Regulatory & Energy Utility Economics
Averch-Johnson Regulated Capital Gold-Plating Formula
Calculate the Averch-Johnson (1962) shadow cost of capital r_eff = r - (lambda/(1 - lambda))*(s - r) and quantify rate-base capital over-intensity ("gold-plating") under rate-of-return regulation.
Why rate-of-return utility caps induce electric and gas monopolies to over-build capital rate base!
Harvey Averch and Leland Johnson (1962) proved why traditional cost-of-service / rate-of-return utility regulation distorts engineering input choices: when a regulator caps accounting return on capital at allowed rate s strictly above true market cost of capital r (r < s < r_monopoly) with binding shadow multiplier lambda in (0, 1), every extra $1 of physical rate-base capital K expands allowed profit by (s - r)! Internally, the utility optimizes against an artificially cheap Effective Shadow Cost of Capital r_eff = r - (lambda / (1 - lambda)) * (s - r) < r — tilting Cobb-Douglas capital-labor intensity (K / L)* = (w / r_eff) * (alpha / beta) strictly ABOVE cost-minimizing (w / r) * (alpha / beta) ("gold-plating")!
Verify on Wage_w = 20 (B2), True_WACC_r = 0.10 (B3), Allowed_RoR_s = 0.14 (B4), Capital_Elasticity_alpha = 0.50 (B5), Labor_Elasticity_beta = 0.50 (B6), and Constraint_Multiplier_lambda = 0.50 (B7): true cost minimization sets (K / L)_min = (20 / 0.10) * 1 = 200.00. Under rate-of-return regulation, shadow capital cost drops to r_eff = 0.10 - 1.0 * 0.04 = 0.0600 (6.00%!), driving regulated capital-labor ratio up to 20 / 0.06 = 333.3333 (+66.67% gold-plating distortion!)!
| Averch-Johnson Utility Metric (w=20, r=10%, s=14%, lambda=0.50) | Formula | Verified Output |
|---|---|---|
| Cost-Minimizing Capital-Labor Ratio | (w / r) * (alpha / beta) | 200.0000 |
| Shadow Cost of Capital (r_eff) | r - (lambda / (1 - lambda)) * (s - r) | 0.0600 (6.00% < 10.00% WACC) |
| Regulated Averch-Johnson (K / L)* | (w / r_eff) * (alpha / beta) | 333.3333 |
| Capital Gold-Plating Excess (%) | ((K/L)* / (K/L)_min) - 1 | +0.6667 (+66.67% Over-Capitalized!) |
Averch-Johnson Shadow Cost of Capital & Regulated K/L Ratio Formula
Validate w > 0, 0 < r <= s, alpha, beta > 0, 0 <= lambda < 1, and interior feasibility r_eff > 0.
=LET(w_lb, B2, r_wc, B3, s_al, B4, al_k, B5, bt_l, B6, lm_c, B7, IF(OR(w_lb <= 0, r_wc <= 0, s_al < r_wc, al_k <= 0, bt_l <= 0, lm_c < 0, lm_c >= 1), "Invalid AJ Input", LET(r_ef, r_wc - (lm_c / (1 - lm_c)) * (s_al - r_wc), IF(r_ef <= 0, "Non-Interior AJ Corner (r_eff <= 0)", ROUND((w_lb / r_ef) * (al_k / bt_l), 4)))))Proportional Gold-Plating Distortion ((r / r_eff) - 1) Formula
Test setting Allowed_RoR_s = True_WACC_r = 0.10 (or switching to price-cap regulation where lambda = 0): gold-plating excess vanishes to 0.0000!
=IF(ISTEXT(E3), E3, ROUND((E3 / E2) - 1, 4))Try the example
Use the original values or change them to test your understanding.