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Table of Contents
THE ECONOMICS OF A BITING MINIMUM WAGE
L.V. Petrides® and B.C. Dangerfield”
Centre for O.R. and Applied Statistics
University of Salford
Salford M5 4WT
UK
Abstract: Conventional wisdom as regards the effects of a biting Minimum Wage
(MW) is challenged in this paper through the findings of a System Dynamics model.
Given a number of different plausible assumptions, a number of counter intuitive
results are found to emerge such as a longer term permanent increase in employment
levels, a greater total number of businesses in the economy associated with lower
total employment levels than originally, and a trade-off in the well being and the
employment levels between those firms whose cost structure was affected by the MW
and the unaffected firms. Finally, two variables that are normally considered to be
irrelevant to the investigation of the economic effects of a biting MW, namely
consumption spending and fixed costs per business, come to the forefront of the
analysis.
Keywords: minimum wage; economics; system dynamics; simulation
1, INTRODUCTION
One of the most politically sensitive issues whose economic effects
remain largely unclear, is that of the Minimum Wage (MW)'. The
conventional and very little challenged - until recently - view of
economists is based on a neoclassical model according to which there can
be only one result from the imposition of a MW: a reduction in
employment. As Dickens et al (1994) argue:
“Too often in past work, the only theoretical models used are competitive
ones in which the only empirical question is not ‘do minimum wages
reduce employment?’ but ‘how much?’ "
It was mainly after the empirical findings of Card and Krueger (1994) for
the US and Machin and Manning (1994) for the UK that doubt was cast
with regard to the validity of the traditional approach. The alternative
theory consequently put forward, that of monopsonistic labour markets,
© E-mail address: lpetrides@ cwcom.net
" E-mail address: B.C.Dangerfield@ salford.ac.uk
‘a MW imposition is not differentiated from a MW increase in this paper as, ultimately, both result (if
the levels of the MW are high enough) to an increase in wage rates. The two nouns will be
consequently used interchangeably throughout.
was based on a slight variation of the conventional neoclassical model,
with firms possessing some influential power instead of being completely
unable to affect wage rates. This assumption proves strong enough to
allow for increased employment levels within an economy, provided that
the MW does not exceed a certain undefined upper limit.
Since both of these approaches adhere to the principles of the neoclassical
paradigm however, attention has inadvertently focused on certain areas
associated with MW, and not on others. While business costs and the
demand and supply of labour for example stand at the very core of the
neoclassical models, key variables and processes such as spending or the
possibility of firms entering/exiting industries, are usually left completely
uncontemplated with. What's more, given the static nature of the
aforementioned models, questions regarding the dynamic behaviour of
any variables that might arise due to the introduction of a MW become
meaningless. As a result, the scheme has come to be considered as either
immediately beneficial or detrimental for an economy making it
impossible to distinguish between different short-term and longer-term
effects. As will be demonstrated below though, by adopting an approach
that is markedly different to the neoclassical one, surprising and counter
intuitive findings emerge which, according to the authors’ opinion, go
some way into bringing new insights as regards the economic effects of a
biting MW.
2. A SYSTEM DYNAMICS MODEL
In an attempt to further our understanding of the economics of a biting
MW, an altogether different line of attack to the one associated with the
neoclassical paradigm is adopted introducing causality, disequilibrium,
imperfect information, and endogenous dynamic behaviour into the
analysis. A generic System Dynamics (SD) model is built and described
below and its results prove to challenge current economic wisdom
2.1 Model structure and causal hypotheses
2.1.1 Identification of main sectors
The model is comprised of two main sectors to capture the fact that a
MW scheme would increase wages paid only in a certain proportion, (1-
a), of total firms in an economy, the affected firms. The proportion of
unaffected firms in the economy is consequently described by (a). As will
be shown later on, the greater the proportion of the unaffected firms
within the economy, the greater the possibility for the products produced
within the unaffected sector to be good substitutes for the ones produced
within the affected sector, and the less the need to resort to imported
products will be in the event of price hikes.
For added realism and in order to allow for a more appropriate treatment
of the differences found between the manufacturing and service firms, the
affected sector gets analysed further into firms dealing with
(manufacturing) goods on the one hand, and services on the other. The
proportion of the affected manufacturing firms’ in the economy is
consequently considered to equal (b), with (1-b) describing the proportion
of firms within the affected service sector’. An analogous treatment for
the unaffected firms was not considered necessary especially after it
became evident that the two sub-sectors of the affected firms behaved
very similarly (as expected).
Figure 1 summarizes the hypothetical distribution of firms in the
simulated economy.
Unaffected firms
a
Manufacturing
Minimum Wage — os finns
a Affected firms
th Service firms
Figure 1 The distribution of firms
2.1.2 Consumption and identification of consumer groups
Consumption is initially spread among the different sectors according to
the way firms are distributed within the economy. As prices in different
sectors vary however, consumption will be diverting away from the
relatively pricier products to the better valued ones (see analysis in
following sections, esp. section 2.1.5).
Figure 2 shows in an aggregate manner the causal relationships that are
associated with consumption in the model.
? Whenever there is any mentioning of “service” or “manufacturing” sectors, it should be understood
that reference is made to the relevant sector within the larger category of the affected firms sector. The
unaffected sector on the other hand will be addressed as such.
enbreprenetirs
ees oS
a
unemployed's
ange renpurs total demand ~ consumption
ye PK +
total sales’
empl gi
unemployment
ra GA nm CA Benelit
i MK
i coatinton meeplae
+ employees’
+ income
+ unemployment
businesses
+ employment an a
MW = wages
Figure 2 Influence diagram describing consumption
After a biting MW is introduced, an increase in wages’ occurs which acts
to boost employees’ income. Assuming that employees will eventually
spend all of their income, employees’ spending will rise, leading to an
increase in sales. At the same time that employees are increasing their
consumption however, a reduction in profits due to the higher wages that
must now be paid out takes place, reducing entrepreneurs’ spending and
consequently influencing total demand and sales adversely. Since the
reduction in profits is of equal magnitude to the increase in wages, total
demand and sales should be expected to remain unaltered from this
process.
A reduction in profits however can also be expected to drive some firms
out of business reducing employment and naturally employees’ income as
well. A drop in the latter variable acts, as already noted, to reduce sales
which, in turn, reduce profits further, causing more businesses to shut
down and so on. In an attempt to break free from this vicious cycle, the
government is assumed to pay out unemployment benefits thereby
creating a controlling (negative feedback) loop by ensuring a minimum
level of consumption for the unemployed. As the number of the
unemployed rises therefore, more people are getting paid unemployment
benefits, consumption from the unemployed rises and total demand and
consequently sales increase hopefully containing the crisis or even
reversing the negative trend.
