This document summarizes a paper about the relationship between capital accumulation, the rate of economic growth, and employment. It makes the following key points:
1) For a capitalist economy to maintain full employment, national income must grow at a rate that matches the combined rate of growth of the labor force and productivity.
2) Investment increases both productive capacity and generates income, so examining growth from the investment perspective may help determine the equilibrium growth rate needed.
3) If investment proceeds at rate I per year, and each $1 invested increases productive capacity by amount s, then new projects will increase potential output by Is annually. However, the overall economy's capacity may increase by less if new projects require transferring labor from
Roberto's favorite subject is math because he finds it easy and enjoys adding and subtracting numbers. He wrote a short note about his interest in math and specifically mentioned that he likes performing basic arithmetic operations like addition and subtraction. Roberto signed his name at the end of the brief document.
Kisi kisi materi tajuk subyek keislaman (TSI-PII-2010-UINSUKA)Tyo SBS
Dokumen tersebut membahas tentang prinsip-prinsip dasar penyusunan tajuk subjek di perpustakaan, jenis-jenis tajuk subjek, sistem sindentik, dan contoh-contoh tajuk subjek."
The document provides guidance on how to write an effective introduction for a formal paper. An introduction should attract the reader's attention with a hook, provide necessary background or definitions, and state the thesis clearly. The thesis should communicate the paper's significance and take an original position that others could challenge or oppose. An introduction typically includes a hook to engage the reader, a brief background if needed, and a clear thesis statement outlining the paper's argument or process. It should be concise and avoid long background details or definitions not essential to understanding the thesis. The goal is to attract and orient the reader to the central idea and purpose of the paper.
Resources and Lessons on Open Data from the World Banktariqkhokhar
Delivered by Tariq Khokhar at the European Association of Development Research and Training Institute's Information Management Working Group Conference in Antwerp, Belgium on September 13th, 2012.
Roberto's favorite subject is math because he finds it easy and enjoys adding and subtracting numbers. He wrote a short note about his interest in math and specifically mentioned that he likes performing basic arithmetic operations like addition and subtraction. Roberto signed his name at the end of the brief document.
Kisi kisi materi tajuk subyek keislaman (TSI-PII-2010-UINSUKA)Tyo SBS
Dokumen tersebut membahas tentang prinsip-prinsip dasar penyusunan tajuk subjek di perpustakaan, jenis-jenis tajuk subjek, sistem sindentik, dan contoh-contoh tajuk subjek."
The document provides guidance on how to write an effective introduction for a formal paper. An introduction should attract the reader's attention with a hook, provide necessary background or definitions, and state the thesis clearly. The thesis should communicate the paper's significance and take an original position that others could challenge or oppose. An introduction typically includes a hook to engage the reader, a brief background if needed, and a clear thesis statement outlining the paper's argument or process. It should be concise and avoid long background details or definitions not essential to understanding the thesis. The goal is to attract and orient the reader to the central idea and purpose of the paper.
Resources and Lessons on Open Data from the World Banktariqkhokhar
Delivered by Tariq Khokhar at the European Association of Development Research and Training Institute's Information Management Working Group Conference in Antwerp, Belgium on September 13th, 2012.
The document describes life in a small neighborhood near a school in Myanmar. It discusses a betel nut shop owner and trishaw driver named Khin Hnin Wey. It shows the small home of a family of five, Oh Ma Cho's house, which has two rooms including a bedroom. It notes that Oh Ma Cho's daughter May Thin Zar Khin is great at English and attends school. The document also comments that some boys in the neighborhood are very skilled at playing soccer without fear. It concludes by thanking several people who helped provide photos and access for the project.
This document summarizes a paper that aims to test the hypothesis that accurately measured real product and real factor input growth can fully explain observed total factor productivity growth. It defines key economic concepts like production functions, real product, real factor input, and total factor productivity. It also outlines the authors' methodology for developing a system of social accounts to more accurately measure real product and real factor input, thereby providing an empirical test of the hypothesis.
Networks allow simultaneous access to shared resources like data, programs, and devices. They facilitate communication between computers by linking them together. Common network types include personal area networks spanning 10 meters, local area networks within an office or building, and wide area networks across multiple cities. Devices like network interface cards, hubs, bridges, routers, and gateways are used to connect computers to networks and other networks using different standards. Networks can have bus, ring, star, mesh, or tree topologies.
