable resource rent 640.00!
| Fishery Regime (r=0.40, K=1,000, q=0.001, p=10, c=2) | Effort E & Steady-State Stock X | Sustainable Harvest & Net Rent |
|---|---|---|
| Maximum Economic Yield (MEY / ITQ) | E_MEY = 160, X_MEY = 600 tons | H = 96 tons | Rent = 640.00 (Peak!) |
| Biological Max Sustainable Yield (MSY) | E_MSY = 200, X_MSY = 500 tons | H = 100 tons | Rent = 600.00 |
| Unregulated Open Access (Commons) | E_OA = 320, X_OA = 200 tons | H = 64 tons | Rent = 0.00 (Dissipated!) |
Open-Access Bionomic Effort E_OA & Optimal MEY Effort E_MEY = E_OA / 2 Formula
Validate positive biological/economic parameters and commercial fishery viability p * q * K > c (if c >= p * q * K, harvesting is unprofitable even at virgin stock K!).
=LET(r_gr, B2, k_cp, B3, q_ct, B4, p_fs, B5, c_bt, B6, IF(OR(r_gr <= 0, k_cp <= 0, q_ct <= 0, p_fs <= 0, c_bt < 0), "Invalid Fishery Input", IF(p_fs * q_ct * k_cp <= c_bt, 0, ROUND(0.5 * (r_gr / q_ct) * (1 - (c_bt / (p_fs * q_ct * k_cp))), 4))))Maximum Sustainable Economic Rent (Rent_MEY) Formula
Evaluate p * q * E_MEY * X_MEY - c * E_MEY to quantify the exact annual value unlocked by Individual Transferable Quotas (ITQs) relative to 0-rent Open Access.
=LET(r_gr, B2, k_cp, B3, q_ct, B4, p_fs, B5, c_bt, B6, IF(OR(r_gr <= 0, k_cp <= 0, q_ct <= 0, p_fs <= 0, c_bt < 0), "Invalid Fishery Input", IF(p_fs * q_ct * k_cp <= c_bt, 0, LET(e_mey, 0.5 * (r_gr / q_ct) * (1 - (c_bt / (p_fs * q_ct * k_cp))), x_mey, k_cp * (1 - (q_ct * e_mey / r_gr)), ROUND(p_fs * q_ct * e_mey * x_mey - c_bt * e_mey, 2)))))Try the example
Use the original values or change them to test your understanding.