The Entrepreneurial
Critique of the Optimization Paradigm
ROBERT F.
MULLIGAN
828-227-3329
Associate
Professor of Economics, Department of Business Computer
Information Systems & Economics,
Abstract.
The optimization paradigm in neoclassical economics is defined and
criticized. Although the optimization
paradigm provides the foundation for most mathematical formalism in modern
technical economics, the paradigm rest in turn on extreme and extremely
unrealistic information assumptions. No
scope for entrepreneurial activity is admitted.
This paper argues that entrepreneurial change is one of the most basic
ingredients for understanding the functioning of markets and the coordination
of economic activity. Several extensions
of the standard model are presented and discussed. Alternative views of market equilibrium
offered by Schumpeter and Kirzner are developed, and the relationship between
the two competing views of equilibrium is examined.
Key words: optimization paradigm, entrepreneur,
resource allocation, productive activity
JEL classification: B41, C61, C62, D11, D40.
"What we cannot speak about we must
pass over in silence."
Ludwig Wittgenstein[1]
This paper
criticizes the optimization paradigm in neoclassical microeconomics with
respect to its treatment of entrepreneurship.
Conventional cost minimization-profit maximization exercises central to
modern neoclassical economics virtually ignore entrepreneurial action. Entrepreneurial managers should be understood
as seeking to (a) adjust the production process to extract more output from
each input or more output from the same level of inputs, (b) switch inputs or
combine new inputs with those already used to produce more or cheaper output,
(c) devise strategies to sell their output or some part of it for a higher
price, (d) attract new buyers and devise new uses for the output, and (e) lower
the costs of their inputs. In the theory
of the consumer, the optimization exercise ignores entrepreneurial innovations
which imply changes in the (a) number of utility function arguments, (b) form
of the utility function, (c) consumer income, (d) prices of consumed goods, and
(e) quality of consumed goods. More
fundamentally, the optimization paradigm ignores entrepreneurial consumers'
alertness to these opportunities to costlessly improve the satisfaction of
their wants.
In addition to
developing an Austrian critique of the prevailing orthodoxy, this paper also
offers some modest extensions which partially address the critique, though they
fail to overcome it. It is hoped that as
the optimization paradigm continues to be central to what is taught in graduate
economics programs and much economic research, its practitioners will come to
accept a more mature understanding of its limitations.
1. Introduction
The optimization
paradigm in neoclassical microeconomics is the modeling of economic behavior as
a series of constrained and unconstrained optimization problems. Market participants are thought of as
knowingly optimizing known objective functions: minimizing cost, maximizing
output, maximizing profit, or maximizing utility, subject to known constraints
(Robbins 1935). However, analytical
functions can never be more than imperfect analogues of the processes of
producing output or obtaining satisfaction through consumption[2]. In a sense, considered as mathematical
models, they do not purport to be anything more. The optimization paradigm is based on
fundamental assumptions precluding the possibility of entrepreneurial activity.
The uncertainty entrepreneurs overcome and exploit to earn entrepreneurial profits
is removed by assumption.
The optimization
paradigm is usually presented through graphical analysis at the undergraduate
level, while graduate courses are typically more formalized (Samuleson 1947,
Debreu 1959, Silberberg 1978, Henderson and Quandt 1980, Chiang 1984, Varian
1984, Takayama 1985). The optimization
paradigm assumes away the entrepreneur and treats all the data of the market as
perfectly known in advance. This
approach fundamentally misrepresents the nature of market competition. The Austrian school has always been skeptical
of mathematical formalism: "in the imaginary construction of an evenly
rotating system nobody is an entrepreneur and speculator. In any real and living economy every actor is
always an entrepreneur and speculator...." (Mises 1949: 252). Entrepreneurial action sometimes improves
market coordination and moves the market toward a hypothetical equilibrium, but
also sometimes increases the level of discoordination, moving the market
further away from idealized equilibrium.
Thus entrepreneurship cannot be defined exclusively in terms of its
relation to either equilibria or coordination among economic planners.
<<Table 1 about here.>>
Entrepreneurial
action is necessarily multifaceted and defies simple quantification. Blaug (1998: 227) cites several different
historical views of entrepreneurship.
Entrepreneurial action includes arbitrage (Cantillon 1755), coordination
(Say 1803; Kirzner 1973), innovation (Schumpeter 1934), uncertainty-bearing
(Knight 1921), and most recently (Casson 1982, 1985) increasing the range of
available judgments on resource allocation. There is no simple way to
incorporate all modes of entrepreneurship in an optimization problem. Entrepreneurs change objective and constraint
functions, subverting the analytic character of the optimization paradigm.
The basic
problem with the optimization paradigm may be formulated as an unwarranted
assumption that all information summarized in market prices, including the
preferences of others, is known to agents in advance of their decision. Thus the optimization model of economic
decision-making is perfectly deterministic. However prices cannot be known with
certainty until after an exchange
occurs. In fact entrepreneurs do not
optimize with respect to any objectively knowable information set.
A more
meaningful way to consider entrepreneurial behavior is that it proceeds
experimentally and so generates the information of the market, which can never
be known in advance of a voluntary exchange, but only after one takes place
(Buchanan 1986), and only as having no necessary implications for potential
subsequent exchanges. Once an individual
has bought or sold a good or service at a certain price, special to the time,
place, and parties to the transaction, unalterable historical information of
the market has been created. But this
information does not necessarily have any significance for the future, and thus
objective knowledge cannot form the basis for market participants' optimizing
behavior.
