distributing this free software
that interactively explains you the basic microeconomic theory of consumption,
we shall briefly introduce you to its tenets, suggesting some easy
experiment with the computer application. More importantly, we shall propose
you the alternative approach for interpreting
real consumers' choices that is taking growing consensus among economists.
The evolutionary economics of consumption and demand is here presented
and contrasted, providing many empirically testable differences
with the standard model, on the background of a broader methodology.
The first chapter and the appendix are mainly for students,
where the second chapter is of great interest for both advanced scholars,
looking for a compact but wide presentation of behavioral and evolutionary
conceptualization, and students.
to the neoclassical model of consumer choice
The standard textbook model of consumer is an outstanding
example of the neoclassical paradigm in economics
: a hyper-rational agent maximises something
by choosing an "optimal" bundle of things.
Here, the hyper-rational consumer maximises utility (i.
e. an overall generic measure of well-being) by exhausting a given budget.
He has a pre-defined income to spend on - for simplicity's
sake - two goods, called X and Y, respectively.
He could spend his entire income buying only X,
thus purchasing a quantity of X equal to income divided by the price of
Let's take a numerical example that you find here in the
animated graph and that you can replicate with the software:
when his income is 50 and the Y price is 10, the consumer can purchase
5 units of Y (higher red point on Y axis).
If the graph is not animated,
just reload this page or pass to a more modern Internet browser.
Or he could spend his entire income buying only X -
the other good - thus purchasing a quantity of X equal to his income
divided by the price of X. If X price is 6, the consumer can purchase
at most 8.33 units of X (lower red point).
Or he can afford (at most) to buy any combination of quantities
of X and Y that costs exactly as the income. These combinations give rise
to the budget line you see between the two red points.
How to choose? Well, by having a consistent set of judgements
about how much utility the consumer will enjoy by consuming each possible
bundle of goods.
The typical well-behaved structure of utility of bundles
is offered by indifference curves, i.e. all bundles giving the
same level of utility to the consumer.
Here below you can see two indifference curves: the higher
indifference curve is characterised by a higher level of utility.
Now, we should consider - at the same time - both
the budget constraint (the budget line) and the utility
structure (the indifference curves).
The optimal bundle of goods belongs to the highest
possible indifference curve crossing the budget line.
The red point is the rational consumer's choice (the
chosen bundle), since it maximises utility, given the budget constraint.
Everything sounds very logical and convincing - within
the unrealistic setting offered by this kind of mathematics. The
deductive style of this microeconomics in consumer theory takes very little
care of empirical analysis and of any reasonably open experimentation.
If you are interesting in understanding its mechanics, please download
this software and read the appendix.
But then come back to the second chapter, which is the most interesting
the neoclassical model with its opposite alternative
How do you really choose in a supermarket,
facing thousands of goods and brands?
Do you have a single figure (utility) attached to any good and any combination
of quantities of every good, expressing your future enjoyment?
Is your choice completely independent from what others decide or what
you have already at home?
Is your pocket empty when exiting? Do you exhaust always
Is what you chose "optimal" so that next time,
given your unchanged income and the same prices, you'll choose exactly
the same thing?
Many students at the end of the course in Microeconomics
are very sceptical about the realism of the neoclassical theory, especially
the part about consumers, since they have direct expericence of buying
acts and they know how they choose. And they find no trace of high mathematics
and optimisation procedures. They don't use computer software to compute
economics is the main competitor of the mainstream perspective in the
micro-foundation of consumption. It
has already reached some clear theoretical foundations
as well as formal models (as this) and empirical
forecasts to be tested to corroborate or falsify the theory. It has been
applied to choices in Point of Sales (such as these).
It embeds the insight of psychology and behavioural approaches, including
prospect theory, while enriching them to the next level.
we present some very schematic comparison of the two approaches.
approach with well-behaved preferences
evolutionary economics approach
context of choice
of material goods and services is the only way to get satisfaction
from life; it's a goal in itself or, better, it's the only way to
get "utility", which is a goal in itself.
are instrumental to "activities" that human
beings plan and actually carry out, usually to fulfill needs and
wants. These activities, often involving other participants, are articulation
of "life" and derive from "lifestyles".
All buying choices are taken at the same time (simultaneously).
are asynchronous and sequential.
they are asynchronous, in one day, certain goods are purchased;
the days after, other goods are purchased.