3 The possibility of an increase in productivity due to the MW is also considered later on. If
productivity increased because of the MW, profits need not reduce due to an increase in wage rates in
the longer term.
There are of course not only three different consumption groups in the
model as suggested in the aggregate influence diagram above, but seven,
since consumers are identified separately according to the sector they
work in (manufacturing firms, service firms, or unaffected firms) and
their status (entrepreneurs or employees), with the unemployed naturally
standing in a separate category -see Table 1.
Table 1. Consumer groups
. Affected)
Categories of ( ‘ (A ffected) :
consumers aoa service firms Unaffected firms
Entrepreneurs m entr s entr u_entr
Employees m emp s emp w_emp
Unemployed unemp
Consumption spending is consequently defined separately for each of
those groups according to their income, which is in tum determined from
profits in the case of entrepreneurs, wages in the case of employees, and a
constant exogenous minimum monthly income rate representing the
unemployment benefit in the case of the unemployed (see further
analysis).
2.1.3 Service sector
Figure 3 presents the main causal relationships within the service sector:
Fi aw
uM, business
— 7 "business
Ne Fl
he
normal we Sac sold ‘i <
per person per business, re © o ;
demand per a
TO business
destred employment
demand directed per businéss
to services f +
+
a A») aes 1 f
consumption employment
total demand Moe per business
+ <businesges> 4.
3 — 4
i: employees’ Be I t Es
‘apors emp pymen nomnal output
ti <=
+ a per business
substitution unemployment Pit:
rate + saan Prices capacity
ee bea average Hin tee Pp
demand directed to selling price
unaffected sector unit costs +
Figure 3 Main causal structure of the service sector
One of the consequences of the minimum wage if normal output per
person remains constant is, as already suggested, the reduction in profits
per business and the consequent reduction in the number of businesses in
operation. With a reduced number of businesses however and an
unchanged demand, existing firms will be faced with increased demand
(demand per business) and services sold per (existing) businesses can be
expected to increase if output can rise. Since productivity in the short run
is at least partially determined by demand conditions, it is assumed that a
short-term increase in output (within limits of course) will be attainable
and a redirection of demand (from the closed to the remaining firms) will
take place closing the (negative feedback) loop, although as will be
demonstrated later on this assumption will be challenged.
With boosted demand per business, desired employment per business will
increase in an attempt to secure a permanently greater supply of services
and, if no constraints exist, actual employment per business will follow
suit boosting employment levels in the economy and thereby mediating
the adverse employment effects due to the closure of businesses. If
employment levels within the simulated economy ultimately reduce,
employees’ consumption will naturally drop and the demand directed to
services will fall reducing services sold per business thereby creating a
positive feedback loop associated with employment levels and
consumption.
Employment per business of course cannot be expected to increase ad
infinitum since at some point or another diminishing‘ returns will kick in
making it unprofitable to keep hiring personnel. Desired employment at
that point will start reducing, limiting employment per business and
therefore normal output per business. If supply cannot match demand
however, capacity pressures will emerge and the selling prices average
selling price) will eventually rise causing consumers to substitute
(substitution rate) away from the service sector into imported products
(imports), in which case total (domestic) demand falls, or to products
produced within the unaffected sector (demand directed to unaffected
sector) naturally reducing the demand directed to services. A controlling
selling price loop therefore emerges regulating demand according to
supply.
Unemployment, or the lack of it to be precise, is, as shown in Figure 3,
another key factor that limits employment per business, and it is also
4 The negative loop will be activated due to increasing returns in the case of a drop in employment
levels per business.
assumed to restrict the opening up of new businesses (latter link not
shown). When the economy is booming and unemployment approaches
its natural rate then, it is considered to become exceedingly difficult for
firms to fill their vacancies and prospective entrepreneurs are also thought
to be put off from going at it on their own due to finding difficulties in
spotting and employing appropriate personnel. Discrepancies between
output and demand again arise and the selling price loop is again
activated to constrain demand. An expansion of the model to include a
pressure to increase wages in such circumstances could have been
included but this was considered to increase the model’s boundary
unnecessarily and at the expense of its intended objective.
Apart from differences arising due to mismatches in demand and supply
however, selling prices can also vary with unit cost alterations that may
occur because of the MW. Different scenarios are consequently explored
with firms either assumed to be passing on their increased costs in terms
of higher prices or refraining themselves from doing so.
Finally it should be added that the possibility of a MW acting as a
stimulus to management for adopting more productive ways of operating
as suggested in Nolan (1986 esp. p.84) and Edwards and Gilman (1998
p.11) has also been contemplated with’. The positive link between MW
and normal output per person therefore suggests that a MW may actually
act to increase normal productivity reducing the number of employees
required to achieve a given level of output thereby potentially reducing
employment per business (relationship not shown). If employees per
business reduced however, wages per business would fall and profits
would naturally increase.
2.1.4 Manufacturing sector
The principal reason for splitting the affected sector into manufacturing
and service firms is to account for the fact that manufacturing firms can
(and for the most part do) hold inventories of their products creating a
time buffer between the supply and demand. The influence diagram
describing the main causal structure of the manufacturing sector therefore
is a slightly augmented version of its service counterpart including the
required inventory related variables and their interconnections - Fig. 4.
5 Many thanks are due to John Dobson from the Management School of the University of Salford for
highlighting this important link, and for providing us with many helpful references supporting this (and
anumber of other) point(s).
wages per
a
+o
= ae per businesses
normal Pe ut musiness Xt of
per %
Noe sold
er business
ge P desired, inventories
per business
demand a a
to manufacturing inventories per
usiness
+
= inventory
ims to
discrepancy
t demand As) cE
consumption gutput per .
business + + +
f + desired employment
employees' —<businesses> per business
consumption + / +
th employment inventory
employment ear pressure
Substitution unemployment
yo a: ain bce
demand directed to average nt costs
selling price
unaffected sector 9 2
Figure 4 Main causal structure of the manufacturing sector
An increase in the number of goods sold per business in this sector apart
from causing desired employment to rise also acts to create inventory
discrepancies by reducing actual inventories per business and increasing
their desired levels. A discrepancy between actual and desired inventory
levels though gives rise to inventory pressures which are then translated
in selling price changes® in an attempt to regulate demand and to
eventually restore equilibrium between actual and desired inventories.