Real behavior is
better captured through less precise "rules of thumb" than through
the supposedly rigorous optimization paradigm.
It seems clear to even casual observers that human behavior is not based
on mathematical optimization, either underlying or explicit. Because much human knowledge is tacit, and
thus inherently decentralized and subjective, it becomes particularly difficult
to justify assumptions of perfect knowledge and foresight which underlie the
optimization paradigm.
The rest of this
paper is organized as follows. Section two
discusses the entrepreneur emphasizing the Austrian tradition. Section three presents a discussion of cost
minimization. Section four presents a parallel discussion of profit
maximization. Section five introduces a
theory of the entrepreneurial consumer.
Section six discusses the distinction between Schumpeter's and Kirzner's
definitions of entrepreneurial action.
Finally, section seven presents concluding remarks.
2. The Entrepreneur's Function in Society
Schumpeter
(1934) identifies five types of entrepreneurial innovation (1) introducing new
outputs or improving the quality of existing outputs, (2) introducing new
methods of production, (3) opening new output markets, especially new export
markets, (4) finding new sources of supply of raw materials or intermediate
inputs, and (5) creating new kinds of industrial organizations. To Schumpeter, entrepreneurs are not
inventors but decision makers who allocate resources to exploit inventions; they are not risk-bearing capitalists but
borrow funds from the capitalists to finance their innovations. Casson (1987: 151) notes that Schumpeterian
entrepreneurs are defined by their managerial or decision-making role.
Mises (1949:
253) defines the entrepreneur as "acting man exclusively seen from the
aspect of the uncertainty inherent in every action." The entrepreneur is not merely a particular
human archetype, but a category of catallactic action (ibid. 251). To Mises uncertainty is everywhere and
consequently, everyone is an entrepreneur.
But in the optimization paradigm, uncertainty has been assumed away
along with the entrepreneur.
Entrepreneurial action always responds to an uncertain future, facing
uncertainties of future consumer demand, changes in demand and supply in factor
markets, and differences in the ability of other entrepreneurs to foresee with
a compatible vision, the prerequisite for mutually compatible plans (Mises 1949:
212-214). The entrepreneur always faces
uncertainty because production takes time, so any entrepreneurial action necessarily
involves "speculation in the anticipation of future events" (Greaves
1974: 39). Lachmann (1986: 65-70,
116-117, ) also emphasizes that entrepreneurial action responds to uncertainty
about the future.
Much of
Kirzner's (1973, 1979, 1984a, 1997) work on entrepreneurship can be
reformulated as a detailed critique of the optimization paradigm. Kirzner and Hayek stress the problem of
dispersed knowledge given to no one in its entirety (Hayek 1949: 77-78), a
problem whose "extent and seriousness cannot be known in advance,"
"arising out of unawareness of one's ignorance" (Kirzner 1984b:
162). Mises emphasizes the
entrepreneurial response to, and exploitation of, market information:
"entrepreneur means acting man in regard to the changes occurring in the
data of the market" (Mises 1949: 254).
The Misesian entrepreneur is alert to arbitrage opportunities which
occur when prices in resource markets are not adjusted to prices in the product
markets (Kirzner 1973: 85). This is a
special case of Hayek's (1949) problem of dispersed knowledge.
In
contrast, in some areas Hayek's (1973: 27) understanding of the entrepreneur is
particularly sterile and defective[3]. In his view, business firms are designed
artifacts like radios, toasters, or telescopes.
Once the laws of economics are put in place, entrepreneurs exploit them
to construct business organizations much the same way engineers employ physical
laws to construct machines. Hayek's
understanding of firm organization proceeds according to a military model,
where the manager issues orders that are followed without question or
exception. Hayek recognizes that the
entrepreneur is endogenous to the firm, but he fails to perceive that once a
business enterprise is set up, its employees enjoy some degree of autonomy, and
the firm in effect takes on a life of its own.
3. The Entrepreneurial Producer I: Cost
Minimization
In the
optimization paradigm, the theory of the firm provides dual and equivalent cost
minimization and profit maximization problems.
Managers exploit a given and static production technology and a given
and static vector of resource and output prices to transform a set of given
inputs into a given output. Furthermore,
the market structure is also given, when in fact it results from the action of
entrepreneurial innovators. Entrepreneurial
action ignored by the optimization paradigm includes seeking to (a) adjust the
production process to extract more output from each input or more output from
the same level of inputs, (b) switch inputs or combine new inputs with those
already used to produce more or cheaper output, (c) devise strategies to sell
their output or some part of it for a higher price, (d) attract new buyers and
devise new uses for the output, and (e) lower the costs of their inputs.
It might be
argued that theories of market segmentation and product differentiation allow
for item (c), but this is only possible if the market is structured in a way
that prevents firms from facing perfectly elastic demand. In theory, market structure is predetermined
by assumption; in reality it results
from the behavior of market participants.
In reformulating the Walrasian theory of perfect competition, Makowski
and Ostroy (2001: 480) recognize "(1) prices are not exogenously given,
they arise from bargaining," and "(2) the set of active markets is
not exogenously given, it results from innovation." Since the conventional view is that
entrepreneurs work primarily through firms, the neoclassical theory of the
firm's inability to accommodate entrepreneurial action is a major shortcoming.
3.1
The Standard Cost Minimization Problem
One way to
formulate the firm's conventional optimization problem is to maximize output
subject to a fixed cost constraint. The objective
function for optimization is the production function relating the inputs x1
and x2 to the quantity of output q, and is given
as
q = f(x1, x2)
though, unlike
the consumer's utility function, the production function always has a
cardinally-measurable physical or value output.