Este documento presenta la nómina quincenal de una organización, dividiendo a los empleados en cuatro departamentos y mostrando los nombres, cantidades y salarios de cuatro empleados. Explica que la nómina se deposita generalmente un día antes de cada quincena, pero cuando éstas caen en fin de semana se depositan los viernes, y que en diciembre se depositan las dos quincenas más el aguinaldo.
Gamification: Μπορεί η ομαδική εργασία να μετατραπεί σε διασκεδαστική διαδικα...FollowSunday
Η παρουσίαση έγινε στο δεύτερο workshop εκπαίδευσης μη κερδοσκοπικών οργανισμών του Volunteer4Greece (http://volunteer4greece.gr) με θέμα "Πρακτικές & Εργαλεία Project Management: Διαχειριστείτε αποτελεσματικά την ομάδα σας!".
Το workshop, που έγινε στις 25 Ιουνίου 2013 στο ALBA Graduate Business School, παρακολούθησαν περίπου 100 συμμετέχοντες προερχόμενοι από παραπάνω από 50 οργανισμούς, όπως οι Μεσόγειος SOS, Σώμα Ελλήνων Προσκόπων, PRAKSIS, Fair Trade Hellas, Ελληνικό Παιδικό Μουσείο, Μεταβάλλον, Γιατροί του Κόσμου και πολλοί άλλοι.
This document presents an alternative account of the productivity slowdown in the United States since the mid-1960s. It argues that declining work intensity and lagging business innovation, which have been overlooked by conventional economic analyses, provide crucial clues. The authors develop a "social" model of productivity growth integrating technical and social factors. An econometric test shows their model can account for almost all of the productivity slowdown. The analysis raises issues for further research but provides a promising approach to solving the puzzle.
Web conferencing allows for live meetings, training, and presentations over the Internet. Participants connect to each other via their computers. While it provides benefits like eliminating travel costs and allowing collaboration over distances, web conferencing also faces challenges like technical difficulties, bandwidth issues, and ensuring all participants have proper equipment. A study of its use at McMaster University found that most viewed it positively as an option when in-person meetings weren't possible, but that improvements were still needed, especially in technical support and training.
The document presents a photo essay about the life of a neighbor, Oh Mah Cho, a mother of 3 children. Some key details:
1) Oh Mah Cho and her neighbors live in small wooden houses due to lack of space and money in the area.
2) Meals are prepared from local market ingredients and include curries and fried chicken.
3) A daily ritual is giving offerings to a household Buddha statue.
4) Oh Mah Cho's husband works as a taxi driver for income instead of a trishaw.
5) The children attend Burmese school and see a local family doctor when sick.
Mr. Tatsuya Yanagi presentation on OVOP - Yogyakarta Workshop 2014Toto Wirjosoemarto
The document discusses OVOP (One Village One Product) projects supported by JICA in various countries. It begins with an overview of OVOP in Japan and its principles of being local yet global, relying on self-help efforts through value addition, and developing human resources. Typical OVOP projects involve selecting local products, providing training and support to producer groups, and working to commercialize and market the products. An example project in Malawi is described in more detail, highlighting achievements like certain products being exported to Japan, as well as ongoing challenges. Overall, the document shares experiences of OVOP projects globally to help improve future initiatives.
La Unión Europea ha acordado un embargo petrolero contra Rusia en respuesta a la invasión de Ucrania. El embargo prohibirá las importaciones marítimas de petróleo ruso a la UE y pondrá fin a las entregas a través de oleoductos dentro de seis meses. Esta medida forma parte de un sexto paquete de sanciones de la UE destinadas a aumentar la presión económica sobre Moscú y privar al Kremlin de fondos para financiar su guerra.
This paper proposes a theoretical model to distinguish between "reproductive cycles" and "nonreproductive cycles" and explain their relationship to long economic expansions and crises. The authors define a reproductive cycle as one where a economic downturn restores conditions for rapid economic growth, while a nonreproductive cycle requires fundamental changes to institutions. They argue long expansions are characterized by reproductive cycles that sustain profitability, while long crises feature nonreproductive cycles that lead to stagnation until a new social structure of accumulation is established. The authors present evidence that business cycles function differently depending on whether it is an expansion or crisis period of the long swing in economic activity.
