405:(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 β with outflows subtracting from the stock. Stocks typically have a certain value at each moment of time β e.g. the number of population at a certain moment, or the quantity of water in a reservoir.
31:
132:
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
133:
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).
412:(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 β e.g., the number of births over a day or month.
227:
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".
1478:
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
355:, 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
1250:
1308:
1116:
367:
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
1468:
1417:
100:
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
1366:
840:
220:
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).
292:
96:
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
1157:
974:
1679:
1008:
933:
789:
1498:
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
758:
896:
868:
1688:
208:
262:
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
192:
utilization. These differ in their units of measurement. Capital is a stock concept which yields a periodic income which is a flow concept.
319:
Stocks and flows also have natural meanings in many contexts outside of economics, business and related fields. The concepts apply to many
1197:
1258:
1520:
69:
is measured at one specific time, and represents a quantity existing at that point in time (say, December 31, 2004), which may have
39:
1182:
1172:
1016:
1425:
1374:
1591:
298:
247:
1720:
1710:
1530:
1160:
936:
113:
254:
of the stock) is equal to the corresponding flow variable per unit of time. For example, if a country's stock of
352:
1319:
1596:
1499:
356:
384:
1595:, 6 (1982), 295β6: "it is the science of confusing stocks with flows. It is this confusion that has kept the
797:
1715:
1525:
360:
250:, the change in a stock variable from one point in time to another point in time one time unit later (the
145:
93:
1515:
398:
originally referred to them as "levels" rather than stocks, together with "rates" or "rates of flow".
265:
1565:
368:
201:
185:
70:
62:
1488:
153:
105:
97:
1124:
941:
1705:
1632:
1545:
364:
320:
189:
149:
82:
1646:, Ch. 3β6. "Section" & arrow-searchable pageChapter ("Section") and arrow-searchable page
1495:
982:
907:
763:
232:
224:
1652:
1624:
1535:
391:
255:
251:
223:
The ratio of a stock over a flow has units of (units)/(units/time) = time. For example, the
181:
741:
1540:
1313:
List of all the equations, in their order of execution in each time, from time = 1 to 36:
388:
348:
336:
314:
302:
258:
on
January 1, 2010 is 20 machines and on January 1, 2011 is 23 machines, then the flow of
1586:
881:
853:
447:
376:
340:
259:
1699:
1647:
1608:
1582:
1503:
1484:
902:
395:
332:
161:
977:
372:
240:
121:
77:
variable is measured over an interval of time. Therefore, a flow would be measured
1572:(2 ed.). Cambridge, Massachusetts: Wright-Allen Press, Inc. pp. 18β19.
380:
236:
173:
165:
157:
1666:
_____, 1954b. "Price
Determination in a Stock-Flow Economy" with D. W. Bushaw,
30:
792:
344:
50:
17:
46:
1010:, then the instantaneous rate of change in the capital stock is given by
871:
328:
1636:
675:
38:
1163:, which is the difference between gross investment and depreciation.
324:
177:
169:
141:
1671:
1660:
1628:
1612:
1245:{\displaystyle \ {\text{Stock A}}=\int _{0}^{t}-{\text{Flow }}\,dt}
1181:
1171:
231:
The ratio of a flow to a stock has units 1/time. For example, the
53:, and related fields often distinguish between quantities that are
1303:{\displaystyle \ {\text{Stock B}}=\int _{0}^{t}{\text{Flow }}\,dt}
1180:
1170:
558:
137:
86:
1655:, 1954a. "An Investigation into the Dynamics of Investment,"
1111:{\displaystyle {\frac {dK(t)}{dt}}=I^{g}(t)-D(t)=I^{n}(t)}
1463:{\displaystyle 2.2)\ {\text{Stock B}}\ +={\text{Flow}}\ }
1412:{\displaystyle 2.1)\ {\text{Stock A}}\ -={\text{Flow}}\ }
387:. Thus stocks and flows are the basic building blocks of
1191:
Equations that change the two stocks via the flow are:
243:; it has units of (dollars / year) / dollars = 1/year.