As could be imagined however, inventory discrepancies can also be
eliminated through adjustments in employment per business’. If desired
inventories are greater than actual inventory levels then, employment per
business will increase boosting supply and building inventories back up
eliminating inventory discrepancies.
® The plus or minus signs in the influence diagram in Figure 4 provide a short cut in indicating that
discrepancies between the desired and actual states of inventories may arise both due to actual
inventories levels being higher than their desired levels and the other way around. In the former case,
the greater the discrepancy, the less desired employment will be and increases in inventory pressure
will serve to reduce selling prices. If desired inventories are greater than their actual levels though,
desired employment will increase and inventory pressure will drive prices up.
2.1.5 Unaffected sector
Since prices and profits within the unaffected sector remain unaffected
from the cost implications of the MW much of the detail that was deemed
necessary for the proper representation of the affected sector was here
considered irrelevant and was consequently omitted. The considerably
more aggregate causal structure of this sector is depicted in Figure 5.
diverted demand
from the affected
sector
products
‘i eee sold
a
demand directed to
unaffected sector * desired
%
f a
mF 7
i an
AZ
ot et
ca
Soomapeaa
\
employees’
impor OE AD -
selling price capacity
a pressure
rate ba +
St erage
selling price
Figure 5 Main causal structure of the unaffected sector
The most important difference between the causal structure of this sector
and the ones described previously is, as suggested from a careful look in
Figure 5, the aggregation of all businesses in a non-differentiated entity
preventing the ‘average business’ to be the basic unit of analysis. Profits,
sales, and employment therefore are all considered from an aggregate
perspective.
Positive consumption feedback loops can again be identified, where
increases in demand boost sales (products sold), profits, entrepreneurs’
consumption, total demand and therefore the demand directed to the
unaffected sector closing the loop, while if employment needs to increase
profits will drop yet employees’ income and employees’ consumption will
rise driving total demand and the demand directed to the unaffected
sector higher.
As ever, a reduction in unemployment will again contain employment
restricting output thereby creating capacity pressures that activate the
(controlling) selling price loop which regulates demand through increases
in imports. Other employment restrictions however are assumed away.
2.1.6 Further assumptions: initial conditions, constants, and table
functions.
In any simulation it is impossible to begin unless numerical values are
assigned to variables. For the purposes of this generic model therefore the
affected and unaffected sectors are of equal proportion (i.e. a=0.5), and
the same holds true for the proportion of manufacturing and service firms
within the affected sector (i.e. b=0.5). If 'a' is chosen to equal less than
0.5, price increases in the affected sector will divert demand outside the
domestic economy more aggressively since it is assumed that the
unaffected sector’ s product range will be limited restricting the number of
substitute products produced within the domestic economy whose prices
remain unaffected from the MW. The need to reside to imported products
in such cases therefore increases. Figure 6 illustrates the relationship.
import rate due to small
0 0.1 0.2 0.3 0.4 0.5
Proportion of the unaffected sector within the economy (1)
Figure 6 Import rate as determined from the proportion of the unaffected sector within the economy in
the face of price increases within the affected sector
Total labour force equals 10 million people and with an average of 10
employees per firm and a 10% initial unemployment rate, the number of
firms in the affected sector total approximately 409,000 ensuring that
employment is equally divided between the two main (affected and
unaffected) sectors.
As previously suggested restrictions as to the minimum and maximum
average number of employees per (affected) firm also apply, the
minimum limit being 8 persons and the maximum 12 persons per firm.
Naturally, if these limits are ever to be reached the process will be
gradual and imprecise since the basic unit of analysis is comprised of
average and not individual "units" as is the case with most traditional
10
neoclassical models (where "units" stand for firms, profits, wages or what
have you). For that reason a fuzzy table function - see Sterman (2000
pp.529-532), or Kosko (1994) for a general introduction into fuzzy
thinking - presented in Figure 7 has been adopted to simulate the process
properly.
12
q@
Effect on desired employment
0.7 08 0.9 i TL 1.2 1.3 1.4
Auxiliary desiredinormal average employment per business (1)
Figure 7 Determination of the effect on desired employment
The effect on desired employment that ultimately determines desired
employment does not allow the latter variable (desired employment) to
reduce below an average of 8 or exceed an average of 12 persons per
(average) firm.
The average wage rate per person per hour in the affected sector next,
equals initially £5, which makes up an average monthly wage rate per
person of approximately £870, while average profits per affected
businesses equal approximately £3260 per month. With the introduction
of a MW, average wage rates in the affected sector increase by 10%
initially, and by a further 5% as time elapses to account for the
differential pressures that a biting MW could bring along with it. In the
unaffected sector on the other hand, the hourly wage rate per person
stands at a constant of £10, while total initial business profits equal their
total equivalent for the whole of the affected sector, i.e. approximately
£1.3e9 per month. The unemployed’s minimum monthly income finally
comes to merely £520 per person.
Productivity figures must also be provided in order for the simulation to
proceed. Average output per person which is thought of as being the same
for both sectors within the larger affected-firms category, stands at
approximately 205 units per person per month initially, while this figure
rises to approximately 390 for the employees in the unaffected sector.
Although productivity may vary with the MW as suggested earlier on, it
may also vary in the short nin according to demand conditions by up to
10% before adjustments in either prices or employment are made.
11
The normal (initial) average price charged within the affected sector
comes to £10 per unit while their unaffected equivalent increases to an
average of £14 per unit. As prices in the affected sector increase, the
substitution of goods occurs according to the table function produced in
Figure 8
Substitution rate (1
1 1.05 dd. 1.15 12 1.25 1.3 1.35 14
Average/normal (average) selling prices (1)
Figure 8 Determination of Substitution rate
The significant difference in the initial prices charged within the affected
and the unaffected sectors causes demand to be relatively insensitive to
small variations in price. As prices increase further however, consumers
will substitute away from the affected sector more aggressively, with a
complete substitution occurring in the (highly unlikely) case of the
affected sector’s prices equalling their unaffected equivalents. A negative
substitution rate could also have been allowed to represent a diversion of
the unaffected firms’ demand into the affected sector in the case of lower
than normal selling price levels; as price cuts in products that already sell
at low prices are not likely to attract large numbers of extra custom
however, and given that quantities exchanged in the unaffected sector
will increase due to an income effect’ anyhow, the substitution rate
remains at 0 (zero).
Imports are also determined from the relationship depicted above
represented by a constant proportion rate of 10% the substitution rate,
although this constant (10%) rate can vary with the initial choice of the
size of the unaffected sector as described in the beginning of this section.
