Stock and flow

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Stock and flow

Economics

File:Ballard Farmers' Market - vegetables.jpgEconomics is the Social sciences that studies the Production theory basics, Distribution , and Consumption of Good and Service ....
, business, accounting, and related fields often distinguish between quantities which are stocks and those which are flows. A stock variable is measured at one specific time, and represents a quantity existing at that point in time, which may have been accumulated

Capital accumulation

Most generally, the accumulation of capital refers simply to the gathering or amassment of objects of value; the increase in wealth; or the creation of wealth....
in the past.

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Economics

Capital accumulation

Most generally, the accumulation of capital refers simply to the gathering or amassment of objects of value; the increase in wealth; or the creation of wealth....
in the past. A flow variable is measured over an interval of time. Therefore a flow would be measured per unit of time.

For example, U.S. nominal gross domestic product

Gross domestic product

File:GDP nominal per capita world map IMF 2008.pngThe gross domestic product or gross domestic income is one of the measures of national income and output for a given country's economy....
refers to a total number of dollars spent during a specific time period, such as a year. Therefore it is a flow variable. In contrast, the U.S. nominal capital stock

Capital (economics)

In economics, capital or capital goods or real capital refers to factors of production used to create goods or services that are not themselves significantly consumed in the production process....
is the total value, in dollars, of equipment, buildings, inventories, and other real assets in the U.S. economy. The diagram

Diagram

A diagram is a 2D geometric model symbolic representation of information according to some visualization technique. Sometimes, the technique uses a Three-dimensional space visualization which is then graphical projection onto the 2D surface....
illustrates how the stock of capital

Capital (economics)

In economics, capital or capital goods or real capital refers to factors of production used to create goods or services that are not themselves significantly consumed in the production process....
currently available is increased by the flow of new investment

Investment

Investment or investing is a term with several closely-related meanings in business management, finance and economics, related to Saving or deferring Consumption ....
and depleted by the flow of depreciation

Depreciation

Depreciation is a term used in accounting, economics and finance to spread the cost of an asset over the span of several years.In simple words we can say that depreciation is the reduction in the value of an asset due to usage, passage of time, wear and tear, technological outdating or obsolescence, depletion, inadequacy, rot, rust, decay o...
.

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

Money is anything that is generally accepted as payment for goods and services and repayment of debts. The main uses of money are as a medium of exchange, a unit of account, and a store of value....
, financial assets, liabilities

Liability

In the most general sense, a liability is anything that is a wikt:hindrance, or puts individuals at a disadvantage. It can also be used as a slang term to describe someone that puts a team or group of which they are a member at a disadvantage, and would thus be better off without....
, wealth

Wealth (economics)

In economics and business, wealth of a person or nation is the value of assets owned net of Liability#Financial accounting owed at a point in time....
, real means of production

Means of production

Means of production , include machines, tools, plant and equipment, infrastructure, and so on: "all those things with the aid of which man acts upon the subject of labor, and transforms it." ....
, capital, and human capital

Human capital

Human capital refers to the stock of skills and knowledge embodied in the ability to perform Labour so as to produce economic value. It is the skills and knowledge gained by a worker through education and experience.Many early economic theories refer to it simply as labor, one of three factors of production, and consider it to be a fungible...
(or labor power

Labor power

Labour power is a crucial concept used by Karl Marx in his critique of capitalism political economy. He regarded labour power as the most important of the productive forces....
). Flow magnitudes besides those shown in the diagram include income

Income

Income, refers to consumption opportunity gained by an entity within a specified time frame, which is generally expressed in monetary terms. However, for households and individuals, "income is the sum of all the wages, salaries, profits, interests payments, rents and other forms of earnings received......
, spending, saving, debt repayment, labor, or stocks averaged over a unit of time, such as the money

Money supply

In economics, money supply, or money stock, is the total amount of money available in an economy at a particular point in time. There are several ways to define "money", but standard measures usually include currency in circulation and demand deposits....
in circulation per year.

More general uses

Stocks and flows also have natural meanings in many contexts outside of business and its related fields. Thus stocks and flows are the basic building blocks of system dynamics

System dynamics

System dynamics is an approach to understanding the behaviour of complex systems over time. It deals with internal feedback loops and time delays that affect the behaviour of the entire system....
models

Model (abstract)

In mathematical logic, the formal languages, formal systems, and theory which are studied have no meaningful content until they are given an interpretation within some other system....
. Jay Forrester originally referred to them as "levels" (for stocks) and "rates" (for flows).

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.

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 - eg. the number of births over a day or month.

Examples

Accounting, finance, etc.:

"Stock"	Possible units	"Inflow(s)"	"Outflow(s)"	Possible units
bank balance	euros	deposits interest	withdrawals	euros per month
inventory of lumber	board feet	incoming lumber	outgoing lumber	board feet per week
housing stock	dollars	housing investment	housing depreciation	dollars per year
equity shareholdings	shares (of 'stock STOCK Software for fixed assets management and stock control developed in 2004. Stocktaking process is carried using a hand-held mobile terminal equipped with barcode reader or RFID technology.... ')	purchases of shares	sales of shares	shares per month

Other contexts:

"Stock"	Possible units	"Inflow(s)"	"Outflow(s)"	Possible units
guests in a hotel	persons	guests arriving	guests leaving	persons per day
population	persons	births immigration	deaths emigration	persons per year
water in bathtub Bathtub A bath , bathtub , or tub is a plumbing fixture used for bathing. Most modern bathtubs are made of acrylic glass or fiberglass, but alternatives are available in Vitreous enamel over steel or cast iron, and occasionally wood....	liters	water pouring in	water draining out	liters per second
waste in disposal site	tons	dumping waste	decay of waste	tons per week
fuel tank	gallons	refueling	fuel consumption	gallons per month

Calculus interpretation

If the quantity of some stock variable at time is , then the derivative

Derivative

In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much a quantity is changing at a given point....
is the flow of changes in the stock. Likewise, the stock is the integral

Integral

Integration is an important concept in mathematics, specifically in the field of calculus and, more broadly, mathematical analysis. Given a function ƒ of a Real number variable x and an interval [a, b] of the real line, the integral...
of the flow.

For example, if the capital stock is increased gradually over time by a flow of gross investment

Investment

Depreciation

Here we used the notation to refer to net investment

Investment

Stock and flow

Stocks and flows in accounting

More general uses

Examples

Accounting, finance, etc.:

Other contexts:

Calculus interpretation

See also