- The document discusses using an aggregate production function to isolate the effects of technical change on output over time.
- It presents a method for estimating an index of technical change (A(t)) based on time series data for output per worker, capital per worker, and the share of capital, using the assumption that factors are paid their marginal products.
- The method is applied to U.S. data from 1909-1949 to generate an estimated index of technical change, which increased steadily over that period.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
La Unión Europea ha acordado un paquete de sanciones contra Rusia por su invasión de Ucrania. Las sanciones incluyen restricciones a las transacciones con bancos rusos clave y la prohibición de la venta de aviones y equipos a Rusia. Los líderes de la UE esperan que las sanciones aumenten la presión económica sobre Rusia y la disuadan de continuar su agresión contra Ucrania.
The document describes life in a small neighborhood near a school in Myanmar. It discusses a betel nut shop owner and trishaw driver named Khin Hnin Wey. It shows the small home of a family of five, Oh Ma Cho's house, which has two rooms including a bedroom. It notes that Oh Ma Cho's daughter May Thin Zar Khin is great at English and attends school. The document also comments that some boys in the neighborhood are very skilled at playing soccer without fear. It concludes by thanking several people who helped provide photos and access for the project.
This document summarizes a paper that aims to test the hypothesis that accurately measured real product and real factor input growth can fully explain observed total factor productivity growth. It defines key economic concepts like production functions, real product, real factor input, and total factor productivity. It also outlines the authors' methodology for developing a system of social accounts to more accurately measure real product and real factor input, thereby providing an empirical test of the hypothesis.
Networks allow simultaneous access to shared resources like data, programs, and devices. They facilitate communication between computers by linking them together. Common network types include personal area networks spanning 10 meters, local area networks within an office or building, and wide area networks across multiple cities. Devices like network interface cards, hubs, bridges, routers, and gateways are used to connect computers to networks and other networks using different standards. Networks can have bus, ring, star, mesh, or tree topologies.
Este documento presenta la nómina quincenal de una organización, dividiendo a los empleados en cuatro departamentos y mostrando los nombres, cantidades y salarios de cuatro empleados. Explica que la nómina se deposita generalmente un día antes de cada quincena, pero cuando éstas caen en fin de semana se depositan los viernes, y que en diciembre se depositan las dos quincenas más el aguinaldo.
Gamification: Μπορεί η ομαδική εργασία να μετατραπεί σε διασκεδαστική διαδικα...FollowSunday
Η παρουσίαση έγινε στο δεύτερο workshop εκπαίδευσης μη κερδοσκοπικών οργανισμών του Volunteer4Greece (http://volunteer4greece.gr) με θέμα "Πρακτικές & Εργαλεία Project Management: Διαχειριστείτε αποτελεσματικά την ομάδα σας!".
Το workshop, που έγινε στις 25 Ιουνίου 2013 στο ALBA Graduate Business School, παρακολούθησαν περίπου 100 συμμετέχοντες προερχόμενοι από παραπάνω από 50 οργανισμούς, όπως οι Μεσόγειος SOS, Σώμα Ελλήνων Προσκόπων, PRAKSIS, Fair Trade Hellas, Ελληνικό Παιδικό Μουσείο, Μεταβάλλον, Γιατροί του Κόσμου και πολλοί άλλοι.
This document presents an alternative account of the productivity slowdown in the United States since the mid-1960s. It argues that declining work intensity and lagging business innovation, which have been overlooked by conventional economic analyses, provide crucial clues. The authors develop a "social" model of productivity growth integrating technical and social factors. An econometric test shows their model can account for almost all of the productivity slowdown. The analysis raises issues for further research but provides a promising approach to solving the puzzle.
Web conferencing allows for live meetings, training, and presentations over the Internet. Participants connect to each other via their computers. While it provides benefits like eliminating travel costs and allowing collaboration over distances, web conferencing also faces challenges like technical difficulties, bandwidth issues, and ensuring all participants have proper equipment. A study of its use at McMaster University found that most viewed it positively as an option when in-person meetings weren't possible, but that improvements were still needed, especially in technical support and training.
