The Averch-Johnson Effect

H. Averch and L. Johnson. "The Behavior of the Firm Under Regulatory Constraint," American Economic Review, December 1962.

Averch and Johnson developed a model to illustrate that public regulation creates an incentive for the firm to over-invest in tangible assets. Since the "allowed profit" is based on the rate base (RB), the firm has an incentive to augment its capital stock.

Over-investment (or over-capitalization) has obvious implications for rates paid by consumers and also for the efficiency of resource

allocation.

Choose quantities of capital and labor to maximize the following profit ( ) function:

is profitR is the revenue functionK is the quantity of capitalL is the quantity of laborw is the wage rater is the cost of capital

s is the allowed rate of return

The model

rKwLLKR ),( [1]

sK

wLLKR

),(subject to

[2]

Averch Johnson assumption: s > r

This would seem a logical assumption--why would the firm take positions in

tangible capital goods (like nuclear plants) if r > s?

Meaning the allowed rate of return on capital (expressed in dollars per unit of capital per time period) exceeds the cost of capital (also dollars per unit of capital is the same time interval).

Maximizing [1] subject to [2] using the Lagrangean method yields the following first order condition:

w

r

MP

MP

L

K

1

)( rs

MPk is the marginal product of capital

MPL is the marginal product of labor

is the Langrangean multiplier (a constant).

[3]

[4]

Note that:

It can be shown that > 0

We assume that s > r

Therefore, > 0The regulatory constraint in effect makes capital cheaper relative to labor and therefore induces the firm to substitute capital for labor.

Averch Johnson effect illustrated using the theory of the firm

Definitions:

•An isoquant (meaning “equal quantity”) is a collection of points giving all possible labor/capital combinations that yield the same quantity of output.

•An isocost (meaning “equal cost”) is a collection of points giving all possible labor/capital combinations that enatil the same cost.

Q = 100

Q = 300

Q = 200

Lab

or (

un

its)

Capital (units)0

Isoquants

is a labor intensive technique

is a capital intensive technique

Lab

or (

un

its )

Capital (units)0 20 25

100

Intercept = C/w = $1000/10

Intercept = C/r = $1000/50

Slope = -w/r

r = 40

Let C = wK + rK, where:

C = $1,000w = $10r = $50

The Averch Johnson Effect

0

Capital (units)

Lab

or (

unit

s)

M

M’

isoquant

E

A

Slope = -r/w

Slope = -(r - )/w

E is an efficient point

A is the Averch Johnson point

N

N’