Nevertheless, it remains debatable whether the production process can
ever be meaningfully captured by an analytic function purporting to be, at
best, an approximation. The possibility
of using additional inputs x3
through xn is
ignored. The key Austrian insight that
production occurs over time (Menger 1871: 152[4];
Hayek 1931, 1933, 1935, 1939, 1941) is ignored.
Non-Austrian economists are hardly ignorant of this fact, but theorize
as if they were.
The constraint
function is the producer's cost constraint which is conventionally given as
C0 = r1x1
+ r2x2 + b
where r1
and r2 are the resource prices of input resources X1
and X2, b is the cost of fixed inputs, and C0 is the fixed total cost. Again, the cost constraint is assumed given
and known in advance. No scope for
entrepreneurial discovery is permitted (Kirzner 1984b: 154). Mises notes
in the imaginary construction of the evenly
rotating economy there is no room left for entrepreneurial activity, because
this construction eliminates any change of data that could affect prices. As soon as one abandons this assumption of
rigidity of data, one finds that action must needs be affected by every change
in the data. As action necessarily is
directed toward influencing a future state of affairs, even if sometimes only
the immediate future of the next instant, it is affected by every incorrectly
anticipated change in the data occurring in the period of time between its
beginning and the end of the period for which it aimed to provide (period of
provision). Thus the outcome of action
is always uncertain. Action is always
speculation. (1949: 252)
The contrasting view of neoclassical microeconomics is that action is
always optimization, and that the "correct" outcome is always
predetermined by the unalterable data of the market. The optimization paradigm fails to recognize
the scope for uncertainty, ignorance, and risk.
The cost constraint also suffers from omission of the same arguments x3
through xn
as the production function, as well as their prices r3 through
rn. One means for
exercising entrepreneurial action is in obtaining lower input prices[5] r1
and r2, or r1 through rn,
or a combination of different inputs that minimizes total cost (Schumpeter
1934: 133-135). Entrepreneurial
alertness might also be exercised in seeking to reduce the "fixed"
cost b. Since b is only
fixed by construction, alert entrepreneurs should seek ways of reducing it
whenever possible. The producer,
having chosen C0 or had it imposed externally, seeks to
produce as much output q as possible.
The constrained output maximization problem is constructed as
V = f(x1, x2)
+ μ(C0 - r1x1 - r2x2
- b)
where μ ≠ 0 is an undetermined Lagrange multiplier. Finding the first partial derivatives of V
with respect to x1, x2, and
μ, and setting them equal to zero:
∂ V |
= |
f1
– μ r1 = 0 |
|
∂ x1 |
||
|
∂ V |
= |
f2
– μ r2 = 0 |
|
∂ x2 |
||
|
∂ V |
= |
C0 - r1x1
- r2x2 - b = 0 |
|
∂ μ |
Algebraic manipulation yields the familiar relation[6]
|
f1 |
= |
r1 |
|
f2 |
r2 |
which states that, at a cost minimum, the ratio of the marginal
products of resource inputs X1 and X2 must be equal
to the ratio between their prices. The
minimum found through optimization is subject to the constraint that the
quantities of other inputs X3 through Xn have been
arbitrarily set at zero. These ratios
between the marginal products and the resource prices define the rate of
technical substitution (RTS) between X1 and X2. The first-order conditions can also be
written as
|
μ = |
f1 |
= |
f2 |
|
r1 |
r2 |
indicating the contribution to output of the last dollar spent on each
input must equal the Lagrange multiplier μ, which is thus the first
derivative of output with respect to cost C with prices r1 and r2 constant and
resource quantities x1 and x2 allowed to
vary.
The cost
minimization problem can be made more realistic by allowing total cost to
vary. When C is allowed to vary,
the differential of the cost equation is
dC = r1dx1 + r2dx2
The fixed cost b
drops out, though if entrepreneurial search aims at lowering b, it
should not drop out of the first-order conditions.
The firm's
problem may also be formulated as minimizing a variable cost function subject
to the constraint that a prescribed quantity of output must be produced with
the given technology described by the production function. The constrained cost minimization problem is
expressed as
Z = r1x1 + r2x2
+ b + λ[q0 - f(x1, x2)]
and the partial
derivatives of Z are set equal to zero to find the first-order
conditions:
|
∂ Z |
= |
r1
– λ f1 = 0 |
|
∂ x1 |
||
|
∂ Z |
= |
r2
– λ f2 = 0 |
|
∂ x2 |
||
|
∂ Z |
= |
q0 – f(x1,x2) = 0 |
|
∂ λ |
The first-order
conditions allow us to solve for the following relations,
|
f1 |
= |
r1 |
|
or |
|
1 |
= |
f1 |
= |
f2 |
|
or |
|
RTS = |
r1 |
|
f2 |
r2 |
|
|
λ |
r1 |
r2 |
|
|
r2 |
The Lagrange
multipliers λ and μ are reciprocals. λ gives the first derivative of
cost with respect to output, that is, the marginal cost[7].
3.2
Limitations of Standard Cost Minimization
The optimization
paradigm is based on the principle of knowingly optimizing a known objective
function subject to known constraints, removing much of the uncertainty with
which real-world market participants have to contend. The standard model of perfect competition
imposes extreme, and extremely unrealistic, information requirements (Makowski
and Ostroy 2001: 480). Furthermore, analytical functions can never be more than
imperfect analogues of the processes of producing output or obtaining
satisfaction through consumption, and the Austrian school has always criticized
excessive mathematical formalism. Limitations of the optimization paradigm
should be recognized in that the true objective function may not be known with
certainty to market participants, and may not be expressible as an analytic
function, even if "known" (Kirzner 1984b: 154).