Being sequential in time,
common phases of decisions are "need awareness", search,
selection, execution, and, after some enjoyment/utilization (which
is not a part of the decision process), a phase of judgement about
it, possibly leading to guidelines for next purchases and to communication
to others (especially in case of particularly bad or particularly
good experience). However the sequence can contain switches (e.g.
with a proposal being analysed to check whether it covers some needs).
the choice of the purchase channel (shop, supermarket, online,...)
and the specific Point of sale is made before the choice of actual
good to purchase (with the open possibility of delaying purchase
and look somewhere else).
Planning and execution may be separated
in time, leaving room for changes of mind.
Consumption and purchases
Consumption decision and their psychological laws
determine purchase acts.
Buyer don't need to be the direct consumer. Buying
decision may have an intrisic logic different from consumption (e.g.
to buy large quantities when the good is cheaper and store them
for long periods).
Information available to consumer
consumer has full information about all existing products, their
use and their effects on his welfare (utility).
Limited information. Awareness of
available set of choices is dependent on what was chosen earlier
and on the process of choosing.
of difficulty of the choice
The choice is always easy, with all pros and cons already evaluated
and compressed in a monotonic measure (utility).
Choice can be easy, moderate
or extremely difficult, depending on the situation. Conversely
it's because a good has the "right" level of difficulty
that it appeal to the consumer (newbies prefer easy things, masters
prefer difficult things).
The role of experience
None. The consumer ex-ante knows everything and actual consumption
does not change his evaluation of the utility.
Households have well defined preferences regarding goods they
never have experienced.
The first-time purchase is characterised by expectations,
raised by observation and by retrieval of memories of past experiences
in similar goods; repurchase
is, at least in part, based on the experience gained through personal
|Origin of tastes
are given. Not known from whom, when, how, and why.
Childhood, exploration and trial, tasting, judging and making mistakes,
exposure to external and (more ore less) authoritative teaching,
all revisited upon personal experience, observation of others and
social communication, including through networks.
In particular, how caring adults anticipate and manage the neophobic
phase of toddler has a relevant role on the imprinting upon which
exploration of new goods will be carried out in later life.
Consumers learn to consume from intersubjective dynamics, including
real persons and media.
Importance of advertising
The consumer has its own tastes and they can't be changed.
The limited information of the consumer can be extended by advertising.
Depending on the decision-making style, advertising can have an
important influence beyond mere information.
Importance of the opinion of others
The consumer stands alone in her/his preferences.
consumer can explicitly ask others or at least have contact with
the opinion of others, who are stratified according to the relationship
to the consumer (e.g. friends, teachers,...) and other network parametres.
Importance of the information flows from the producer
via e.g. the label
consumer can receive instruction to appropriately use the product
and enjoy it better.
label can show third party certification of quality, e.g. environmental
friendliness by ECOLABEL.
consumer does never make mistakes in computation and choices.
consumer can make mistakes. He/she may regret or being for
long period unaware of having made a mistake.
||The consumer is always
served or the refusal to sell
of one specific firm is motivated by short-run marginal costs being
higher than the current price. The consumer does not suffer from the
refusal and promptly switches to another firm with an identical product.
may happen, is usually painful but not motivated by marginal cost
The place where choice is made
Non explicit; it's a virtual decision in the consumer's
In shops, supermarkets, and other Point of Sales;
through Internet or other non-store distribution channels. The available
does influence final
The shopping experience
Irrelevant. The utility depends on the good, not
on the time spent on shopping.
Some people enjoy going shopping, show their knowledge
and skills in choosing (or good luck in finding amazing bargains).
Other feel that shopping is boring and try to spend as little time
as possible on it. Still others have different attitudes to the
issue. This adds to the number of reasons why people are heterogeneous.
Relationship between choice and execution of choice
No difference: all choices are executed.
Actual purchase can be postponed, modified or cancelled because
of external pressure and conditions.
Execution takes time.
Never. The customer is always free not to buy.
On certain markets, such as insurance
, the regulatory authority can mandate the purchase.
the consumer decides
Full rationality based on consumer's huge mathematical
The consumer has a money budget limit which is systematically
exhausted (the budget constraints are always binding and reached).
There is one overall budget for all kind of expenditures. All
sources of income are fungible for all types of expenditure purposes.
