Stock And Flow
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Economics Economics () is the social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analy ...
, business, accounting, and related fields often distinguish between quantities that are stocks and those that are flows. These differ in their
units of measurement A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can be expressed as a mul ...
. A ''stock'' is measured at one specific time, and represents a quantity existing at that point in time (say, December 31, 2004), which may have accumulated in the past. A ''flow'' variable is measured over an interval of time. Therefore, a flow would be measured ''per unit of time'' (say a year). Flow is roughly analogous to
rate Rate or rates may refer to: Finance * Rates (tax), a type of taxation system in the United Kingdom used to fund local government * Exchange rate, rate at which one currency will be exchanged for another Mathematics and science * Rate (mathema ...
or
speed In everyday use and in kinematics, the speed (commonly referred to as ''v'') of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quantity ...
in this sense. For example, U.S. nominal
gross domestic product Gross domestic product (GDP) is a money, monetary Measurement in economics, measure of the market value of all the final goods and services produced and sold (not resold) in a specific time period by countries. Due to its complex and subjec ...
refers to a total number of dollars spent over a time period, such as a year. Therefore, it is a flow variable, and has units of dollars/year. In contrast, the U.S. nominal
capital stock A corporation's share capital, commonly referred to as capital stock in the United States, is the portion of a corporation's equity that has been derived by the issue of shares in the corporation to a shareholder, usually for cash. "Share capit ...
is the total value, in dollars, of equipment, buildings, and other real productive assets in the U.S. economy, and has units of dollars. The diagram provides an intuitive illustration of how the ''stock'' of capital currently available is increased by the ''flow'' of new investment and depleted by the ''flow'' of
depreciation In accountancy, depreciation is a term that refers to two aspects of the same concept: first, the actual decrease of fair value of an asset, such as the decrease in value of factory equipment each year as it is used and wear, and second, the a ...
.


Stocks and flows in accounting

Thus, a stock refers to the value of an asset at a balance date (or point in time), while a flow refers to the total value of transactions (sales or purchases, incomes or expenditures) during an accounting period. If the flow value of an economic activity is divided by the average stock value during an accounting period, we obtain a measure of the number of turnovers (or rotations) of a stock in that accounting period. Some accounting entries are normally always represented as a flow (e.g. profit or income), while others may be represented both as a stock or as a flow (e.g. capital). A person or country might have stocks of
money Money is any item or verifiable record that is generally accepted as payment for goods and services and repayment of debts, such as taxes, in a particular country or socio-economic context. The primary functions which distinguish money ar ...
, financial assets, liabilities,
wealth Wealth is the abundance of valuable financial assets or physical possessions which can be converted into a form that can be used for transactions. This includes the core meaning as held in the originating Old English word , which is from an ...
, real
means of production The means of production is a term which describes land, Work (human activity), labor and capital (economics), capital that can be used to produce products (such as goods or Service (economics), services); however, the term can also refer to anyth ...
, capital,
inventories Inventory (American English) or stock (British English) refers to the goods and materials that a business holds for the ultimate goal of resale, production or utilisation. Inventory management is a discipline primarily about specifying the sh ...
, and
human capital Human capital is a concept used by social scientists to designate personal attributes considered useful in the production process. It encompasses employee knowledge, skills, know-how, good health, and education. Human capital has a substanti ...
(or labor power). Flow magnitudes include
income Income is the consumption and saving opportunity gained by an entity within a specified timeframe, which is generally expressed in monetary terms. Income is difficult to define conceptually and the definition may be different across fields. F ...
,
spending Consumption is the act of using resources to satisfy current needs and wants. It is seen in contrast to investing, which is spending for acquisition of ''future'' income. Consumption is a major concept in economics and is also studied in many o ...
,
saving Saving is income not spent, or deferred consumption. Methods of saving include putting money aside in, for example, a deposit account, a pension account, an investment fund, or as cash. Saving also involves reducing expenditures, such as recur ...
, debt repayment, fixed investment, inventory investment, and labor utilization. These differ in their units of measurement. Capital is a stock concept which yields a periodic income which is a flow concept.