An alert
entrepreneur would always seek to discover ways to adjust the production
process to extract more output from each input, or equivalently, extract the
same level of output from fewer inputs (Schumpeter 1934: 129-133). Instead, the optimization problem assumes a
static, given technology. The
optimization problem is necessarily untenable unless the technology has been
optimized in advance. In reality,
production technology results from the creative process of human action
and entrepreneurial discovery.
Technology is created, not given.[8]
(a) Static Input
Set
Entrepreneurial
alertness might also be applied in discovering new inputs X3 and
X4 to either substitute or complement X1 and
X2 in producing a given output.
Because the optimization paradigm arbitrarily excludes inputs X3 through Xn, a more realistic optimum
is defined by
|
μ = |
f1 |
= |
f2 |
= |
... |
= |
fn |
|
r1 |
r2 |
rn |
This more global
optimum still assumes a pre-determined and static technology, and can never be
fully realized, as the scope for entrepreneurial alertness in discovering new
inputs is inexhaustible. In neoclassical
microeconomics the optimization problem is constrained by arbitrarily setting
the quantities of potential inputs X3 through Xn
equal to zero. Even in the context of
the optimization paradigm, imposing this indefinite number of constraints,
though analytically necessary, is also necessarily unrealistic. Also this
exercise, even as modified, ignores the possible choice of different outputs
(Schumpeter 1934: 134).
Entrepreneurial
managers may switch inputs, use new inputs, or both to produce cheaper
output. This is not an optimization
process. If the production technology A
which is assumed uses inputs a and b, and a different production technology B
uses c and d, and can produce the same output at a lower unit cost, obviously
technology B should be used, but the optimization paradigm assumes this is
known in advance. In fact it can only be
discovered through experience, trial-and-error, entrepreneurial alertness, discovery,
etc. These less tractable transactions
of economic behavior cannot be modeled as optimization processes because they
cannot meaningfully be represented as having predetermined outcomes.
Commitment to
the more expensive, less efficient, technology A may preclude discovery of
benefits potentially offered by technology B.
There are always better versus worse ways to combine inputs, but never a
final best, the optimum, which forever precludes discovery of improved
technology. This holds even when the
input set is fixed.
(b) Information
Constraints
One fault of the
optimization paradigm is that it assumes as given both the objective function
and constraints. Provided this
information is attainable, it can only be uncovered through extensive search
and entrepreneurial alertness. Perhaps
the most severe criticism against the optimization paradigm is that an
entrepreneurial producer can carry out a valid optimization exercise based on
unique, subjective, and fallible expectations of prices at which the inputs can
be bought and output sold (Kirzner 1990: 167).
If these expectations are not realized, the producer may lose money in
spite of having optimized, because market participants often fail to optimize with
respect to their true circumstances.
True circumstances can only be known ex post and can only be discovered
through experience, but by then it is too late.
This first kind of knowledge problem (Kirzner's Knowledge Problem A)
causes planned exchanges to be impossible to fulfill. Kirzner notes that these kinds of problems
are self-correcting (Kirzner 1990: 169-171), as market participants either
adjust their plans to recognize the realities of the market, or withdraw from
the market.
It is also
possible for the optimization exercise to lead to the erroneous conclusions
that inputs cannot be obtained, or output sold, at sufficiently low or high
prices, or that production technology, input quality, or consumer demand for
the output, are actually better than anticipated by entrepreneurial planners
(Kirzner 1990: 168-9). In these cases,
(Kirzner's Knowledge Problem B), exchanges which are theoretically feasible,
and could be seen ex post to have been feasible, are never planned or
undertaken, because market participants are unaware of the feasibility of the
potential exchanges. Entrepreneurs
always seek to discover such opportunities, but many must go undiscovered. These kinds of problems are not
self-correcting, and await entrepreneurial discovery before anyone can be aware
of them. The entrepreneur can profit by
uncovering, and remedying, instances of Knowledge Problem B.
These objections
based on Kirzner's two knowledge problems can be given an alternative
formulation, drawing mainly from Hayek (1949) and Kirzner (1984a, 1984b, 1990):
the information set assumed by the optimization paradigm does not exist in
reality. No person possesses it in its
totality, but the optimization paradigm assumes perfect information shared by
all market participants. In reality, it
is more accurate to suggest that each market participant possesses some
relevant information, much of which is purely subjective. Much of this information is held exclusively
by a certain individual, for example, that individual's subjective preferences
or his or her plans for future consumption and production. Individuals also differ in their alertness,
both in terms of intensity and application (Kirzner 1979: 170). Entrepreneurs overcome the social problem of
information dispersal whenever they generate flows of information that
stimulate revision of uncoordinated decisions toward greater mutual
coordination (Kirzner 1984a: 147) moving the market toward a never-realized
equilibrium state. The very concept of
market equilibrium is merely an analytical convenience with little practical
relevance (Nelson and Winter 1982; Makowski and Ostroy 2001).
Prices summarize
relevant information which would otherwise be useless to market participants in
satisfying their wants, but the inadequacies in market prices also create the
profit-and-loss incentives for entrepreneurs to adjust prices (Kirzner 1984a:
149). A price may summarize economic
information regarding the supply and demand conditions in the relevant markets,
without signaling whether the price represents an equilibrium or a disequilibrium. Entrepreneurs compete in adjusting prices in
a "competitive process which digs out what is in fact
discovered" (Kirzner 1984a: 150).