Hence, assuming that the unaffected sector is at least half the size of the
economy if consumers are to redirect £100 of their spending out of the
affected sector, £90 will be spent in the unaffected sector and the
remaining £10 will go into consumption of imported goods. Naturally,
’ The income effect is defined as the change in consumers’ real income resulting from a change in
product prices. The assumption here is that the increase in real income will allow for an increase in
quantities exchanged within the affected sector.
12
increases in the unaffected sector's prices also lead to greater import rates
again according to the relationship depicted in Figure 8.
The precise relationship between the desired businesses that will
eventually be in operation within the affected sector and profits is
illustrated in Figure 9.
oN BD DH
Desired business ratio (1)
coos
0 0.2 0.4 0.6 0.8 1
Average/normal real profits (1)
Figure 9 Determination of Desired business ratio
This relationship is again assumed to be sigmoid being flatter near unity
since firms are thought to be relatively insensitive to small variations in
profits. A further reduction in average profits however, will eventually
drive ever more firms out of business, aggravating the drop of the curve.
If profits end up exceeding their normal (initial) levels on the other hand,
a linear relationship between the two variables will hold, where for, say, a
10% increase in average real profits, new firms will enter the industries at
a rate of 5%, with the basis for the percentage calculation of new firms
being the normal (initial) number of businesses.
Finally, tight unemployment conditions, i.e. the effect low unemployment
has on employment as suggested in sections 2.1.3-2.1.5, are defined
according to the relationship shown below.
0.92 0.94 0.96 0.98 1
(Total employment)/(Total labour force) (1)
Figure 7 Determination of tight unemployment conditions
Initial unemployment will be remembered stands at 10% the total labour
force, with the effect of tight unemployment conditions exerting no
influence at those levels. As unemployment drops however, the effects of
13
its reduction will become more and more evident causing discrepancies
between the desired and the actual employment levels and setting barriers
for new businesses entering the market.
2.2 A note regarding the chosen constants of the model and
parameter estimation in general.
It would be fair to say that this section would have been restricted to a
small paragraph if it was not for a reply John Sterman (SD 3408) posted in
an SD discussion list® recently, illuminating implicitly the extent of the
problems created by a lack of understanding of non-SD experts as regards
the use of, among others, “non-scientifically "- verified parameters in some
SD models.
It is of course true that none of the parameters used in this model have
been based on “scientific” data cropping out of research. They are all
“say” figures that are meant to generally approximate the processes they
describe. A number of points regarding this practice associated with this
particular model should be made clear here:
Firstly, this model is not meant to be simulating any existing economy. It
is a generic model in its nature aimed at enhancing our understanding of
the economics of the MW. Had there been an attempt to simulate the
effects of a MW in a particular economy, this model would have been
further disaggregated into specific industries, and estimates would have
been obtained for the model’s parameters. It should be perhaps added that
SD modelling has, and has had for over 20-25 years” now, in its disposal
very powerful optimisation techniques’” that allow for an altemative
means of estimating parameter values, even if some “scientific” data are
vague, imprecise or, at times, plainly wrong.
Secondly, because of the non-linear nature, the multiple interconnections
and feedback loops, and the ultimately limited number of variables and
parameters responsible for the behaviour of an SD model, the sensitivity
of an SD model's results is greatly reduced to even unrealistic changes in
most parameters’. This is the reason for the extreme, according to many
®Qne can find information and subscribe to this list by visiting the following web address:
http://www.vensim.com/sdmail/sdmail.html
° The earliest study known to this author which experimented with optimisation techniques was by
Nelson and Krisbergh and it dates back to 1974.
1° For an explanation of how optimisation works and how it can be put to practice see Dangerfield and
Roberts (1996), and Coyle (1996) or (1999).
11 Forrester (1991 p.27) writes: “One author criticized the Urban Dynamics book on the basis that it
contained a very bad model because the critic had been unable to find any policy [policy explorations
14
standards, way sensitivity analysis is usually carried in SD modelling, ie
by the doubling and/or halving of parameter values. In this model
circumstances are no different. Apart from a few parameters whose
identification should certainly be most welcome by policy makers as they
highlight those areas that warrant careful attention before such a scheme
is introduced, the model’s findings are robust despite considerable
alterations in parameter values (see section 2.4).
Finally and as a concluding remark, it seems to the authors that
methodologies whose models produce results that are highly insensitive
to parameter changes should be clearly preferred over their alternatives
especially when carrying out economic-related research, given the
uncertain, to say the least, accuracy of ‘scientific’ economic
measurements. The following example found in Mayer (1993 p.73)
should probably convince the reader:
“the US trade deficit with Canada in 1982 was either $12.8 or $7.9
billion depending on whether this number came from US or Canadian
publications...”
2.3 Model output and analysis
Given the highly aggregate structure of this model the (transitory)
dynamics produced should not be expected to match in great precision the
actual (transitory) dynamics that would be experienced within a real
economy after a biting MW gets imposed. Saying that of course, it should
be added that no method has been devised as yet that enables one to
disentangle the effects a MW has in an economy from all other economic
influences in order to actually make it possible to determine empirically
what those effects really are and contrast them with the model’s output.
As regards the presentation of the model’s results and the consequent
analysis, it should be added that the similarity between the structures of
the manufacturing and the service firm sectors allows for an aggregate
‘affected firms sector’ analysis which will be adopted throughout for
simplicity and economy of space.
2.3.1 First run: No extra spending, no permanent productivity gains.
Initially, we will assume that consumers will not spend the extra income
they receive in terms of higher wages breaking the link between
include both parameter and structural changes] in the model that substantially changed the behaviour of
the model.” (emphasis added)
15
employees’ income and spending (Fig. 2), and explore what happens in
the case of firms not being able to match the increased wages in terms of
increased productivity.
-1- 11,000.00
-2- 6,600.00
-3- — 410,000.0
~~ 4,500,000 ——Affected_sector_Wages_per_business
5 10.20 ____Affected_sector_Real_profits_per_busine
~—- 4e10 ss
= 8,000.00 —3—Affected_sector_Businesses
~~ 2,000.00 -4- Affected_sector_Total_employment
-3- — 300,000.0 —5— Affected_sector_Average_selling_prices
—4- 2,000,000
a 9:90 -g- Total_consumption
=5- .
6 3.2e10
Months
Figure 8 First main run: No extra spending, no permanent increases in productivity. Plot of wages per
business, real profits per business, the number of businesses, total employment and average selling
prices within the affected sector, and of total overall consumption.