The consumer keeps always a reserve of slack resources to cope
with further expenditures. Many mental accounting budgets are
kept separate by the consumer (who for instance separates capital
expenditure from current expenditure and different lines of current
expenditures, e.g. by need). The source of income can impact its
||Whole personal income
||It implements a "mental
accounting" in which specific budget lines (distinguishing e.g.
current expenditures from capital expenditures) are not fungible.
Consumer cannot take a loan, unless you switch model
and focus on savings, leaving aside the problem of which goods to
consume. In the latter case, loans are automatically granted by
The institutional setting can facilitate consumer credit (apart
from banks, also directly at the Point of Sale), while the use
of credit cards can further relax immediate budget constraints.
Moral self-directive guidelines
by the consumer and his/her family may exert an influence on how
much to seize this opportunity and the corresponding risks.
Conversely, credit providers evaluate the debtor
Treatment of multiple requirements over the
good (e.g. shape, weight, colour, safety, energy consumption,
social acceptability, etc.)
Automatic and implicit: all features of the good can be measured,
balanced, and summarised in a unique global value (utility).
Explicit; the consumer can have minimum / maximum thresholds
of acceptability for each requirement.
Different algorithms available
for using the information about how the good fits the requirements.
Mathematics used in formal models to solve the problem
of the consumer
Equations and systems of equations are the main
Tree algorithms and disequations
are the main formal devices; extensive use of IF-THEN statements.
A dual selection can occur, with both the seller and the customer
posing conditions and price thresholds, as explored in this
formal model of insurance.
a non-monetary, non-purchasable constraint in many choice (shopping
being aside work time, travel time. free time, and other uses of
time); in grocery purchases, at physical
of the purchased basket
can be a constraint (lower for consumer coming back home by foot
and higher for car users).
|Product-dependent process of choice
None. All goods are purchase after a standard process of evaluation.
Low involvement goods are chosen differently from high-stakes goods:
certain goods are purchased according to unsophisticated routines;
other involve conscious thinking, possibly
with systematic search of further information and conditions.
|Consideration of past purchases
||Past purchases built up a cumulative
bundle of goods, whose properties influence present purchases.
For instance, the consumer might not duplicate an item that has already
at home, even if he/she could afford it and likes it very much.
Two goods are substitutes when a fall in consumed
quantity in one can be perfectly compensated by an additional quantity
of the second (so that consumer's utility is constant).
Two goods are substitutes
when they fulfill the same need(s).
Completely subjective, given, expressed in terms
of a linear or non-linear indifference curve.
Interpersonally validated: many people think that the two goods
can be used alternatively as for the same phase or need.
For instance, going by train or by car to a place makes train
and cars substitutes. They differ in many respect but for the
purpose of that trip they are substitutes. Apples and trains are
not substitutes (irrespective of whether some consumer may have
a certain subjective indifference curve relating the two).
|Aggregation and comparison
across different needs
||Automatic: a stable global
preference ordering over different kinds and degrees of want satisfaction
is assumed as given.
||Consurmers are more at
ease in comparing goods that satify the same needs than goods crossing
the boundaries and meeting widely different sets of needs.
|Equivalence between a
fall in price and a rise in income
in the sense that a fall in price of a good that attracted a positive
amount of income at the previous higher price is interpreted by the
consumer as an increase in real income, leading to higher demanded
quantities in all normal goods.
Mental accounting separates events in price variations from wage
/ non-wage income changes.
In particular, small changes in goods whose monthly expenditure
is tiny and erratic in total consumer budget are totally ignored
and have no effects in explicit decisionmaking. Their effect - if
anything - will be cumulative.
Large changes in important categories of consumptions set in motion
a chain of reflections about lifestyles, the need to save / the
opportunity to spend more, e.g. new activities and new and better
categories of goods.
||Utility is a property
of the good, irrespective of consumer skills
||The capability of a good
to satisfy needs depends on both the good and consumer characteristics,
including skills to manipulate the good in goal oriented and nongoal
|Pros and cons
||No explicit balancing
of pros and cons. Every argument is mathematical only, not qualitative.
||Arguments for and against
doing something or buying something could be generated and evaluated.