The competitive process Hayek (1978: 180) describes, where
"competition is valuable only because, and so far as, its results are
unpredictable and on the whole different from those which anyone has, or could
have, deliberately aimed at," is utterly incompatible with the
optimization paradigm.
Kirzner's
(1984b: 160) view is that disequilibrium prices offer pure profit opportunities
for alert entrepreneurs who can arbitrage among different prices temporarily
prevailing in different markets. This
incentive allows entrepreneurs to effect adjustment of the disequilibrium price
vector towards equilibrium. Although, by
construction, an equilibrium is never reached, and if it were reached, is never
persistent, the Kirznerian entrepreneur always acts to lessen the extent of the
disequilibrium. The equilibrium which is approached constitutes a spontaneous
order, a level of coordination which results from human action but not from
human design (Hayek 1967). In contrast, a Schumpeterian entrepreneur moves the
market price vector away from equilibrium, by introducing new production
technologies, marketing and distribution media, and creating new plans which
increase the social dispersion of knowledge.
This distinction is explored more fully in section 6. Both kinds of entrepreneurship are ignored by
the optimization paradigm.
The
cost-minimization problem also fails to recognize the mode of entrepreneurial
action which occurs when a firm incurs additional production or selling costs
to make the product more desirable to the consumer (Kirzner 1973: 24). Schumpeter (1934: 135) mentions a kind of
entrepreneurship consisting of a search for new markets for an existing
product. In the optimization paradigm,
output quantity is the decision variable, and selling price is fixed along with
production technology. Increased
consumer preference can (a) justify increased production or selling costs, (b)
enable the firm to increase product price, and (c) be engineered by improving
product quality or marketing, but these issues are ignored. This category of entrepreneurial action
includes both increased production costs incurred to improve the subjective
quality of the product in consumers' eyes, and increased selling costs which
also aim at improving subjective quality.
Table 2
summarizes some of the limitations of the optimization paradigm and cites some
instances of more realistic, less restrictive, though also less mathematically
formalized, treatment of entrepreneurship given by the Austrian school.
<<Table 2 about here.>>
3.3
Extensions of Standard Cost Minimization
The production
function can be adapted to demonstrate entrepreneurial innovation, but only at
the cost of excessive delimitation of the choice faced by entrepreneurs.
(a) Additional
Inputs
Within the
optimization paradigm, additional arguments can be introduced to capture some,
though not all, potential for entrepreneurial action. At least three inputs must be included, each
of which can be considered a composite commodity: X1, the
bundle of inputs already used in producing output Q; X2, the
bundle of inputs subject to entrepreneurial discovery; and X3,
the bundle of inputs remaining undiscovered.
The constrained cost minimization problem is then
Z = r1x1 + r2x2
+ r3x3 + b + λ[q0 - f(x1, x2,
x3)]
and the partial
derivatives of Z are set equal to zero to find the first-order
conditions. The entrepreneur introduces
the innovation of violating the constraint that x2 = 0, but
the constraint remains that x3 = 0. Before entrepreneurial action, the first
order conditions are:
|
∂ Z |
= |
r1
– λ f1 = 0 |
|
∂ x1 |
||
|
∂ Z |
= |
q0 – f(x1, x2,
x3) = 0 |
|
∂ λ |
After
entrepreneurial innovation, the first order conditions become:
∂ Z |
= |
r1
– λ f1 = 0 |
|
∂ x1 |
||
|
∂ Z |
= |
r2
– λ f2 = 0 |
|
∂ x2 |
||
|
∂ Z |
= |
q0 – f(x1, x2,
x3) = 0 |
|
∂ λ |
Because a linear
restriction has been removed, the cost minimum after entrepreneurship must
always be below the before-entrepreneurship minimum, provided the constraint
was initially binding. Although this
optimization exercise, constructed to show the optimum before and after
entrepreneurial innovation, does capture one highly delimited, highly stylized
species of entrepreneurial action, many other kinds are not amenable to
analysis or representation in the optimization paradigm. The kind of predefined innovation modeled
here thus could not have been particularly valuable. No one learns anything terribly profound
about the process of entrepreneurial innovation from conducting such augmented
optimization exercises.
(b)
Technological Improvement
Suppose the
Cobb-Douglas production function q = f(x1, x2) = Cx1ax2b,
represents the production technology understood by managers and engineers prior
to an innovation. The prior, restricted
production function has the logarithmic form
ln q
= ln C + a ln x1 + b ln x2.
It is nested in
the more general transcendental-logarithmic (translog)[9]
form
ln q
= ln C + a ln x1 + b ln x2
+ c ln x12 + d ln x1x2
+ e ln x22.
Suppose a
particular entrepreneurial discovery consists of learning how to make use of
the second-order combinations of inputs in the translog. The resulting, more flexible, optimization
exercise will realize lower costs and higher profits, because restrictions on
the second order terms in the production function have been lifted.[10]
The difficulty
faced by the approach of modeling entrepreneurship as a removal of known
constraints is that if the less restrictive technology were known to the
entrepreneur in advance, they would have made full use of it. This construction can only be set up in an
environment where the before and after optima are both fully determined, and only
the entrepreneur is ignorant of the difference.
This is a particularly sterile way of modeling entrepreneurship, because
it constrains the entrepreneur exclusively to realizing artificial productivity
gains only as defined in advance by the theorist. Real world entrepreneurs recognize no such
constraints. Thus one way of expressing
the limitations the optimization paradigm imposes on modeling entrepreneurial
behavior is that it reduces entrepreneurship to an Easter egg hunt, where the
only prizes which can be uncovered by entrepreneurial discovery, must always be
defined in advance by the theorist. This
is a reductio ad absurdum against the optimization paradigm. The real state of affairs is that
entrepreneurs often uncover advances undreamed of by anyone else, or even by
themselves prior to the discovery.