Comparing stocks and flows

Stocks and flows have different units and are thus not ''
commensurable Two concepts or things are commensurable if they are measurable or comparable by a common standard. Commensurability most commonly refers to commensurability (mathematics). It may also refer to: * Commensurability (astronomy), whether two orbit ...
'' – they cannot be meaningfully ''compared, equated, added, or subtracted.'' However, one may meaningfully take ''ratios'' of stocks and flows, or multiply or divide them. This is a point of some confusion for some economics students, as some confuse taking ratios (valid) with comparing (invalid). The ratio of a stock over a flow has units of (units)/(units/time) = time. For example, the debt to GDP ratio has units of years (as GDP is measured in, for example, dollars per year whereas debt is measured in dollars), which yields the interpretation of the debt to GDP ratio as "number of years to pay off all debt, assuming all GDP devoted to debt repayment". The ratio of a flow to a stock has units 1/time. For example, the velocity of money is defined as nominal GDP / nominal
money supply In macroeconomics, the money supply (or money stock) refers to the total volume of currency held by the public at a particular point in time. There are several ways to define "money", but standard measures usually include Circulation (curren ...
; it has units of (dollars / year) / dollars = 1/year. In discrete time, the change in a stock variable from one point in time to another point in time one time unit later (the first difference of the stock) is equal to the corresponding flow variable per unit of time. For example, if a country's stock of
physical capital Physical capital represents in economics one of the three primary factors of production. Physical capital is the apparatus used to produce a good and services. Physical capital represents the tangible man-made goods that help and support the pro ...
on January 1, 2010 is 20 machines and on January 1, 2011 is 23 machines, then the flow of net investment during 2010 was 3 machines per year. If it then has 27 machines on January 1, 2012, the flow of net investment during 2010 and 2011 averaged 3 \tfrac machines per year. In continuous time, the time derivative of a stock variable is a flow variable.


More general uses

Stocks and flows also have natural meanings in many contexts outside of economics, business and related fields. The concepts apply to many conserved quantities such as
energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of hea ...
, and to
material Material is a substance or mixture of substances that constitutes an object. Materials can be pure or impure, living or non-living matter. Materials can be classified on the basis of their physical and chemical properties, or on their geolo ...
s such as in
stoichiometry Stoichiometry refers to the relationship between the quantities of reactants and products before, during, and following chemical reactions. Stoichiometry is founded on the law of conservation of mass where the total mass of the reactants equ ...
, water reservoir management, and
greenhouse gases A greenhouse gas (GHG or GhG) is a gas that absorbs and emits radiant energy within the thermal infrared range, causing the greenhouse effect. The primary greenhouse gases in Earth's atmosphere are water vapor (), carbon dioxide (), meth ...
and other durable pollutants that accumulate in the environment or in organisms.
Climate change mitigation Climate change mitigation is action to limit climate change by reducing emissions of greenhouse gases or removing those gases from the atmosphere. The recent rise in global average temperature is mostly caused by emissions from fossil fuels bu ...
, for example, is a fairly straightforward stock and flow problem with the primary goal of reducing the stock (the concentration of durable greenhouse gases in the atmosphere) by manipulating the flows (reducing inflows such as
greenhouse gas emissions Greenhouse gas emissions from human activities strengthen the greenhouse effect, contributing to climate change. Most is carbon dioxide from burning fossil fuels: coal, oil, and natural gas. The largest emitters include coal in China and ...
into the atmosphere, and increasing outflows such as
carbon dioxide removal Carbon dioxide removal (CDR), also known as negative emissions, is a process in which carbon dioxide gas () is removed from the atmosphere and sequestered for long periods of time. Similarly, greenhouse gas removal (GGR) or negative greenho ...
). In living systems, such as the human body, energy homeostasis describes the linear relationship between flows (the food we eat and the energy we expend along with the wastes we excrete) and the stock (manifesting as our gain or loss of body weight over time). In Earth system science, many stock and flow problems arise, such as in the
carbon cycle The carbon cycle is the biogeochemical cycle by which carbon is exchanged among the biosphere, pedosphere, geosphere, hydrosphere, and atmosphere of the Earth. Carbon is the main component of biological compounds as well as a major componen ...
, the
nitrogen cycle The nitrogen cycle is the biogeochemical cycle by which nitrogen is converted into multiple chemical forms as it circulates among atmospheric, terrestrial, and marine ecosystems. The conversion of nitrogen can be carried out through both biolo ...
, the
water cycle The water cycle, also known as the hydrologic cycle or the hydrological cycle, is a biogeochemical cycle that describes the continuous movement of water on, above and below the surface of the Earth. The mass of water on Earth remains fairly cons ...
, and Earth's energy budget. Thus stocks and flows are the basic building blocks of
system dynamics System dynamics (SD) is an approach to understanding the nonlinear behaviour of complex systems over time using stocks, flows, internal feedback loops, table functions and time delays. Overview System dynamics is a methodology and mathematic ...
models. Jay Forrester originally referred to them as "levels" rather than stocks, together with "rates" or "rates of flow". A stock (or "level variable") in this broader sense is some entity that is accumulated over time by inflows and/or depleted by outflows. Stocks can only be changed via flows. Mathematically a stock can be seen as an accumulation or integration of flows over time – with outflows subtracting from the stock. Stocks typically have a certain value at each moment of time – e.g. the number of population at a certain moment, or the quantity of water in a reservoir. A flow (or "rate") changes a stock over time. Usually we can clearly distinguish inflows (adding to the stock) and outflows (subtracting from the stock). Flows typically are measured over a certain interval of time – e.g., the number of births over a day or month. Synonyms


Examples


Accounting, finance, etc.