However, this is yet implemented in current evolutionary models. It
would be a very interesting development.
||None. The consumers makes
an ex-ante rational choice.
||Not yet implemented in
current evolutionary models. However, it can be incorporated, with
e.g. affordability and irrational likeability leading to choice, which
is ex-post rationalised with positive and negative arguments.
the consumer buys
Chosen set of goods
The chosen bundle of goods maximises utility (graphically:
it is on the highest indifference curve) and exhausts the budget
(it is on the budget line).
The chosen good is the "first solution matching certain
sufficiency criteria" or is selected across simple
comparisons, possibly taking into account the cumulative
bundle. The consumer may take into account the effects of
the puchased good on his future consumptions, including of energy.
||The quantity of two goods
(or one good and a composite bundle in fixed proportions) that maximises
utility. The quantity can be any "real number", with an
arbitrary high number of decimals (or even an irrational number).
||Goods that "cannot
miss" from the cumulative
bundle at the disposal of consumer will be purchased in the quantity
deriving from multiplying a "consumption dose" (typical
of satisfaction of the want for a while, in absence of trends) and
the number of consumption occasions, with the time horizon being the
next opportunity to purchase, less the number of consumption doses
already present at home.
By contrast, goods that represent "pleasant surprises" for
the consumer (but do not enter routinely in its cumulative bundle)
will be purchased in erratic occasions (e.g. depending on mood), in
quantities dictated by satisfaction (and the number of people taking
part to the "party"). In every case, the quantity purchased
is a natural number of "packages" or a number with limited
decimals (e.g. weight with a gram limit).
Effects of marginal changes in prices
Small changes in one price modify the quantity bought
of all goods.
No change of quantity or discrete changes on the
few goods concerned
Range of purchased goods
All good (X, Y,..) are bought by the consumer.
A specific consumer buys only a small selection
of all existing goods.
|Purchases at the same
shop, separated by just a short period of time
||Since in a short period
of time, income, prices and product available are the same, the consumer
purchases exactly the same goods in the same quantity
||Each time the consumer
goes to a shop, he can purchase widely different things, e.g. because
at home he has still some inventories
of goods purchased in advance
|Dependence on past prices
||The quantity purchased
depends only on current price, not on previous prices (e.g. increases
or reductions of prices leading to the same final prices generate
the same sold quantity)
||The memory of past prices
exerts an effect on quantity purchased. In particular, durable goods
whose previous lower price led to widening the cumulative
bundle will have lower sales than if the previous prices were
higher than the current. Non-durable goods whose experience increases
the willingness to repurchase
will exhibit the opposite situation than abovementioned durables.
If previous prices were used to guess quality,
a fall in prices is conducive to a higher sale level than an increase.
|Reaction to new goods
All goods were present since the beginning. No new goods.
If in special neoclassical models new goods are allowed, they can
be compared to existing ones by features, so a simple extension
of indifference curves is possible.
New goods are systematically introduced by innovative firms. New
goods can serve as input to current consumption activities and/or
to new activities, covering in turn existing or new need (in
formal terms here described, new goods have certain percentage of
contribution to existing columns of needs and/or to new additional
Certain consumer are prone to test and try every novelty, other
are more or less neophobic. Those who try have the ability to judge,
both based on previously held system of evaluation and by genuine
new judgement. The diffusion of opinions will provide clues for
those who did not try personally.
to a price of "zero"
The quantity demanded and purchased jump to infinity.
The quantity continue to be finite, with "sufficiency"
and other constraits holding (e.g. time for consumption,..). Many
goods are not purchased even when their prices is zero, e.g. because
the consumer (temporarily or definitely) consider them not useful
for his/her activities.
Satisfaction from purchased good
Always equal to expectations, by design.
However, an explicit consideration of a possible random component
of expectation in addition to the "real value", maximization
of expected utility would systematically produce disappointment.
This argument was first made by March,
Dependent on mood at the moment of consumption and the occurrence
of overlooked features that can increase or reduce satisfaction.
Over time, the consumer can get used to the good, get bored or
annoyed and desire something else, including totally new goods.
The consumer talks about her/his purchases to friends
and other people in networks and social/mass/narrow media, especially
if the good turns out to be extraordinarily positive or negative.
Network effects, with news spreading. Generalist and specialized
magazines, websites and blogs host descriptions and evaluations
of the good.
The consumer builds up a structured set of durable and stored
non-durable goods, at the disposal for her/his immediate use.