4. The Entrepreneurial Producer II: Profit
Maximization
4.1
Standard Profit Maximization
The firm's cost
minimization problem is often represented by its dual. Since the entrepreneur is free to vary cost
along with output, the unconstrained profit maximization problem is written as
π = pq – C
where p
is the output price, assumed to be given.
Substituting in the production and cost functions, the profit function
is conventionally written as
π = p f(x1, x2)
– r1x1 - r2x2 - b
which is
maximized with respect to the choice variables x1 and x2. Again, limitations imposed by assumptions of
static technology and limited inputs invalidate the exercise. It should be emphasized that this
algebraically unconstrained optimization problem yields an economically
constrained solution, as a consequence of the assumptions which are
imposed. The first-order conditions[11]
are
|
∂ π |
= |
pf1
– r1 = 0 |
|
∂ x1 |
||
|
|
|
|
|
∂ π |
= |
pf2
– r2 = 0 |
|
∂ x2 |
which can be
written as
pf1 = r1 and pf2 = r2
The partial
derivatives of the production function with respect to the inputs are the
marginal products. Multiplied by price,
they provide the marginal revenue products, which are set equal to the input
prices r1 and r2 at the profit maximum.
This is the familiar condition that an input is used as long as its marginal
revenue product exceeds or equals its cost to the producer. However, the constraints that the quantities
of additional potential inputs X3 through Xn are fixed at
zero, guarantee this is a constrained optimum.
4.2
Limitations of Standard Profit Maximization
Because all
search activity is ignored, important features of economizing action are
disregarded and assumed away (Kirzner 1984: 156) For example, one forum for
entrepreneurial action is to seek monopoly ownership of a resource. This broad category of human action includes
both cornering the market for a particular input, and creation of any form of
intellectual property. Schumpeter (1934:
152) discusses how temporary monopoly profits always accrue to innovators. Entrepreneurs pursue such strategies all the
time. Because the optimization paradigm
assumes input and output prices as given, this mode of entrepreneurial action
is necessarily ignored. Entrepreneurs
should always desire to be monopolist resource owners because that allows them
to charge a higher price for their output than non-monopolists (Kirzner 1973:
21). Entrepreneurs also seek to increase
output price through becoming monopoly suppliers of the output, or
monopolistic-competitive suppliers, for example, through creating intellectual
property in their output, or through advertising. Recognizing that market structure is
determined by the competitive process of the market is part of Makowski and
Ostroy's (2001) reformulation of the Walrasian general equilibrium model of
perfect competition.
The price of
output is assumed given, thus the vector of prices is not permitted to adjust
to realize efficient allocation.
Producers are not permitted to adjust the type of output, which is also
assumed given. One obvious area for
entrepreneurial innovation is offering different kinds of output for sale to
consumers (Schumpeter 1934: 134-135).
The role flexible prices and their adjustments play in overcoming
Hayek's (1949) problem of dispersed knowledge and coordinating the plans of
producers and consumers, is similarly ignored (Kirzner 1984a: 139-140). Kirzner notes that equilibrium prices, if
they could persist, would signal market participants' plans to each other, and
thus guide future planning. In contrast,
disequilibrium prices signal to alert market participants how revised plans may
benefit market participants in the future.
In Kirzner's view, disequilibrium prices predominate, thus
entrepreneurial opportunities are everywhere.
Entrepreneurial consumers and producers who take advantage of these
disequilibrium prices move the market toward dynamic equilibria which are
generally never realized.
4.3 An Expanded Profit Maximization Exercise
The profit maximization exercise could be expanded to realize a more
global optimum, which would be represented by the n conditions
pf1 = r1, pf2
= r2, ... , pfn = rn
but it should be
emphasized that this optimum can never be realized. In reality, most of the n conditions
for a global profit maximum are necessarily invalidated. Economic agents' ignorance sets all but a few
of the xis equal to zero.
Thus the realized profit maximum is constrained. The solution also
assumes a fixed output price p and fixed input prices ri,
and the assumption of static production technology ensures the first and second
derivatives (fis and fijs) of the
production function are also constant. Entrepreneurial
activity can be described analytically as removing constraints on p, and
the xis, ris, fis, and fijs,
however, this fails to capture all entrepreneurial action, as entrepreneurs
also seek to produce those outputs which will yield the highest profits.
5. The Entrepreneurial Consumer
We do not
generally think of entrepreneurship outside firms. However, given Mises' definition,
"acting man exclusively seen from the aspect of the uncertainty inherent
in every action," (1966: 253) it is clear the consumer can be an
entrepreneur in the act of consumption.
In the neoclassical theory of the consumer, consumers maximize an
unknown and unobservable utility function, which must be specified in a finite
number of arguments, subject to a budget constraint. In a formal sense, an entrepreneurial
consumer would always be (a) trying out new arguments in the utility function,
as well as (b) trying out new ways of extracting additional utility from old
arguments. For example, entrepreneurial
consumers would experiment with new preference functions in an effort to shift
their indifference curves inward. The
neoclassical conception ignores both kinds of entrepreneurial behavior, by
assuming they have been carried out in advance.