The document presents a photo essay about the life of a neighbor, Oh Mah Cho, a mother of 3 children. Some key details:
1) Oh Mah Cho and her neighbors live in small wooden houses due to lack of space and money in the area.
2) Meals are prepared from local market ingredients and include curries and fried chicken.
3) A daily ritual is giving offerings to a household Buddha statue.
4) Oh Mah Cho's husband works as a taxi driver for income instead of a trishaw.
5) The children attend Burmese school and see a local family doctor when sick.
Mr. Tatsuya Yanagi presentation on OVOP - Yogyakarta Workshop 2014Toto Wirjosoemarto
The document discusses OVOP (One Village One Product) projects supported by JICA in various countries. It begins with an overview of OVOP in Japan and its principles of being local yet global, relying on self-help efforts through value addition, and developing human resources. Typical OVOP projects involve selecting local products, providing training and support to producer groups, and working to commercialize and market the products. An example project in Malawi is described in more detail, highlighting achievements like certain products being exported to Japan, as well as ongoing challenges. Overall, the document shares experiences of OVOP projects globally to help improve future initiatives.
La Unión Europea ha acordado un embargo petrolero contra Rusia en respuesta a la invasión de Ucrania. El embargo prohibirá las importaciones marítimas de petróleo ruso a la UE y pondrá fin a las entregas a través de oleoductos dentro de seis meses. Esta medida forma parte de un sexto paquete de sanciones de la UE destinadas a aumentar la presión económica sobre Moscú y privar al Kremlin de fondos para financiar su guerra.
This paper proposes a theoretical model to distinguish between "reproductive cycles" and "nonreproductive cycles" and explain their relationship to long economic expansions and crises. The authors define a reproductive cycle as one where a economic downturn restores conditions for rapid economic growth, while a nonreproductive cycle requires fundamental changes to institutions. They argue long expansions are characterized by reproductive cycles that sustain profitability, while long crises feature nonreproductive cycles that lead to stagnation until a new social structure of accumulation is established. The authors present evidence that business cycles function differently depending on whether it is an expansion or crisis period of the long swing in economic activity.
- The document discusses using an aggregate production function to isolate the effects of technical change on output over time.
- It presents a method for estimating an index of technical change (A(t)) based on time series data for output per worker, capital per worker, and the share of capital, using the assumption that factors are paid their marginal products.
- The method is applied to U.S. data from 1909-1949 to generate an estimated index of technical change, which increased steadily over that period.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
La Unión Europea ha acordado un paquete de sanciones contra Rusia por su invasión de Ucrania. Las sanciones incluyen restricciones a las transacciones con bancos rusos clave y la prohibición de la venta de aviones y equipos a Rusia. Los líderes de la UE esperan que las sanciones aumenten la presión económica sobre Rusia y la disuadan de continuar su agresión contra Ucrania.
This document summarizes an article titled "Increasing Returns and Long-Run Growth" by Paul M. Romer. It proposes an economic growth model where knowledge is assumed to have increasing marginal productivity, unlike standard models that assume diminishing returns. The key aspects of the model are: 1) Knowledge exhibits increasing returns in production but decreasing returns in creation; 2) Knowledge spillovers create externalities; 3) The model can generate unbounded long-run growth without exogenous technological change. The model aims to explain how long-run growth rates may increase over time and initial conditions can have permanent effects, challenging standard neoclassical assumptions.
This document discusses the concept of increasing returns and economic progress. It begins by noting that while economists have developed complex models to analyze industries with increasing returns, these models can obscure more general aspects of the phenomena. It argues that the growth of indirect or roundabout production methods, enabled by greater specialization and division of labor, is a key source of increasing returns. However, the extent of these returns depends on the size of the market, as larger markets allow for greater specialization and use of capital-intensive production methods. While rationalization may improve efficiency, the fundamental driver of economic progress is the expansion of markets that comes from overall economic growth and development.