Market demand is the sum of individual demand of
totally independent consumers.
Market demand is the sum of individual demand but
consumers may interact (e.g. imitate
) and communicate
Heterogeneneity of consumers
Consumer differ because of income.
Heterogeneneity of consumers
Consumers differ because of utility functions (Cobb-Douglas,
sum-of-squares,...) - never used in real marketing research.
Who reacts to changes in prices
Changes in prices modify the behaviour of all consumers.
Most consumers continue to behave as before, Only
some change so to produce the entire market effect.
Diffusion of a specific good in the population
All consumers buy the good.
Most consumer do not buy.
|Shape of demand curve
||Depending on individual
preferences, usually assumed of the same shape for all consumers.
||Mainly depending on income
distribution, with polarised income distribution leading to
convex demand curves and wide-middle-class
society having concave demand curves.
|Contribution to different
social groups to total demand
||People differ by income
levels but there is no segmentation by social groups.
higher the absolute price of the good, the larger the market share
due to the rich. This means that the product features will be
modelled by their tastes, which can be different from the poor, what
has far-reacing consequences on the goals of R&D and the actual
technological trajectory of expensive and cheap goods.
|Determinants of the speed
and scope of diffusion of the good in the population
and features of the good and of its substitutes
of income, personal traits (e.g. neophoby), skills, social networks;
lock-in effects and complementary assets. The cumulative
bundle of people, having or not having products coherent with
the new one.
|Externalities from public
||Demand would change only
if such policies change the prices, since the consumer reacts only
to price signals.
||There are several channels
that can be used by public policies to influence consumption level
and composition. Complex goods (difficult to use) might face a barrier
and a vicious cycle (nobody is buying because of lack of skill but
the skill cannot be gained without use) which might require a free
and external intervention (e.g. education for free for several years
is necessary for many cultural goods to be appreciated and enjoyed).
Low-emission green goods, requested in sustainable consumption and
lifestyles, might require further
As you can see, there are many empirically testable
differences that can be used to discriminate between the evolutionary
economics consumer theory and the neoclassical one.
You can also compare neoclassical maximization choices
and evolutionary routines in their capability of mimicking real data using
our testbed for stochastic
In short, with some simplifications, some would say
that the textbook neoclassical rational consumer is stupid because ignores
his own preferences' origins and dynamics, does not allow for experience
during actual consumption to modify its judgement, can't express substantive
reasons why he chose to buy (e.g. which needs will be fulfilled and whether
in full or not), he buys every good (his only choice is quantity, not
the same fact to buy) instead of selecting which good to buy and which
not, does not search across different points of sale but think that the
price is the same everywhere (established by the producer). Understanding
the theory of consumer choice is easier for consumers than for scholars!
neoclassical model of consumer, widely presented in standard textbooks
as it is, does not represent the "unique game in town". The
evolutionary paradigm, taking up many lessons from managerial marketing
science, is offering an interesting alternative, seemingly a step forward
in the dynamics of consumer theory.
see how it works, we offer you a first model with
bounded rational consumers facing competiting goods. Consumers in
the model follows alternatively three rules of
behaviour. These rules are so common, that you
can even check here to which group of consumer you belong (or not).
choice is up to you. What we can do is to invite you to explore the evolutionary
perspective throughout this site and beyond.
How to use the software on the neoclassical textbook consumer
Based on Hicksian approach to indifference curves and
budget lines, this is a free software
to draw economic graphs, diagrams, demand curves, singling out individual
choices of (hyper)rational consumers choosing the optimal bundle. If you
are a student, you can use as interactive exam preparation guide.
The program starts with a consumer having 50 as income
and facing the price of some X good of 6 and the price of Y of 10.
The "Draw" button produce the graphical representation
of the budget line, i.e. the quantities of X and Y that the consumer
can afford exhausting his income.
Push it a first time: you are drawing the budget line
and computing the value of its slope, equal - in absolute value - to the
relative price of X to Y.
Increase income and re-draw the graph. The quantities
on the budget line are systematically higher. No surprise.
Make more experiments varying income and prices. What
happens when you increase the price of X? See it on the screen rotations
and traslations and ask yourself the reasons.
