Averch–Johnson Effect

Averch–Johnson Effect (often abbreviated as the A–J Effect or rate-base padding) is a foundational theorem in regulatory economics and industrial organization demonstrating that when a public utility regulator constrains a Monopoly to earn no more than a fixed "fair" rate of return (s) on its physical capital stock (K), and that allowed return s exceeds the firm's true market cost of capital (r), the regulated firm has a systematic incentive to over-invest in capital relative to labor (L), operating with an inefficiently high capital-labor ratio (K ÷ L) for whatever level of output it produces. Published by Harvey Averch and Leland L. Johnson in the American Economic Review in 1962 ("Behavior of the Firm Under Regulatory Constraint"), the theorem is a centerpiece of Business & Economics Theory that explains "gold-plating" in regulated electricity, telecommunications, gas, and water utilities and motivated the late-twentieth-century regulatory shift toward incentive-based price-cap regulation.

Public utilities such as electric power grids, local water distribution networks, and landline telecommunications pipelines exhibit large fixed infrastructure costs and declining average cost over the relevant range of market demand—the defining characteristic of a natural monopoly. Because an unregulated monopolist restricts output and charges a price above marginal cost, generating a deadweight welfare loss (Harberger Triangle), governments historically established public utility commissions to regulate utility prices while allowing private ownership.

Under traditional rate-of-return (cost-of-service) regulation, the commission audits the utility's operating expenses (wages wL, fuel, and maintenance) and values the utility's physical capital stock—the rate base (K)—to set tariffs such that total revenue R(K, L) covers operating costs plus an allowed rate of return s per unit of capital:

Equivalently, subtracting the true economic cost of capital rK from both sides shows that the firm's pure economic profit π(K, L) = R(K, L) − wL − rK is bounded above by a ceiling that grows linearly with the size of the physical capital stock K:

Here, the parameter ordering across regulatory regimes satisfies:

where r is the market cost of capital (the Opportunity Cost of investor funds), s is the regulator's allowed rate of return, and r_M is the unconstrained monopoly rate of return. If s < r, the firm cannot cover its cost of capital and exits in the long run; if s ≥ r_M, the regulatory constraint does not bind. In the relevant interior regime r < s < r_M, each additional dollar of physical capital K added to the rate base expands the firm's legally permissible profit ceiling by (s − r) > 0 dollars.

Consider a monopolist with a twice-differentiable production function Q = F(K, L) (such as a Cobb–Douglas Production Function) facing a downward-sloping inverse demand schedule P(Q), yielding total revenue R(K, L) = P(F(K, L)) × F(K, L). Input prices for capital (r) and labor (w) are competitive and constant.

Unconstrained Cost-Minimizing Benchmark

An unconstrained firm (whether a competitive firm or an unregulated monopolist) minimizes the cost rK + wL of producing any chosen output level Q₀ by equating the Marginal Rate of Technical Substitution (MRTS) between labor and capital to the market factor-price ratio:

where F_K = ∂F ÷ ∂K and F_L = ∂F ÷ ∂L are the marginal physical products of capital and labor, and R_K = MR × F_K and R_L = MR × F_L are the marginal revenue products.

The Averch–Johnson Lagrangian Problem

Under a binding rate-of-return constraint (r < s < r_M), the regulated utility maximizes economic profit subject to the regulatory ceiling:

Forming the Lagrangian function ℒ(K, L, λ) with Kuhn–Tucker multiplier λ establishes:

Differentiating ℒ with respect to L, K, and λ at an interior binding solution yields the first-order conditions:

1. Labor Condition (∂ℒ ÷ ∂L = 0):

Thus, provided λ ≠ 1, the regulated firm hires labor up to the normal condition where the marginal revenue product of labor equals the wage rate w.

1. Capital Condition (∂ℒ ÷ ∂K = 0):

As proved rigorously by Akira Takayama (1969) and William Baumol and Alvin Klevorick (1970), when the constraint binds in the regular region where R_K < s, the shadow multiplier λ lies inside the open unit interval:

Dividing the capital condition by (1 − λ) > 0 and rearranging expresses the marginal revenue product of capital as:

where α ≡ [λ ÷ (1 − λ)] × (s − r) > 0 is the implicit regulatory subsidy to capital. Dividing the capital condition (R_K = r − α) by the labor condition (R_L = w) yields the Averch–Johnson Distortion Equation:

Because the regulated firm equates its marginal rate of technical substitution to (r − α) ÷ w rather than the true social factor-price ratio r ÷ w, the firm treats capital as if its private shadow price were artificially cheap (r − α < r). By diminishing marginal rate of technical substitution along a convex isoquant, the utility moves downward and to the right along the isoquant, selecting a capital-labor ratio (K ÷ L)_AJ higher than the cost-minimizing ratio (K ÷ L)^*.