The results of this scenario prove to be quite disheartening (Fig. 8). After
the introduction of the MW at the tenth month of the simulation, monthly
wage rates increase (not shown explicitly) and businessmen are forced to
pay out higher wages reducing profits. Lowered profits per business
however cause some firms to shut down and employment is reduced. With
remaining firms assumed to have enough slack capacity initially, almost
all of the (excess redirected) demand is met without having to increase
prices” (to adjust demand according to supply) dramatically and an
increase in sales and profits does follow suit. The permanent reduction in
total consumption however due to the (remaining) employees’
preferences to increase savings rather than eventually spending the extra
funds they receive ultimately causes both profits and employment levels
to settle at lower levels than initially.
The situation within the unaffected sector is not much different as
evidenced in Figure 9. Despite the unaffected cost structure, the reduction
in total consumption causes the consumption directed to that sector to fall,
and both profits and employment levels are consequently adversely
12 The initial reduction in prices is caused due to the reduced total consumption levels. As businesses
shut down, supply also gets restricted, and prices end up somewhat higher.
16
affected. The resulting reduction in total employment’® and total profit
levels therefore (also) depicted in Figure 9 should not come as a surprise.
“17 2.5e10
7 al 4,600,000
37 269
a 9,300,000
ns 2.7e9,
1 22ne10 —1—Consumption_directed_to_unaffected_sector
Sy a 4,450,000
‘ 1.25¢9 —7— Unaffected_sector_Employment
37 25e
_ _3- Unaffected_sector_Real_profits
4 8,650,000 3 ha! es he
5° 1.7529 —4—Total_employment
= 2e10 —5—Total_real_profit
a 4,300,000
-3- 500,000,000
-4- 8,000,000
-5— 800,000,000
0 50 100 150 200
Months
Figure 9 First main run: No extra spending, no permanent increases in productivity. Plot of
consumption directed to unaffected sector, unaffected sector's employment and real profits levels and
total employment and real profits
Finally, the reasons for the transitory oscillatory behaviour that emerges
from this run, which will be considerably more evident in the subsequent
reruns, provide some basic understanding into the causes of the herdish
behaviour that is generally observed in many real world situations after a
sudden crisis or a profitable opportunity emerges. Because of both the
(material and information) delays that are involved in the decision
making process of opening up or closing down businesses and the
bounded and intended rationality of entrepreneurs, too many firms close
down after the initial severe reduction in profits leaving only a few ones
operating behind which get all the benefits associated with the redirection
in demand. As a result these remaining firms eventually see their profits
skyrocket. Once it is realized that greater profits than normally are
realized by existing firms, too many businesses open back up again in an
attempt to benefit from the arisen situation overcrowding the market and
causing the whole process to start anew albeit at a lower intensity until,
eventually, ‘normal’ profits are achieved by the ‘right’ number of
businesses.
13 Figure 2 shows that the consumption from the unemployed acts as a balancing force to total
consumption if employment levels divert from their initial levels. The fact that equilibrium is
established at lower employment and consumption levels than initially implies therefore that the
adverse effect of the employees’ new saving habits on total consumption outweighs the increase in
consumption that stems from higher spending from the unemployed. The stabilizing role of the
unemployment benefits will be further discussed in the next section.
17
2.3.2 Second run: Increased spending, no permanent productivity gains
Because a MW would generally affect the lower-income employees, it is
more likely than not that the additional wages will be eventually spent. In
the remaining runs then, adjustments are made to account for this more
realistic alternative. In this run in particular, the output of the model in
the face of no permanent productivity gains is explored.
= 1,100
-2- 9,300,000 Py
2
oa ae 3e9. $3 3
= u| 3 ee
1 950 “2 ‘ 1
an aa 1 = Wage_rates_per_month
7 8,650,000
— 2.5e9 —2- Total_employment
== all —3—Total_real_profits
—— 8,000,000
37 |
0 20 40 60 80 100
Months
Figure 10 Second main run: Increased spending, no permanent productivity gains. Plot of wage rates
per month, total employment and total real profits.
Figure 10 above, illustrates that a biting MW in these circumstances will
initially hurt total employment and total real profit levels, yet, as time
elapses a recovery will emerge and equilibrium will ultimately be
established at higher levels than originally. In order to best explain the
reasons for this kind of behaviour we will slightly divert from the main
analysis of the MW, revisit the model’s structure, and carry a number of
partial model tests.
As highlighted in section 2.1.2, the introduction of a biting MW if no
closures of businesses occurred would not be expected to affect total
consumption. This is indeed the case as demonstrated by total
consumption 1 (tcs 1) in Figure 11 where the imposition of the MW is
thought to leave the number of businesses along with consumption from
the unemployed and prices (i.e. the two remaining variables that can
influence total consumption) unaffected.
18
4e10
4e104 ey eee
3e105 2 ___ Total_consumption_1st_partial_mo
3e10- i 1 1 1 ~1" del_test_tcs1
3e107 -2- Tcs_2
3e104
3e10. ; + { 3 TCs_3
0 50 100 150 200
Months
Figure 11 Comparison plot of total consumption for partial model tests 1,2 and 3
If on the other hand we do allow firms to close down as normally
expected and hypothesised, still keeping prices and consumption from the
unemployed out of the picture, total consumption as we can see from
tcs/2 in Figure 11 ends up at higher levels than originally. The influence
diagram presented in Figure 12 sheds some light into what causes this
increase in total consumption.
Minimum wage
2)
redirection in + Profits per
deh business Sage
. Total,
economies of AD + consumption
. magnification
+ NO ot Businesses
Fixed AD +
multiplier
Products sold
per business
Affected firms'
consumption
Figure 12 Influence diagram identifying the responsible structure for the behaviour produced in section
2.3.2
After profits per business reduce and some firms close down, all
consumption is redirected to existing firms boosting products and profits
per business. Since supply is now increased utilizing less fixed resources
however, economies of scale are realized and profits per business
increase even more thereby rising total consumption. In other words, the
funds that were getting directed to fixed cost payments lowering profits
per business are now going into the pockets of (the remaining)
entrepreneurs who are assumed to be able to meet the excess demand
from existing resources and as a result (since they don’t have to spend
any more money in terms of fixed costs than they used to) they realize a
further increase in profits increasing consumption.
19
Indeed, if we make the extreme assumption that fixed costs are zero for
all affected businesses, total consumption is shown to remain unaffected
despite the closure of businesses matching tcs1 exactly (see tcs3, Fig 11).