La Unión Europea ha acordado un paquete de sanciones contra Rusia por su invasión de Ucrania. Las sanciones incluyen restricciones a las transacciones con bancos rusos clave y la prohibición de la venta de aviones y equipos a Rusia. Los líderes de la UE esperan que las sanciones aumenten la presión económica sobre Rusia y la disuadan de continuar su agresión contra Ucrania.
This document summarizes a paper by Richard R. Nelson and Sidney G. Winter titled "The Schumpeterian Tradeoff Revisited". It discusses Joseph Schumpeter's view that competition between firms involves research and development and innovation, and that technological progress provides greater long-term gains to society than competitive pricing. It also discusses the "Schumpeterian Hypothesis" that market power and large firms are necessary for rapid technological advancement, representing a tradeoff between static efficiency and dynamic innovation. The document outlines the authors' model of Schumpeterian competition and how it examines the relationship between technological change, market structure, and industry performance under different conditions.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help alleviate symptoms of mental illness and boost overall mental well-being.
This document is a response by Nicholas Kaldor to criticism from Professor Wright regarding Kaldor's previous work on economic methodology and models of business cycles. Kaldor argues that Wright misunderstood the purpose of analytical models, which is to isolate causal factors, not prove hypotheses as absolutely "true". Kaldor also defends using simplified assumptions and examples to illustrate essential features, noting more realistic assumptions were introduced later. While acknowledging room for improvement, Kaldor maintains Wright failed to demonstrate any logical flaws or inconsistencies in the work.
This document summarizes an article titled "Increasing Returns and Long-Run Growth" by Paul M. Romer. It proposes an alternative model of long-run economic growth where knowledge, rather than physical capital, is the main driver of growth. Knowledge exhibits increasing marginal returns in production but decreasing returns in research and development. This allows for perpetual economic growth without limits in a competitive market equilibrium framework. The model overturns conventional assumptions that growth rates decrease and countries converge over time by introducing externalities from new knowledge and increasing rather than diminishing returns to knowledge accumulation.
This document summarizes an academic paper about the origins of uneven economic development between India and Britain from the 17th century to Indian independence in 1947. It presents a theoretical model showing how small initial differences in capital accumulation between two regions can lead to increasing specialization through trade, with one region industrializing while the other declines. It argues this helps explain India's relative economic stagnation under British colonial rule from 1757-1947, as British policies disrupted India's manufacturing industries and shifted its trade to primary goods exports and imports of British manufactures. While various factors contributed, these policies may have exacerbated India's deindustrialization according to the theoretical framework presented. The document considers some counterarguments but maintains British rule likely reduced India's
This document summarizes an academic paper that examines how increasing returns to scale in industry can allow for unlimited economic growth even with diminishing returns in agriculture. It presents a model of an economy with three sectors: agriculture, manufacturing, and investment goods. Agriculture has constant returns to scale while manufacturing and investment goods have increasing returns at the plant level. The model analyzes short, medium, and long run equilibriums under different assumptions about factor supplies and returns to scale. The key finding is that large enough increasing returns in investment goods can outweigh decreasing returns in agriculture, allowing overall growth without constraints from agricultural productivity.
This book provides an in-depth treatment of the overlapping generations model in economics incorporating production. It analyzes competitive equilibria and dynamics, optimal allocations, and various policy issues. The first chapter investigates existence, uniqueness, and stability of equilibrium as well as capital dynamics. The second chapter analyzes optimality of allocations using value functions and conditions. Later chapters discuss policy issues like transfers, pensions, spending, and debt sustainability. The book emphasizes global dynamics, general preferences and technologies, and tools for policy analysis involving intergenerational transfers.
This document provides a critical analysis of Thirlwall's formal presentation of Kaldor's model of growth and development. It develops its own formal Kaldorian model with two sectors (agriculture and industry) and analyzes the underlying dynamics and equilibrium conditions. The key points made are:
1) Thirlwall's specification of the industrial sector assumes non-competitive pricing through markups, which is inconsistent with the rest of the model that assumes perfect competition.
2) The model assumes full capacity utilization in both sectors, which is also inconsistent with Kalecki's markup pricing theory that Thirlwall references.