206:
Stocks and flows have different units and are thus not
273:
1428:
1377:
1322:
1261:
1200:
1127:
1019:
985:
944:
910:
884:
856:
800:
766:
744:
371:, many stock and flow problems arise, such as in the
359:
into the atmosphere, and increasing outflows such as
268:
1462:
1411:
1360:
1302:
1244:
1151:
1110:
1002:
968:
927:
890:
862:
834:
783:
752:
286:
1680:International Encyclopedia of the Social Sciences
976:and decreased gradually over time by a flow of
1686:Glenn W. Harrison, 1987 . "Stocks and flows,"
935:is increased gradually over time by a flow of
363:). In living systems, such as the human body,
8:
202:Dimensional analysis Β§ Commensurability
1689:The New Palgrave: A Dictionary of Economics
81:(say a year). Flow is roughly analogous to
1361:{\displaystyle 1)\ {\text{Flow}}=\sin(5t)}
1452:
1438:
1427:
1401:
1387:
1376:
1332:
1321:
1293:
1288:
1282:
1277:
1265:
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1235:
1230:
1221:
1216:
1204:
1199:
1167:Example of dynamic stock and flow diagram
1148:
1133:
1128:
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1093:
1056:
1020:
1018:
999:
986:
984:
965:
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911:
909:
883:
855:
831:
802:
801:
799:
780:
767:
765:
749:
745:
743:
272:
267:
136:A person or country might have stocks of
878:from some moment set as zero until time
580:
466:
419:
305:of a stock variable is a flow variable.
214:compared, equated, added, or subtracted.
108:currently available is increased by the
37:
29:
1557:
846:of changes in the stock. Likewise, the
835:{\displaystyle \,{\frac {dQ(t)}{dt}}\,}
27:Types of quantities in financial fields
1644:Introduction to Mathematical Economics
1480:
347:that accumulate in the environment or
7:
1677:_____, 1968. "Stock-flow analysis,"
1642:D.W. Bushaw and R.W. Clower, 1957.
216:However, one may meaningfully take
1521:Intensive and extensive properties
1502:(circa 1936, frequently quoted by
25:
1186:Ten first stocks and flow values
287:{\displaystyle 3{\tfrac {1}{2}}}
1592:Cambridge Journal of Economics
1432:
1381:
1355:
1346:
1326:
1176:Dynamic stock and flow diagram
1145:
1139:
1105:
1099:
1083:
1077:
1068:
1062:
1035:
1029:
996:
990:
962:
956:
921:
915:
817:
811:
777:
771:
212:β they cannot be meaningfully
128:Stocks and flows in accounting
42:Dynamic stock and flow diagram
1:
1152:{\displaystyle \,I^{n}(t)\,}
969:{\displaystyle \,I^{g}(t)\,}
1531:Stock-Flow consistent model
168:). Flow magnitudes include
1737:
312:
199:
196:Comparing stocks and flows
92:For example, U.S. nominal
463:Accounting, finance, etc.
353:Climate change mitigation
1692:, v. 4, pp. 506β09.
1657:American Economic Review
1597:Quantity Theory of Money
1500:quantity theory of money
1003:{\displaystyle \,D(t)\,}
928:{\displaystyle \,K(t)\,}
784:{\displaystyle \,Q(t)\,}
734:If the quantity of some
357:greenhouse gas emissions
61:. These differ in their
730:Calculus interpretation
1526:Stock (disambiguation)
1464:
1413:
1362:
1304:
1246:
1188:
1178:
1159:refers to the flow of
1153:
1112:
1004:
970:
929:
892:
864:
836:
785:
754:
694:waste in disposal site
361:carbon dioxide removal
288:
94:gross domestic product
43:
35:
1516:Flow (disambiguation)
1465:
1414:
1363:
1305:
1247:
1184:
1174:
1154:
1113:
1005:
971:
930:
893:
865:
837:
786:
755:
753:{\displaystyle \,t\,}
385:Earth's energy budget
289:
200:Further information:
41:
33:
1617:The Economic Journal
1426:
1375:
1320:
1259:
1198:
1125:
1017:
983:
942:
908:
901:For example, if the
882:
854:
798:
764:
742:
554:equity shareholdings
546:housing depreciation
532:board feet per week
369:Earth system science
321:conserved quantities
266:
186:inventory investment
116:and depleted by the
63:units of measurement
1599:alive until today."
1287:
1226:
1121:where the notation
564:purchases of shares
520:inventory of lumber
294:machines per year.
154:means of production
57:and those that are
1721:Economics and time
1711:Accounting systems
1613:"What is Capital?"
