The Averch-Johnson Effect

1
The Averch-Johnson Effect
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.
H. Averch and L. Johnson. "The Behavior of the
Firm Under Regulatory Constraint," American
Economic Review, December 1962.
2
Over-investment (or over-capitalization) has
obvious implications for rates paid by consumers
and also for the efficiency of resource
allocation.
3
The model
Choose quantities of capital and labor to
maximize the following profit (? ) function
1
subject to
2
? is profitR is the revenue functionK is the
quantity of capitalL is the quantity of laborw
is the wage rater is the cost of capitals is
the allowed rate of return
4
Averch Johnson assumption s gt r
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).
This would seem a logical assumption--why would
the firm take positions in tangible capital goods
(like nuclear plants) if r gt s?
5
Maximizing 1 subject to 2 using the
Lagrangean method yields the following first
order condition
3
Note that
4
MPk is the marginal product of capitalMPL is the
marginal product of laborl is the Langrangean
multiplier (a constant).
6
Moral of the story

• It can be shown that ? gt 0
• We assume that s gt r
• Therefore, ? gt 0

The regulatory constraint in effect makes capital
cheaper relative to labor and therefore induces
the firm to substitute capital for labor.
7
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.

8
Isoquants
Labor (units)
? is a labor intensive technique
?
? is a capital intensive technique
?
Q 300
Q 200
Q 100
0
Capital (units)
9
Intercept C/w 1000/10
Labor (units)
100
Let C wK rK, where C 1,000w 10r
50
Slope -w/r
Intercept C/r 1000/50
r 40
0
20
25
Capital (units)
10
The Averch Johnson Effect
E is an efficient point
A is the Averch Johnson point
Labor (units)
M
E
N
Slope -(r - ?)/w
A
Slope -r/w
isoquant
0
M
N
Capital (units)