As we said, the neoclassical approach uses "indifference
curves" to represent the preferences of the consumer. By choosing
an indifference curve type (instead of "none" - the default),
you'll see - always with the button "Draw" - which combination
of X and Y the consumer will optimally choose. For instance, by choosing
the well-behaved Cobb-Douglas type you obtain (in the default position
of income = 50, px = 6, py = 10) that the consumer buys 5.83 units of
X and 1.5 units of Y. In this way he reaches a utility level (a
general happiness) of 3.88.
You can see the effect of changes in income and prices
on demanded quantities (so-called "income elasticity"
and "price elasticity) and on utility by changing the input data.
In particular, an increase of income will normally boost both quantities
of X and Y 
- as well as the utility enjoyed.
Instead, the effect of price on demanded quantities shows that the increase
of the price of X is a damage: utility falls and the quantity of X decreases
as well. Try on the contrary to fix a (almost) zero price of X or Y: what
does it occur? And what when X or Y are absolutely free? The optimal quantity
goes to infinity... Since air is free, how much of it a human would inhale,
according to this model?
Try now some systematic experiment. Keeping income at the same level,
gradually increase the price of X, as it would happen maybe due to rising
business costs. How does the quantity
bought of X change? By collecting your observations, you'll get the demand
function, linking the quantity purchased of a good with its price.
To see the computer do the same, click on the "Issues" Menu,
on its line "Demand" - and the new "Draw" button -
You'll find out - not surprisingly - that demand curves are negatively
sloped, i.e. that an increase of price produces a fall in the quantity
bought (try to modify both prices of X and Y to see the effect of general
price level changes). If consumers are identical, this graph software
generates the market demand curve.
Simmetrically, by keeping prices at the same level, changes in income
give rise to the Engel curve, as you can see from the graph in
the screen activated by the line "Engel's curve" in the "Issues"
The (indirect) link from income to utility - mediated by the optimally
chosen bundle of goods - can be represented by the so-called "indirect
utility function". The indirect utility function is the maximum
utility attained with given prices and income.
You should first experiment in the basic screen by annotating the utility
levels obtained at different levels of income, then draw more systematic
curves in the new screen opened by the "Effects of income and prices
on utility" line of the "Issues" Menu.
Now reflect: if an increase of income fosters utility whereas an increase
of price depresses it - and everything is very precise - there should
be the possibility of keeping the consumer exactly at the same level of
utility by giving some additional amount of income to compensate for the
This is exactly the idea of the so-called "Hicksian compensation":
the consumer is given sufficient income to reach his original utility
level, the price increase notwithstanding.
Try out to compensate price changes with income movements or simply go
to the "Substitution and income effects" screen accessible from
the usual "Issues" Menu .
If you are new to these arguments, you'll need some weeks to understand
all details and have a complete picture of the whole thing. But, then,
come back again, because the story hasn't finished, yet.
 Think for instance to Hal Varian "Intermediate Microeconomics:
A Modern Approach", to Paul Samuelson "Economics", Pindyck
and Rubinfeld "Microeconomics", Gregory Mankiw "Principles
of Microeconomics", David Besanko and Ronald Braeutigam "Microeconomics"
with a special reference to parts devoted to "Consumer behavior",
"Consumer preferences", "Indifference maps", "Budget
constraints", "Revealed Preferences". Flynn and McConnell
"Microeconomics: Principles, Problems, and Policies" includes
some elements of behavioral economics but just small bits, to suggest
that it extends neoclassical theory rather than replacing it.
lies the neoclassical explanation of the macroeconomic relationship from
income to consumption.
 The name mirrors
the important Engel's Law, stating - in 1857 - that food expenditure rises
less than proportionally at the increase of income (the rich spend for
food a smaller percentage of his income than the poor).
To see data confirming even today the Engel's Law
see here. The interesting fact is that
a well-behaved Cobb-Douglas curves is in contrast with Engel's Law because
it generates constant budget shares devoted to the different class of
goods. For an evolutionary economics account of Engel's curves see here
This paper has been quoted, among others, by the following
Problem with the Concept of Utility and its Measurement, L Keller
- Polish Journal of Political Science, 2015 - ceeol.com
Hahnel, U.J.J., Chatelain, G., Conte, B., Piana V., Brosch T., Mental
accounting mechanisms in energy decision-making and behaviour. Nat Energy
(2020). https://doi.org/10.1038/s41560-020-00704-6., freely available