1546:Wealth (economics)
1460:
1409:
1358:
1300:
1273:
1242:
1212:
1189:
1179:
1149:
1108:
1000:
966:
925:
888:
860:
832:
781:
750:
723:gallons per month
689:liters per second
686:water draining out
543:housing investment
365:energy homeostasis
343:and other durable
284:
282:
180:, debt repayment,
44:
36:
1611:(December 1896),
1587:Shedding Darkness
1494:Polish economist
1459:
1455:
1445:
1441:
1437:
1408:
1404:
1394:
1390:
1386:
1335:
1331:
1291:
1268:
1264:
1233:
1207:
1203:
1047:
891:{\displaystyle t}
863:{\displaystyle t}
829:
738:variable at time
727:
726:
669:persons per year
636:guests in a hotel
574:
573:
570:shares per month
549:dollars per year
455:
454:
309:More general uses
281:
233:velocity of money
225:debt to GDP ratio
16:(Redirected from
1728:
1653:Robert W. Clower
1639:
1600:
1580:
1574:
1573:
1562:
1536:Systems thinking
1469:
1467:
1466:
1461:
1457:
1456:
1453:
1443:
1442:
1439:
1435:
1418:
1416:
1415:
1410:
1406:
1405:
1402:
1392:
1391:
1388:
1384:
1367:
1365:
1364:
1359:
1336:
1333:
1329:
1309:
1307:
1306:
1301:
1292:
1289:
1286:
1281:
1269:
1266:
1262:
1251:
1249:
1248:
1243:
1234:
1231:
1225:
1220:
1208:
1205:
1201:
1158:
1156:
1155:
1150:
1138:
1137:
1117:
1115:
1114:
1109:
1098:
1097:
1061:
1060:
1048:
1046:
1038:
1021:
1009:
1007:
1006:
1001:
975:
973:
972:
967:
955:
954:
937:gross investment
934:
932:
931:
926:
897:
895:
894:
889:
869:
867:
866:
861:
841:
839:
838:
833:
830:
828:
820:
803:
790:
788:
787:
782:
759:
757:
756:
751:
720:fuel consumption
683:water pouring in
648:persons per day
628:tons sequestered
581:
467:
420:
341:greenhouse gases
339:management, and
293:
291:
290:
285:
283:
274:
256:physical capital
252:first difference
182:fixed investment
79:per unit of time
21:
1736:
1735:
1731:
1730:
1729:
1727:
1726:
1725:
1696:
1695:
1629:10.2307/2957184
1623:(24): 509β534,
1607:
1604:
1603:
1581:
1577:
1564:
1563:
1559:
1554:
1541:System dynamics
1512:
1476:
1424:
1423:
1373:
1372:
1318:
1317:
1257:
1256:
1196:
1195:
1169:
1129:
1123:
1122:
1089:
1052:
1039:
1022:
1015:
1014:
981:
980:
946:
940:
939:
906:
905:
880:
879:
852:
851:
821:
804:
796:
795:
762:
761:
740:
739:
732:
665:
660:
642:guests arriving
618:
579:
567:sales of shares
529:outgoing lumber
526:incoming lumber
508:
465:
460:
389:system dynamics
337:water reservoir
317:
315:System dynamics
311:
303:time derivative
299:continuous time
264:
263:
204:
198:
130:
89:in this sense.
73:in the past. A
28:
23:
22:
15:
12:
11:
5:
1734:
1732:
1724:
1723:
1718:
1716:Systems theory
1713:
1708:
1698:
1697:
1694:
1693:
1684:
1675:
1664:
1650:
1640:
1609:Fisher, Irving
1602:
1601:
1575:
1570:World Dynamics
1566:Forrester, Jay
1556:
1555:
1553:
1550:
1549:
1548:
1543:
1538:
1533:
1528:
1523:
1518:
1511:
1508:
1496:MichaΕ Kalecki
1491:(as a stock).