To account for
the possibility of entrepreneurial consumption, the number of arguments in the
utility function and budget constraint must be made indefinite, as with the
cost and profit functions. In addition,
the entrepreneurial consumer is always trying to increase his or her income, as
well as searching for lower prices and higher quality arguments for
consumption. Entrepreneurial consumers
are alert to improving (a) the number of utility function arguments, (b) the
form of the utility function, (c) consumer income, (d) the prices of consumed
goods, and (e) the quality of consumed goods.
More fundamentally, the optimization paradigm ignores entrepreneurial
consumers' alertness to these opportunities to costlessly improve satisfaction
of their wants.
5.1
Conventional Utility Maximization
Kirzner (1973:
18) notes the convention of treating consumers as merely passive price-takers
is only an analytical convenience. The
consumer's optimization problem is usually defined as maximizing a preference
or utility function subject to a budget constraint. In the two-good case the budget constraint is
y0 = p1q1
+ p2q2
where y0
is the consumer's fixed income and p1 and p2
are the prices of commodities Q1 and Q2 respectively. Thus unreality is introduced by arbitrarily
setting the quantities of commodities Q3 through Qn
at zero. Entrepreneurial alertness which
might be exercised through discovering additional arguments is assumed away and
ignored. The price vector facing the
consumer is assumed to be given. Thus
any entrepreneurial activity aiming at improving the price vector from the
consumer's perspective is also ignored. The consumer seeks to maximize the
subjective, unobservable, ordinal utility function
U = f(q1, q2)
where q1 and q2 are the quantities of Q1
and Q2 the consumer consumes, subject to the budget
constraint (Debreu 1959: 55-58, Silberberg
1979: 214-233, Henderson and Quandt 1980: 8-18, Chiang 1984: 400, Varian 1984:
113-115, Takayama 1985: 179-183.) For
generality, no explicit functional form (such as Ut = Acta
ltb) is assumed. (Varian 1984: 128-130 discusses explicit
functional forms, including Cobb-Douglas and
constant-elasticity-of-substitution utility.)
Because the utility function is assumed
to be fixed, no scope is allowed for the entrepreneurial consumer to extract
additional well-being from equal amounts of the same consumption goods. However, imagine a household budgeting for a
fixed amount of fixed-price consumption goods over a period of time. A household which experimented with new food
recipes could enjoy higher well-being by discovering recipes they prefer, (or
recipes they dislike and avoiding them).
This would shift the utility function closer to the origin. The optimization paradigm ignores this
possibility of entrepreneurship in consumption.
Entrepreneurial consumers would also seek to negotiate lower prices for
consumer goods, and higher household incomes (Rothbard 1962: 183-200). This entrepreneurial behavior is all ignored
by convention. Conventionally, the
Lagrangean is
V = f(q1, q2) + λ(y0
- p1q1 - p2q2)
where λ
is the as yet undetermined Lagrange multiplier.
First-order conditions for an optimum are obtained by setting the first
partial derivatives with respect to q1, q2,
and λ equal to zero:
|
∂ V |
= |
f1
– λp1 = 0 |
|
∂ q1 |
||
|
∂ V |
= |
f2
– λp2 = 0 |
|
∂ q2 |
||
|
∂ V |
= |
y0
- p1q1 - p2q2 = 0 |
|
∂ λ |
Transposing the
second terms in the first two equations and dividing yields the condition that
the marginal utilities must be equal to the price ratio for a maximum[12],
|
f1 |
= |
p1 |
|
f2 |
p2 |
The ratio of the
first partial derivatives of the utility function, f1/f2
is the rate of commodity substitution or marginal rate of substitution between Q1
and Q2. The first-order condition for a maximum expresses the
equality between the rate of commodity substitution and the price ratio. The first two equations can also be written
as,
|
f1 |
= |
f2 |
= λ |
|
|
p1 |
p2 |
||
5.2
Limitations of Utility Maximization
Hayek notes the
dispersal of knowledge as an economic problem, "a problem of the
utilization of knowledge which is not given to anyone in its totality"
(Hayek 1949: 77-78). Dispersed knowledge
provides one forum for entrepreneurial activity. Entrepreneurs seek out, or at least remain
alert to, the dispersed character of this knowledge, hoping to profit through
offering information to those who can benefit from it, but do not yet possess
it. Thus, entrepreneurs act to overcome
the dispersal of knowledge. This kind of
entrepreneurial activity overcomes disequilibria based on information
asymmetries, acting to move the market toward equilibrium and symmetric information. This equilibrium can never be realized,
furthermore, in the act of overcoming asymmetric information disequilibria,
entrepreneurs upset the entrepreneurial plans of others, preventing
coordination of individual plans, ensuring a disequilibrium state even as they
move the market toward equilibrium. This interpretation of the entrepreneurial
function leaves room for both Schumpeter's and Kirzner's views of the
entrepreneur. Entrepreneurs profit from
removing information imbalances and bring about a movement toward information
equilibrium, where everyone enjoys equal, and more complete, information
(Kirzner 1973: 66-67).
4. Market Coordination, Equilibrium, and the
Entrepreneur: Schumpeter's and Kirzner's Views
Kirzner and
Schumpeter give competing views of the role of the entrepreneur. For Schumpeter the entrepreneur seeks to
shift the production function and cost function (Triffin 1940: 168, Schumpeter
1962: 104-105, 132). For Kirzner the
entrepreneurial function consists of noticing that the cost and revenue
functions have shifted: "entrepreneurship for me is not so much the
introduction of new products or of new techniques of production as the ability
to see where new products have become unexpectedly valuable to consumers
and where new methods of production have, unknown to others, become
feasible" (Kirzner 1973: 81).