With an increase in total consumption then, the positive multiplier
feedback loop is set in motion driving consumption ever higher, until new
businesses start entering into the economy activating the balancing
magnification effect feedback loop (Fig 12). The number of the affected
businesses plotted in Figure 13 (tbus/2) which is derived from the second
partial model (i.e. assuming positive fixed costs and business closures)
demonstrates however that the aforementioned balancing loop is not
strong enough to associate a particular number of businesses to a
particular consumption level. Thus, even though the number of affected
firms almost fully rebounds to its initial levels, the corresponding total
consumption (tcs2 Fig. 11) settles at higher levels than originally due to
the previous (permanent) multiplier effects. In the meantime, the boosted
demand drives total employment noticeably higher than it originally was
(temp/2 Fig.13).
—1——1
tel, 1 -\- Affected_sector_Total_businesses 2
1 -354——=9°3-g—
geoPPe 27342
2
. % —2—Total_employment_temp2
os)
37 Temp_4
=4- Temp_5
5 Temp_6
0 50 100 150 200
Months
Figure 13 Comparison plot of total employment levels as produced in partial model tests 2,4,5 and 6,
and the total number of business in the affected sector as derived from partial model test 2.
The reasons for the considerably higher levels of total employment
reached in this run (temp2 Fig 13) as compared to the ones found in
Figure 10 have of course to do with the fact that in the second partial
model test (as in all other partial model tests) both selling prices and
consumption from the unemployed” have been assumed away leaving the
multiplier loop to exert its maximum influence in the economy. The
14 When assuming a constant consumption of the unemployed the mass balance check for the flow of
money (see section 2.4) diverts, as expected, from zero.
20
constraining effect these two variables have on the multiplier loop is not
hard to comprehend. Higher prices, as shown in both Figures 3 and 4, act
to divert demand away from the affected into the unaffected sector and
into imports. To the extent that it is the unaffected sector's demand that
increases no major harm is done in the economy since the multiplication
effects simply work around the unaffected sector more intensively than
before and total employment (temp) levels ultimately reach their top
levels (see Fig. 13, temp/4 as compared to temp/2). To the extent that
demand gets redirected into imports however, the effect on consumption
can be dire as can be imagined since it will be foreign businessmen that
will be realizing greater profits in the expense of domestic profitability
and consumption. Nevertheless, given the chosen parameters and
hypotheses for this run, the demand that gets redirected to imported
products because of the MW is miniscule since prices in the affected
sector do not rise high enough. Total employment levels therefore fall
only slightly below their maximum levels (see Fig 13 temp/5) and very
little -if any - damage is done to the economy overall.
The greatest actual constrain to the multiplier loop previously described
therefore is identified in the face of one of the most widely known
automatic stabilizers, the consumption from the unemployed which
naturally results from the unemployment benefits that are paid out to
them by govemment. As total employment increases, less money are
injected into the economy in terms of unemployment benefits and total
consumption naturally falls. As a result, total employment drops
considerably below its maximum values (see Fig 12 temp/6), matching
exactly the levels produced in Figure 10.
2.3.3 Third run: Increased spending and margin restoration pricing policy
In this run we explore some of the consequences that could be expected if
the affected firms decided to pass on the increased costs in terms of
higher prices, thereby attempting to restore their initial profit margins.
Figure 14 shows the behaviour of total employment and total profits that
would result along with the average selling price levels that would be
charged in the economy.
21
= 9,100,000
=> 3.5e9 i
3+ 7 1
3 13.0 Lo 1
—— 8,950,000 1 — 3 3
2.75e9 3 —— Total_employment
= :
3F 12.0, = Total_real_profits
== 8,800,000 —3— Average_selling_prices
bs ca 2e9 >t + + + ,
3 11.0 J
0 50 100 150 200
Months
Figure 14 Third main run: Increased spending and margin restoration pricing policy. Plot of total
employment, total real profits, and average selling prices
As predicted from the analysis in section 2.3.2, the affected firms’
decision to pass on the increase in selling prices clearly compromises the
ultimate employment and profit levels that are eventually reached. The
reason for this kind of behaviour is none other than the previously
identified increase in imports (Fig. 15).
A further point that emerges from this run and warrants further attention
is the possibility of an inversely related relationship between the
employment levels within the affected and the unaffected sectors because
of the affected sector's price hikes. Since the initial hypothesis (see Fig 3
&4) was that an increase in the selling prices within the affected sector
would redirected at least part of the affected demand into the unaffected
sector, the employment levels in that (the unaffected) sector should be
expected to increase to the detriment of the ones found in the affected
sector. Indeed, as demonstrated by the behaviour of the three remaining
variables plotted in Figure 15, this line of events does occur for the
reasons just explained.
== 500,000,000
=} 5,000,000
=
—4- 1.5e9 —1— !mports
= Unaffected_sector_ Employment
== 0 -3- Affected_sector_total_employment
= 4,000,000 ___ Diverted_consumption_away_from_affe
3- 3,500,000 cted_into_unaffected_sec
aye 0
0 50 100 150 200
Months
Figure 15 Third main run: Increased spending and margin restoration pricing policy. Plot of imports,
affected and unaffected sectors’ employment levels, and of the consumption that gets diverted away
from the affected into the unaffected sector.
22:
The full repercussions of this important point will be made clear in the
following section.
2.3.4 Fourth run: Increased spending and matching permanent
productivity gains.
A commonly held view regarding the effects of a biting MW when
matching increases in productivity levels are hypothesized, is that any
adverse effects usually experienced will be minimized due to the largely
unchanged cost structure of businesses. In this run we explore the
consequences of an upsurge in productivity within the affected sector of
equivalent magnitude as the hike in the MW that could possibly result as
a result of the MW introduction, and we identify the reasons for the
produced behaviour.
Figure 16 depicts the total real profits and employment levels that are
produced within the affected sector.
-- 1,000
2 8,300
37 5,000,000
> 900
-y- 5,400
_— 4,150,000
> wal
-y- 2,500
37 3,300,000.
ya 111
=
iy ‘ 3 3 -)- Wage_rate_per_month
2 __ Affected_sector_Real_profits_per_b
usiness
37 Affected_sector_Total_employment
0 20 40 60 80 100
Months
Figure 16 Fourth main run: Increased spending and permanent productivity gains. Plot of wage rate
per months, and of the affected sectors’ real profits per business and employment levels.