Other contexts


Calculus interpretation

If the quantity of some ''stock'' variable at time \,t\, is \,Q(t)\,, then the
derivative In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. ...
\,\frac\, is the ''flow'' of changes in the stock. Likewise, the ''stock'' at some time t is the
integral In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with ...
of the ''flow'' from some moment set as zero until time t. For example, if the
capital stock A corporation's share capital, commonly referred to as capital stock in the United States, is the portion of a corporation's equity that has been derived by the issue of shares in the corporation to a shareholder, usually for cash. "Share capit ...
\,K(t)\, is increased gradually over time by a flow of gross investment \,I^g(t)\, and decreased gradually over time by a flow of
depreciation In accountancy, depreciation is a term that refers to two aspects of the same concept: first, the actual decrease of fair value of an asset, such as the decrease in value of factory equipment each year as it is used and wear, and second, the a ...
\,D(t)\,, then the instantaneous rate of change in the capital stock is given by : \frac = I^g(t) - D(t) = I^n(t) where the notation \,I^n(t)\, refers to the flow of net investment, which is the difference between gross investment and depreciation.


Example of dynamic stock and flow diagram

Equations that change the two stocks via the flow are: : \ \text = \int_0^t -\text\,dt : \ \text = \int_0^t \text\,dt List of all the equations, in their order of execution in each time, from time = 1 to 36: : 1) \ \text= \sin( 5t ) : 2.1) \ \text\ -= \text\ : 2.2) \ \text\ += \text\


History

The distinction between a stock and a flow variable is elementary, and dates back centuries in accounting practice (distinction between an asset and income, for instance). In economics, the distinction was formalized and terms were set in , in which Irving Fisher formalized capital (as a stock). Polish economist Michał Kalecki emphasized the centrality of the distinction of stocks and flows, caustically calling economics "the science of confusing stocks with flows" in his critique of the
quantity theory of money In monetary economics, the quantity theory of money (often abbreviated QTM) is one of the directions of Western economic thought that emerged in the 16th-17th centuries. The QTM states that the general price level of goods and services is directl ...
(circa 1936, frequently quoted by
Joan Robinson Joan Violet Robinson (''née'' Maurice; 31 October 1903 – 5 August 1983) was a British economist well known for her wide-ranging contributions to economic theory. She was a central figure in what became known as post-Keynesian economics. ...
).
Joan Robinson Joan Violet Robinson (''née'' Maurice; 31 October 1903 – 5 August 1983) was a British economist well known for her wide-ranging contributions to economic theory. She was a central figure in what became known as post-Keynesian economics. ...
,
Shedding Darkness
, '' Cambridge Journal of Economics'', 6 (1982), 295–6: "it is the science of confusing stocks with flows. It is this confusion that has kept the
Quantity Theory of Money In monetary economics, the quantity theory of money (often abbreviated QTM) is one of the directions of Western economic thought that emerged in the 16th-17th centuries. The QTM states that the general price level of goods and services is directl ...
alive until today."


See also

*
Flow (disambiguation) Flow may refer to: Science and technology * Fluid flow, the motion of a gas or liquid * Flow (geomorphology), a type of mass wasting or slope movement in geomorphology * Flow (mathematics), a group action of the real numbers on a set * Flow (psych ...
* Intensive and extensive properties * Stock (disambiguation) * Stock-Flow consistent model *
Systems thinking Systems thinking is a way of making sense of the complexity of the world by looking at it in terms of wholes and relationships rather than by splitting it down into its parts. It has been used as a way of exploring and developing effective actio ...
*
System dynamics System dynamics (SD) is an approach to understanding the nonlinear behaviour of complex systems over time using stocks, flows, internal feedback loops, table functions and time delays. Overview System dynamics is a methodology and mathematic ...
* Wealth (economics)


References

* {{citation , title = What is Capital? , authorlink = Irving Fisher , first = Irving , last = Fisher , journal = The Economic Journal , volume = 6 , date=December 1896 , pages = 509–534 , jstor = 2957184 , issue = 24 , doi = 10.2307/2957184 , url = https://zenodo.org/record/1449667 * D.W. Bushaw and R.W. Clower, 1957. ''Introduction to Mathematical Economics'', Ch. 3–6. "Section" & arrow-searchable pageChapter ("Section") and arrow-searchable pag
links.
* Robert W. Clower, 1954a. "An Investigation into the Dynamics of Investment," ''American Economic Review''. 44(l), pp
64
81. * _____, 1954b. "Price Determination in a Stock-Flow Economy" with D. W. Bushaw, ''Econometrica '' 22(3),
p. 328
343. * _____, 1968. "Stock-flow analysis," '' International Encyclopedia of the Social Sciences'', v. 12. * Glenn W. Harrison, 1987 008 "Stocks and flows," '' The New Palgrave: A Dictionary of Economics'', v. 4, pp. 506–09. Inventory Accounting systems Systems theory Economics and time