1475:
1472:
1471:
1470:
1451:
1448:
1434:
1431:
1420:
1419:
1400:
1397:
1383:
1380:
1369:
1368:
1357:
1354:
1351:
1348:
1345:
1342:
1339:
1328:
1325:
1311:
1310:
1299:
1296:
1285:
1280:
1276:
1272:
1253:
1252:
1241:
1238:
1229:
1224:
1219:
1215:
1211:
1168:
1165:
1161:net investment
1147:
1144:
1141:
1136:
1132:
1119:
1118:
1107:
1104:
1101:
1096:
1092:
1088:
1085:
1082:
1079:
1076:
1073:
1070:
1067:
1064:
1059:
1055:
1051:
1045:
1042:
1037:
1034:
1031:
1028:
1025:
998:
995:
992:
989:
964:
961:
958:
953:
949:
923:
920:
917:
914:
887:
859:
827:
824:
819:
816:
813:
810:
807:
779:
776:
773:
770:
748:
731:
728:
725:
724:
721:
718:
715:
712:
708:
707:
706:tons per week
704:
703:decay of waste
701:
698:
695:
691:
690:
687:
684:
681:
678:
671:
670:
667:
662:
657:
654:
650:
649:
646:
645:guests leaving
643:
640:
637:
633:
632:
629:
626:
623:
620:
616:
612:
611:
604:
599:
594:
587:
578:
577:Other contexts
575:
572:
571:
568:
565:
562:
555:
551:
550:
547:
544:
541:
538:
534:
533:
530:
527:
524:
521:
517:
516:
515:yen per month
513:
510:
505:
502:
498:
497:
490:
485:
480:
473:
464:
461:
459:
456:
453:
452:
450:
448:State Variable
444:
443:
440:
436:
435:
432:
428:
427:
424:
377:nitrogen cycle
313:Main article:
310:
307:
280:
277:
271:
260:net investment
235:is defined as
197:
194:
129:
126:
34:Stock vs. flow
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1733:
1722:
1719:
1717:
1714:
1712:
1709:
1707:
1704:
1703:
1701:
1691:
1690:
1685:
1682:
1681:
1676:
1673:
1669:
1668:Econometrica
1665:
1662:
1659:. 44(l), pp.
1658:
1654:
1651:
1649:
1645:
1641:
1638:
1634:
1630:
1626:
1622:
1618:
1614:
1610:
1606:
1605:
1598:
1594:
1593:
1588:
1584:
1583:Joan Robinson
1579:
1576:
1571:
1567:
1561:
1558:
1551:
1547:
1544:
1542:
1539:
1537:
1534:
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1529:
1527:
1524:
1522:
1519:
1517:
1514:
1513:
1509:
1507:
1505:
1504:Joan Robinson
1501:
1497:
1492:
1490:
1486:
1485:Irving Fisher
1482:
1473:
1449:
1446:
1429:
1422:
1421:
1398:
1395:
1378:
1371:
1370:
1352:
1349:
1343:
1340:
1337:
1323:
1316:
1315:
1314:
1297:
1294:
1283:
1278:
1274:
1270:
1255:
1254:
1239:
1236:
1227:
1222:
1217:
1213:
1209:
1194:
1193:
1192:
1187:
1183:
1177:
1173:
1166:
1164:
1162:
1142:
1134:
1130:
1102:
1094:
1090:
1086:
1080:
1074:
1071:
1065:
1057:
1053:
1049:
1043:
1040:
1032:
1026:
1023:
1013:
1012:
1011:
993:
987:
979:
959:
951:
947:
938:
918:
912:
904:
903:capital stock
899:
885:
877:
873:
857:
850:at some time
849:
845:
825:
822:
814:
808:
805:
794:
774:
768:
746:
737:
729:
722:
719:
716:
713:
710:
709:
705:
702:
700:dumping waste
699:
696:
693:
692:
688:
685:
682:
679:
677:
673:
672:
668:
663:
658:
655:
652:
651:
647:
644:
641:
638:
635:
634:
631:tons per day
630:
627:
624:
621:
619:in atmosphere
614:
613:
609:
605:
603:
600:
598:
595:
592:
588:
586:
583:
582:
576:
569:
566:
563:
560:
556:
553:
552:
548:
545:
542:
539:
537:housing stock
536:
535:
531:
528:
525:
522:
519:
518:
514:
511:
506:
503:
500:
499:
495:
491:
489:
486:
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481:
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457:
451:
449:
446:
445:
441:
438:
437:
433:
430:
429:
425:
422:
421:
418:
417:
413:
411:
406:
404:
399:
397:
396:Jay Forrester
393:
390:
386:
382:
378:
374:
370:
366:
362:
358:
354:
350:
346:
342:
338:
334:
333:stoichiometry
330:
326:
322:
316:
308:
306:
304:
300:
295:
278:
275:
269:
261:
257:
253:
249:
248:discrete time
244:
242:
238:
234:
229:
226:
221:
219:
215:
211:
210:
209:commensurable