Contrary to what may have been expected, it can be seen that once again
the MW will initially reduce real profits per business immediately after
its imposition, even though businesses will ultimately benefit from the
productivity increases and they will manage to permanently increase their
profits’. As regards employment on the other hand, it clearly ends up in
lower levels than it was originally.
The cause for the reduction in employment has much to do with the initial
reduction in firms’ profits. Given that total consumption does not change
initially with the MW, a permanent increase in normal productivity levels
15 The fact that boosts in productivity are considered to be realized gradually and not instantaneously
makes very little difference to the overall dynamics produced. The equations for an instantaneous
productivity increase have been included in the model that would allow the reader to carry the
experiment themselves.
23
cannot benefit firms’ profits since the extra output that can be now
produced cannot be sold to bring in more money. With permanently
increased costs to be paid out and a constant demand then, firms start
losing money. In the face of this situation, the firms that do manage to
survive the initial drop in profits reduce their employment levels thereby
adjusting their supply to the demand levels, cutting wages, and increasing
profits. Since profits are then seen to increase, new firms are drawn into
the economy and given that a permanent increase in real profits per
business has been achieved due to permanently higher productivity, the
number of businesses within the affected sector rises while the number of
employees per business drops. Figure 17 confirms this hypothesis.
1 11.0
-2~- 430,000
1 9.5
___ Affected_sector_Employment_per__
-2- 390,000 1™ business
-— 8.0
= Affected_sector_Businesses
0 50 100 150 200
Months
Figure 17 Fourth main run: Increased spending and permanent productivity gains. Plot of the number
of businesses and the employment levels per business within the affected sector
The results depicted in Figures 15 and 17 however, cast serious doubt to
the implicit assumption taken by many that the effects of a MW can be
empirically assessed in a proper manner by merely looking at the
employment levels of particular expected-to-be-affected firms before and
after a MW imposition. In particular, this appears to be the very
assumption that Card and Krueger made when they attempted to
empirically assess the effects of a MW hike in the state of New Jersey
back in 1992. Card and Krueger (1994 and 1995) surveyed 410 fast-food
restaurants before and after a MW increase at stores in New Jersey
(where the MW was imposed) and eastem Pennsylvania (where the MW
was unaltered) and produced one of the most widely known and
referenced MW paper in the economics literature that managed to alter
the conceptions of many economists as regards the potential MW effects
in an economy. As suggested in this model however, not only would this
kind of treatment fail to take into account any possible trade offs between
the affected and unaffected sectors, but it would also ignore any
alterations in the numbers of businesses within an economy. Such
simplifications appear therefore to be quite risky.
2.3.5 Fifth run: Challenging the implicit fixed cost assumption
24
Up until now the implicit assumption that fixed costs simply constitute a
flow that merely reduces entrepreneurs’ income was made. Indeed, the
beneficial results in total employment and profits levels that were
evidenced in section 2.3.2 had been attributed initially to the reduction of
this outflow which then acted to increase total consumption setting the
multiplier loop in motion. This assumption is now challenged by both
extending the model boundary to include an additional consumer group,
the rentiers, and by making the extreme additional assumption that all
fixed costs are simply rent costs. Any reduction in fixed costs therefore
now acts to restrict rentiers’ income and consumption leaving total
consumption levels unaffected from the number of business in the
simulated economy.
Figure 18 shows that even in such conditions, the MW does not
ultimately reduce employment levels.
= 9,100,000
> 1,000
nd 8,950,000
—_ 900 —,— Total_employment
=2- Wage_rate_per_month
aot ie 8,800,000
=> 800
Time
Figure 18 Fifth main run: Plot of total employment, unaffected and affected sectors’ employment and
the affected sector's average silling price
2.3.6 Sixth-ninth runs: Increased spending, constant productivity, cyclical
demand.
In the final runs considered in this paper, an effort is made to identify the
effects a MW would have when introduced in different phases of an
economy’s business cycle. Assuming increased spending and no
permanent productivity increases (i.e. adopting the assumptions of section
2.3.2) an oscillatory exogenous consumption is introduced with a
periodicity of 60 months to capture the typical 5-year duration of a
business cycle, and the MW is imposed when the economy is recovering,
booming, going in recession, or is in depression. For the fourth run (run
4) a MW is not included at all to provide a basis for the comparison of the
results of nuns 5-8.
25
9,500,001
2
§ Base_case_no_MW_imposed_Total_employme
als VS at I ana
i 3 __MW_imposed_when_when_economy_is_growi
3
~ 2” ng _Total_employment
9,000,000 | \ —3—MW_imposed_when_economy_is___booming
13 __,_MW_imposed_when_in_recession__Total_empl
2 4 4 oyment
i Ef ____ MW_imposed_when_in_slump_Total_employme
nt
8,500,000+ + + + 1
0 50 100 150 200
Months
Figure 17 Runs 4-8. Comparison plot of employment
Two things emerge quite eminently from Figure 17. The most surprising
of the two perhaps, is the fact that the time of the introduction of the MW
in the economy makes absolutely no difference for the longer term well-
being of the economy. Under the chosen assumptions then, the MW will
eventually act to boost employment levels whenever it is introduced. It
must be added of course, that this result is in complete harmony with the
previous analysis in section 2.3.2, where under the same assumptions as
regards spending and productivity the same results, namely a permanent
increase in employment levels, were produced.
Secondly, it is shown that the best time to introduce a biting MW in terms
of experiencing the smaller transient effects in total employment levels is
either when an economy goes through a recovery stage or when she is
booming. It should be intuitively evident that with the introduction of the
MW at times of growing demand the initial reduction in firms’ profits due
to higher costs will be counterbalanced by the stronger sales and
consequently profits. As a result fewer firms will close down and the
pressure on employment will be limited. When the economy proceeds
into the recessionary phase then, the longer term beneficial effects of the
MW will make their appearance and the reduction in total employment
levels will again be somewhat contained.
It is on similar grounds that the analysis in favour of a MW imposition
when the economy is booming is made, although, as shown in Figure 17,
the transient dynamics are not exactly the same as with the previously
described situation. By imposing the MW at times when demand is about
to drop, the fall in employment is somewhat exacerbated, yet because of
the quite quick emergence of the beneficial effects of the MW, recession
is cut short and the economy gets back on track faster than it would have
done otherwise. Conversely, a MW introduced at times when demand is
26
low or getting lower, will further exacerbate the low employment
situation before the beneficial effects of the MW kick in.
Even though this last finding appeals very much to common sense, there
have been occasions where it has been disputed by some economists in
the past, as George Stigler had done for example some time ago -
Stigler(1946 p.362)- arguing that a MW should be imposed when an
economy is during a recessionary stage.