Kirzner and
Schumpeter offer diametrically opposed views of the role of the entrepreneur in
relation to market equilibria.
Schumpeterian entrepreneurs destroy equilibria (Schumpeter 1934: 64),
whereas Kirznerian entrepreneurs effect adjustment toward new equilibria
(Kirzner 1973: 72-73). Although a new
attempt at reconciling these competing views risks oversimplifying them, it
seems hopeful to suggest the two views of the entrepreneurial function arise
from differing concepts of the underlying reference equilibrium. In Schumpeter's scheme, the hypothesized
equilibrium is associated with the ideal state of an evenly rotating
economy. This hypothetical reference
equilibrium is unrealized because entrepreneurial action prevents the economy
from settling in an evenly rotating state.
Schumpeter defines entrepreneurial action with reference to an ex ante
equilibrium which was never actually realized; the hypothesized equilibrium is ex
ante to the entrepreneurial action, and provides alert entrepreneurs with
profit opportunities to exploit.
Kirzner views
entrepreneurship as moving the market toward a hypothesized equilibrium. This equilibrium is never realized but can be
seen as the goal of the entrepreneurial action ex post; Kirzner's equilibrium
is moved toward after the entrepreneurial action. In Kirzner's view the "final"
equilibrium is the goal of entrepreneurial action, a goal that is never
reached. Schumpeterian entrepreneurs
create information asymmetries. The
actual dispersion of the asymmetric information created by Schumpeterian
entrepreneurs lessens the coordination of economic plans. Kirznerian entrepreneurs exercise alertness
to discover already-existing information asymmetries. The Schumpeterian and Kirznerian entrepreneur
may well be two different persons, but can equally well be the same. Kirznerian entrepreneurs exploit information
asymmetries to earn entrepreneurial profits.
Imagine an
initial state of affairs, where information is dispersed, but market
participants, ignorant of their own ignorance, are unaware of the asymmetric
character of the information they possess.
In this context, are market prices equilibrium prices? Not in the Schumpeterian sense, but
certainly in the Kirznerian sense. A
Kirznerian entrepreneur can exploit this opportunity by brokering information
about resource and product prices, but only after discovering the information
asymmetry. Then the extent of the
entrepreneur's success eliminates the asymmetry, ultimately eliminating the
entrepreneurial profit opportunity.
In Kirzner's
view, prices remain in equilibrium until entrepreneurial alertness discovers
information dispersal and asymmetry, and acts to take advantage of the
arbitrage opportunity, forcing prices to adjust. Price adjustments effected by Kirznerian
entrepreneurs act to reestablish a new equilibrium where market participants'
plans are better coordinated and their wants can be better satisfied (Kirzner
1984b: 160)[13]. A
Schumpeterian entrepreneur exploits the asymmetric information in such a way
that they might seek to extend or maintain the dispersal of knowledge. The Schumpeterian entrepreneur disturbs and
destroys the old equilibrium; the Kirznerian entrepreneur moves the market
toward a new one. Kirznerian
entrepreneurs avoid risk and cost (Blaug 1998: 223) because they move the
market toward a new equilibrium which could only exist hypothetically after the
entrepreneurial action. Schumpeterian
entrepreneurs move the market away from the pre-established, though equally
hypothetical equilibrium which is destroyed, or at least left behind, by the
entrepreneurial action. The
Schumpeterian entrepreneur may succeed at moving the market out of equilibrium,
or at least away from a hypothesized equilibrium state; the Kirznerian
entrepreneur can never really succeed in establishing a new equilibrium.
6. Conclusion
Entrepreneurship
is not amenable to limits imposed by an arid mathematical formalism. This is partly due to the facts that (a) the
concept of entrepreneurship remains vague and ill-defined, (b) several
competing concepts, e.g., Schumpeterian versus Kirznerian entrepreneurship, are
floating around, (c) these concepts are often used interchangeably, and most
importantly, (d) entrepreneurs are so innovative their behavior often defies
categorization.
The neoclassical optimization paradigm largely ignores entrepreneurial
activity, thus ignoring much of what is interesting in economic behavior. Although some kinds of entrepreneurial action
can be described within the optimization paradigm, many cannot. For example, production technology, created
through one species of entrepreneurial discovery, and implemented through
another, is taken as given for analytical convenience. The nature of the entrepreneurial function is
treated as beyond the scope of the discipline because it does not result from
optimization. Entrepreneurial discovery
results from something other than optimization because entrepreneurs act to remove
optimization constraints. There is no
global optimum to an entrepreneur, only constraints which eventually fall
before the onslaught of the human action of inquisitive, profit-seeking
entrepreneurs.
Successful entrepreneurs should always move the market from a less
optimal to a more optimal state of affairs by removing constraints imposed by
ignorance and uncertainty[14]. However, in the optimization paradigm, agents
purposely optimize with respect to known objective and constraint
functions. Their understanding of these
analytic functions may be imperfect or uncertain, resulting in imperfectly
implemented human action on which Kirznerian entrepreneurs can always
improve. Naturally entrepreneurs profit
from providing this service.
It may also happen that Schumpeterian entrepreneurs can enter the scene
and change the objective and constraint functions. Apart from the fact that this species of
human action automatically creates an opportunity for Kirznerian
entrepreneurship, as market participants may not be immediately aware that
their objective and constraint functions have changed, initially imperfect
human action is driven even further off the mark by changing the analytic
functions market participants assumed when they made their production and
consumption plans, or were analytically modeled as assuming.
Acknowledgement
Robert F. Mulligan is associate professor of economics in the Department
of