The Baumol–Klevorick (1970) Paradox as s Approaches r

A counterintuitive comparative-statics result proved by Takayama (1969) and Baumol and Klevorick (1970) is that tightening the regulator's allowed rate of return s closer to the true cost of capital r (ds < 0 with s > r) actually worsens the capital-labor distortion (d(K ÷ L) ÷ ds < 0). As the profit margin per unit of capital (s − r) shrinks, the profit-maximizing utility must expand its physical rate base K even more substantially to capture the remaining profit available under its demand curve, until the constraint hits the zero-profit locus at s = r where any feasible input bundle becomes indifferent.

Real-World "Gold-Plating" and Peak-Load Bias

In practice, the Averch–Johnson Effect manifests through several institutional channels in regulated utilities:

• Capital-Intensive Generation Choices: Electric utilities historically favored capital-heavy nuclear, hydroelectric, or coal baseload plants (which enter the rate base K) over less capital-intensive gas turbines or purchased power agreements (which are passed through at zero markup as operating expenses).
• Excess Standby Capacity and Reliability Padding: Utilities maintain higher reserve margins and more redundant transmission hardware than warranted by cost-benefit analysis, particularly to serve peak-load demand (Bailey and White, 1974).
• Cross-Subsidization into Competitive Markets: As Averch and Johnson (1962) showed in the second half of their paper, a utility regulated across an aggregate multi-market rate base has an incentive to enter adjacent competitive markets even at prices below long-run marginal cost, because the extra capital installed in the competitive subsidiary expands the total rate base K and permits higher monopoly profits to be extracted from captive core ratepayers—a primary rationale for the 1984 breakup of the Bell System (AT&T).

Transition to RPI − X Price-Cap Regulation

To eliminate the Averch–Johnson bias without sacrificing consumer price protection, Stephen Littlechild (1983) designed RPI − X price-cap regulation for UK telecommunications and electric utilities. By capping the rate of growth of a basket of utility output prices at the retail price index minus an exogenous productivity offset X—independently of the firm's capital stock K—price-cap regulation decouples allowed revenue from the rate base, restoring the cost-minimizing tangency F_K ÷ F_L = r ÷ w and achieving higher Pareto Efficiency.

Does the Averch–Johnson Effect mean the regulated firm buys unproductive "useless" capital?

In the baseline Averch–Johnson model with a single-valued production function, the utility does not purchase purely unproductive "phantom" capital (F_K = 0) unless λ > r ÷ s; rather, it installs productive capital to a point where its marginal revenue product is positive or slightly negative (R_K = r − α < r), substituting capital for labor along a productive isoquant. Only when the regulator permits genuinely idle assets into the rate base does pure waste ("padding") occur.

How does regulatory lag mitigate the Averch–Johnson Effect?

As Elizabeth Bailey and Roger Coleman (1971) demonstrated, rate cases do not occur continuously; instead, there is a regulatory lag of several years between tariff reviews. During the interval between rate hearings, the utility's output prices are temporarily fixed, so the firm retains 100% of any cost savings from choosing an efficient input mix, dampening the A–J over-capitalization incentive.

What did empirical econometric tests find in the U.S. electric power industry?

Classic econometric studies of steam-electric power generation by Léon Courville (1974), H. Craig Petersen (1975), and Robert Spann (1974) estimated production and cost functions for investor-owned utilities under state rate-of-return regulation, finding that the shadow price ratio of capital to labor was significantly below the market factor-price ratio r ÷ w and that over-capitalization increased production costs by 3% to 12%.

1. Averch, H., & Johnson, L. L. (1962). "Behavior of the Firm Under Regulatory Constraint." American Economic Review, 52(5), 1052–1069. https://www.jstor.org/stable/1812181
2. Baumol, W. J., & Klevorick, A. K. (1970). "Input Choices and Rate-of-Return Regulation: An Overview of the Discussion." Bell Journal of Economics and Management Science, 1(2), 162–190. https://doi.org/10.2307/3003179
3. Takayama, A. (1969). "Behavior of the Firm Under Regulatory Constraint." American Economic Review, 59(3), 255–260. https://www.jstor.org/stable/1808955
4. Courville, L. (1974). "Regulation and Efficiency in the Electric Utility Industry." Bell Journal of Economics and Management Science, 5(1), 53–74. https://doi.org/10.2307/3003092
5. Joskow, P. L. (2007). "Regulation of Natural Monopolies." In A. M. Polinsky & S. Shavell (Eds.), Handbook of Law and Economics (Vol. 2, pp. 1227–1348). Elsevier. https://doi.org/10.1016/S1574-0730(07)02016-602016-6)