2.4 Model testing
A number of different tests were carried in order to build confidence in
the model and its findings. Firstly, an attempt was made for the causal
structure (described in section 2.1) to be as realistic as possible and
disaggregated enough to enable one to draw a number of safe conclusions
as regards the potential economic effects of a biting MW. To the
knowledge of the authors therefore, the model structure does not include
any assumptions that would be contradicted by the structure of a real
economy, although a number of simplifications have naturally been
made.
Secondly, the fact that the output that gets produced from a number of
different partial model tests and reruns can be directly associated to the
identified causal structure giving no rise to any suspicious conflicting
dynamics goes some way into establishing that no fundamental mistakes
should exist in the equations of the model.
Next, some extreme conditions tests were carried, with both the affected
and the unaffected sectors assuming values of zero and one in tum’®,
while all firms were also considered to shut down in the event of even
small reductions in profits. As regards increased prices, the extreme
situation where all demand was diverted to imports was tested while, as
already described, fixed cost per business have also been assumed to
equal zero. The particular modifications required in the model’s equations
for these altemative runs are all presented at the very bottom of the
model’s listing.
Fourthly, in an attempt to test the robustness of the firm’s conclusions in
the face of different time constants, a great number of different
combinations was tried. Although it would have been impossible to
16 The continuous use of the ‘ratio’ function throughout the model whose purpose is not to allow the
denominator of a particular ratio to equal zero was indeed required in order to handle the zeroing out of
the sectors if extreme parameter values for a and b were chosen.
27
provide the output for even a small part of them, in Figure 20 the degree
of this model’s robustness is presented through the plot of the total
employment levels derived from the assumptions made in section 2.3.2
given a doubling and a halving in all time constants.
9,400,000-
Phys
9,200,000 13% -9=3——9 ——_
3 _, _ Extra_spending_run_Actual_delay_times
9,000,000: 1~ used
8,800,000: —2~—€xtra_spending_run_Halving_delays
8,600,000: —3—Extra_spending_run_Doubling_delays
r t t t 1
0 50 100 150 200
Months
Figure 20 Sensitivity test. Doubling and halving delay times
Consistent with all other observations made from other such time varying
combinations, Figure 2.3.2 shows that whether the chosen time constants
approximate reality or not is of little significance in this particular case.
Lastly, the model’s behaviour has been tested with a reduced time step
(ie. dt=0.125 instead of dt=0.25) and the length of the simulation was
doubled to make sure that no surprising dynamics were produced, while
mass balance checks have been calculated for the flow of money due to
its highly cyclical nature. A dimensional consistency check and an
inspection of whether any premature dynamics are produced were also
performed.
3 CONCLUSIONS
The traditional neoclassical approaches to the effects of the MW fail to
take into account the vast complexities associated with this scheme, and
their results, having unfortunately shaped current economic and political
thinking, appear to do no justice to the richness of outcomes that may be
ultimately produced because of such a scheme. When considering the
potential likely effects of a MW therefore, attention is almost exclusively
centered on issues that have to do with the immediate changes in
businesses’ wage bills, profits, product prices and employment levels.
The possibility of any dynamics occurring after the MW imposition is
generally not contemplated with, with the only exception probably being
that if the MW is set at too high a level differential pressures could
emerge driving wages higher still.
28
In this paper a model is presented that tries to do some justice to the
complexities involved with the MW. An approximately 210 variable
model is consequently described that allows for a series of different
assumptions to be tried and tested and its result prove to challenge current
economic wisdom in many ways. It is demonstrated that variables that are
not even contemplated within the traditional neoclassical framework such
as consumption spending and fixed costs should be at the forefront of the
economic analysis since they, alongside imports, are the ultimate
determinants of the economic effects of the MW. The possibility and the
reasons behind a longer term permanent increase in both profit and
employment levels is also highlighted and trade offs in both of these
variables between firms whose wage structure remains unaffected from
the MW and affected firms, are also shown to be more likely than not.
Finally it is shown that the MW can result in an increase in the number of
businesses and a parallel reduction in the employment levels per business,
or a reduction in the number of firms and an increase in their associated
employment levels.
REFERENCES
Card, D. and A. Krueger, 1994. Minimum wages and employment: a
case study of the fast food industry in New Jersey and Pennsylvania.
American Economic Review, vol. 84(4), pp. 772-793.
Card, D. and A. Krueger, 1995. Myth and Measurement - the New
Economics of the Minimum Wage. (Princeton New Jersey: Princeton
University Press).
Coyle R.G., 1996. System Dynamics Modelling: A practical approach.
(Chapman and Hall).
Coyle R.G., 1999. Simulation by repeated optimization. Journal of the
Operational Research Society, vol. 50(4) pp.429-438
Dangerfield B. and C. Roberts ,1996. An overview of strategy and
tactics in system dynamics optimization. Journal of the Operational
Research Society, vol. 47, pp.405-423
Dickens, R., S. Machin and A. Manning, 1994. Minimum wages and
employment: a theoretical framework with an application to the UK
Wages Councils. International Journal of Manpower, vol. 15(2/3), pp.
26-48.
29
Edwards, P. and M. Gilman, 1998. A national minimum wage: stimulus
to economic efficiency? Warwick Papers in Industrial Relations No. 59.
(Manchester: USDAW).
Forrester J., 1965. Industrial Dynamics (4 printing, MIT press)
Forrester J., 1991. System Dynamics and the Lessons of 35 Y ears, in
The Systemic Basis of Policy Making in the 1990s, ed. De Greene,
Kenyon B.
Also freely available in:
http://web.mit.edu/sysdyn/people/jay-forrester.html
Kosko, B.,1994. Fuzzy Thinking. The New Science of Fuzzy Logic.
(Flamingo)
Machin, S. and A. Manning, 1994. Minimum wages, wage dispersion
and employment: evidence from UK Wages Councils. Industrial and
Labor Relations Review, vol. 47(2), pp. 319-329.
Mayer T., 1993. Truth versus Precision in Economics. (series of:
Advances in economic methodology, Edward Elgar Publishing Ltd)
Nolan, P., 1989. Walking on water? Performance and industrial relations
under Thatcher. Industrial Relations J ournal, vol. 20 (2), pp.81-92
Sterman, J., 2000. Business Dynamics: Systems Thinking and Modeling
for a Complex World. (Irwin McGraw-Hill)
Stigler, G.J., 1946, The economics of minimum wage legislation,
American Economic Review, vol.36, June, pp.358-365
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