משתמש:יובל מדר/טיוטה

מלאי לעומת זרם

Dynamic stock and flow diagram

בתחומי הכלכלה, מנהל העסקים, החשבונאות ותחומים קרובים נוספים נעשית הבדלה בין משתני מלאי ומשתני זרם. שני סוגי משתנים אלה נבדלים ביחידות המידה המודדות אותם. בעוד שמשתני מלאי מודדים כמות מסוימת בנקודה בודדת בזמן, (למשל, יתרת המזומנים של חברה ברגע נתון) מודדים משתני זרם כמות המאפיינת תקופת זמן. (הכנסה שנתית של חברה)

למשל, התמ"ג הישראלי נמדד ביחס לתקופת זמן מסוימת (שנה, למשל) מהווה משתנה זרם, ונאמד ביחידות של שקלים לשנה. לעומת זאת, הון של חברה הוא משתנה מלאי היות והוא מודד את כמות ההון המוחזקת בידי החברה בנקודת זמן ספציפית. (ובהתאם, נמדד במטבע המקומי, שקלים למשל)

השוואת משתני זרם ומלאי

משתני זרם ומלאי נמדדים ביחידות מידה שונות, ולכן אינם ניתנים להשוואה או קיזוז אלה עם אלה. כן ניתן להתייחס ליחס ביניהם, עם זאת, אשר נאמד ביחידות זמן. (מטבע / (מטבע / יחידת זמן) = יחידת זמן)

למשל, יחס חוב תוצר נמדד ביחידות של שנים, ומובנו מספר השנים הנדרשות לתשלום החוב של המשק אם כל התוצר שלו היה מופנה להחזר חובות.

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; 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 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 $3{\tfrac {1}{2}}$ 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. Thus stocks and flows are the basic building blocks of system dynamics models. 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 – e.g., the number of births over a day or month.

Synonyms

Stock	Flow
Level	Rate
Integral	Derivative
State Variable

Examples

Accounting, finance, etc.

"Stock"	Possible units of stock	"Inflow(s)"	"Outflow(s)"	Possible units of flow
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')	purchases of shares	sales of shares	shares per month

Other contexts

"Stock"	Possible units of stock	"Inflow(s)"	"Outflow(s)"	Possible units of flow
CO2 in atmosphere	tons	tons emitted	tons sequestered	tons per day
guests in a hotel	persons	guests arriving	guests leaving	persons per day
population	persons	births immigration	deaths emigration	persons per year
water in bathtub	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 $\,t\,$ is $\,Q(t)\,$, then the derivative $\,{\frac {dQ(t)}{dt}}\,$ is the flow of changes in the stock. Likewise, the stock at some time t is the integral of the flow from some time when the time was zero until time t.

For example, if the capital stock $\,K(t)\,$ is increased gradually over time by a flow of gross investment $\,I^{g}(t)\,$ and decreased gradually over time by a flow of depreciation $\,D(t)\,$, then the instantaneous rate of change in the capital stock is given by

${\frac {dK(t)}{dt}}=I^{g}(t)-D(t)=I^{n}(t)$

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

Dynamic stock and flow diagram

Ten first stocks and flow values

Equations that change the two stocks via the flow are:

$\ {\text{Stock A}}=\int _{0}^{t}-{\text{Flow }}\,dt$

$\ {\text{Stock B}}=\int _{0}^{t}{\text{Flow }}\,dt$

List of all the equations, in their order of execution in each time, from time = 1 to 36:

$1)\ {\text{Flow}}=\sin(5t)$

$2.1)\ {\text{Stock A}}\ -={\text{Flow}}\$

$2.2)\ {\text{Stock B}}\ +={\text{Flow}}\$

History

The distinction between a stock and a flow 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 (Fisher 1896), 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 (circa 1936, frequently quoted by Joan Robinson).

לקריאה נוספת

• Fisher, Irving (בדצמבר 1896), "What is Capital?", The Economic Journal, 6 (24): 509–534, doi:10.2307/2957184, JSTOR 2957184 {{citation}}: (עזרה)
• D.W. Bushaw and R.W. Clower, 1957. Introduction to Mathematical Economics, Ch. 3–6. "Section" & arrow-searchable pageChapter ("Section") and arrow-searchable page 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 p. 328–343.
• _____, 1968. "Stock-flow analysis," International Encyclopedia of the Social Sciences, v. 12.
• Glenn W. Harrison, 1987 [2008]. "Stocks and flows," The New Palgrave: A Dictionary of Economics, v. 4, pp. 506–09.