203:
195:
193:
191:
187:
183:
179:
175:
171:
167:
163:
162:human capital
159:
155:
151:
147:
143:
139:
134:
127:
125:
123:
119:
115:
111:
107:
103:
99:
98:capital stock
95:
90:
88:
84:
80:
76:
72:
68:
64:
60:
56:
52:
48:
40:
32:
19:
18:Flow variable
1687:
1678:
1667:
1656:
1643:
1620:
1616:
1590:
1578:
1569:
1560:
1493:
1483:), in which
1477:
1312:
1190:
1185:
1175:
1120:
978:depreciation
900:
875:
847:
843:
735:
733:
625:tons emitted
607:
602:"Outflow(s)"
601:
596:
590:
584:
557:shares (of '
501:bank balance
493:
488:"Outflow(s)"
487:
482:
476:
470:
415:
414:
409:
407:
402:
400:
373:carbon cycle
349:in organisms
318:
296:
245:
241:money supply
230:
222:
217:
213:
207:
205:
140:, financial
135:
131:
122:depreciation
117:
109:
101:
91:
78:
74:
66:
58:
54:
49:, business,
45:
1487:formalized
1481:Fisher 1896
791:, then the
661:immigration
597:"Inflow(s)"
512:withdrawals
483:"Inflow(s)"
442:Derivative
381:water cycle
331:such as in
237:nominal GDP
166:labor power
158:inventories
156:, capital,
146:liabilities
71:accumulated
1700:Categories
1552:References
1290:Flow
1232:Flow
793:derivative
666:emigration
653:population
523:board feet
345:pollutants
239:/ nominal
114:investment
51:accounting
1706:Inventory
1670:22(3), p
1396:−
1344:
1275:∫
1228:−
1214:∫
1072:−
717:refueling
711:fuel tank
674:water in
606:Possible
589:Possible
492:Possible
475:Possible
329:materials
327:, and to
47:Economics
1683:, v. 12.
1568:(1973).
1510:See also
872:integral
610:of flow
593:of stock
509:interest
507:deposits
496:of flow
479:of stock
458:Examples
439:Integral
416:Synonyms
323:such as
174:spending
1637:2957184
1489:capital
1474:History
1440:Stock B
1389:Stock A
1267:Stock B
1206:Stock A
874:of the
870:is the
842:is the
714:gallons
676:bathtub
656:persons
639:persons
585:"Stock"
540:dollars
471:"Stock"
152:, real
112:of new
106:capital
1672:p. 328
1648:links.
1635:
1458:
1444:
1436:
1407:
1393:
1385:
1330:
1263:
1202:
680:liters
664:deaths
659:births
392:models
383:, and
379:, the
375:, the
325:energy
301:, the
218:ratios
188:, and
178:saving
170:income
160:, and
150:wealth
142:assets
55:stocks
1674:β343.
1633:JSTOR
848:stock
736:stock
608:units
591:units
559:stock
494:units
477:units
434:Rate
431:Level
426:Flow
423:Stock
403:stock
190:labor
138:money
102:stock
87:speed
67:stock
59:flows
1663:β81.
1454:Flow
1403:Flow
1334:Flow
876:flow
844:flow
697:tons
622:tons
410:flow
164:(or
118:flow
110:flow
83:rate
75:flow
65:. A
1625:doi
1589:",
1585:, "
1506:).
1430:2.2
1379:2.1
1341:sin
760:is
504:yen
297:In
246:In
120:of
104:of
85:or
1702::
1661:64
1631:,
1619:,
1615:,
898:.
615:CO
561:')
408:A
401:A
394:.
351:.
335:,
184:,
176:,
172:,
148:,
144:,
124:.
1627::
1621:6
1479:(
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1433:)
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1347:(
1338:=
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1324:1
1298:t
1295:d
1284:t
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1146:)
1143:t
1140:(
1135:n
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1106:)
1103:t
1100:(
1095:n
1091:I
1087:=
1084:)
1081:t
1078:(
1075:D
1069:)
1066:t
1063:(
1058:g
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1024:d
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960:t
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952:g
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812:(
809:Q
806:d
778:)
775:t
772:(
769:Q
747:t
617:2
279:2
276:1
270:3
20:)
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