3) The paper argues the model's dynamics and stability cannot be properly analyzed using
This document summarizes a model of economic growth through creative destruction. The model departs from existing endogenous growth models by emphasizing that technological progress both creates new opportunities but also renders old skills, goods, and processes obsolete. This creative destruction process has positive and normative implications for growth. The model views growth as discontinuous and driven by random innovations that have economy-wide effects. It aims to endogenize both the distribution and size of technological changes based on the level of research activity.
1. Capital Expansion, Rate of Growth, and Employment
Author(s): Evsey D. Domar
Source: Econometrica, Vol. 14, No. 2 (Apr., 1946), pp. 137-147
Published by: The Econometric Society
Stable URL: http://www.jstor.org/stable/1905364
Accessed: 26/10/2010 15:27
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2. CAPITAL EXPANSION, RATE OF GROWTH,
AND EMPLOYMENT'
By EVSEY D. DOMAR
I. INTRODUCTION
Thispaperdealswitha problemthatisbotholdandnew-therela-
tionbetweencapitalaccumulationandemployment.Ineconomiclitera-
tureithasbeendiscusseda numberoftimes,themostnotablecontribu-
tionbelongingtoMarx.Morerecently,itwasbroughtforthbyKeynes
andhisfollowers.
A thoroughanalysisofeconomicaspectsofcapitalaccumulationis
a tremendousjob.Theonlywayinwhichtheproblemcanbeexamined
at all ina shortpaperlikethisis byisolatingitfromthegeneraleco-
nomicstructureandintroducinga numberofsimplifyingassumptions.
Someofthemare notentirelynecessaryand,as theargumentpro-
gresses,thereaderwillseehowtheycanbe modifiedorremoved.
The followingassumptionsand definitionsshouldbe notedat the
outset:(a) thereis a constantgeneralpricelevel;(b) nolagsarepres-
ent;(c) savingsandinvestmentrefertotheincomeofthesameperiod;
(d) botharenet,i.e.,overandabovedepreciation;(e) depreciationis
measurednotinrespecttohistoricalcosts,buttothecostofreplace-
mentofthedepreciatedassetby anotherone ofthesameproductive
capacity;2(f)productivecapacityofan assetorofthewholeeconomy
is a measurableconcept.
Thelastassumption,onwhich(e) alsodepends,isnotentirelysafe.
Whethera certainpieceofcapitalequipmentorthewholeeconomyis
considered,theirproductivecapacitiesdependnotonlyonphysicaland
technicalfactors,butonthewholeinterplayofeconomicandinstitu-
tionalforces,suchas distributionofincome,consumers'preferences,
1 This is a summaryofa paperpresentedbeforea jointsessionoftheEcono-
metricSocietyandtheAmericanStatisticalAssociationin ClevelandonJanuary
24, 1946. It containsthe logicalessenceof the argumentwithrelativelylittle
economicdetail.I hopeto developthelatterin a separatepaperto be published
in one oftheothereconomicjournals.
Many thanksforhelp and criticismgo to myfellowmembersofthe "Little
Seminar":Paul Baran,SvendLaursen,LloydA. Metzler,RichardA. Musgrave,
MaryS. Painter,MelvinW. Reder,Tiborde Scitovszky,AlfredSherrard,Mary
WiseSmelker,MerlinSmelker,and mostofall to JamesS. Duesenberry.
2 If theoriginalmachineworth$1,000and producing100unitsis replacedby
anotherone worthalso $1,000,but producing120 units,only$833.33 will be
regardedas replacement,and theremaining$166.67as newinvestment.A simi-
lar correctionis madewhenthenewmachinecostsmoreorlessthantheoriginal
one. The treatmentof depreciation,particularlywhenaccompaniedby sharp
technologicaland pricechanges,presentsan extremelydifficultproblem.It is
quite possiblethat our approach,whileconvenientforpresentpurposes,may
giveriseto seriousdifficultiesin thefuture.
137
3. 138 EVSEY D. DOMAR
wagerates,relativeprices,structureofindustry,andso on,manyof
whicharein turnaffectedby thebehaviorofthevariablesanalyzed
here.We shallneverthelessassumeall theseconditionsas givenand
shallmeanbytheproductivecapacityofan economy(oran asset)its
totaloutputwhenallproductivefactorsarefullyemployedunderthese
conditions.3
The economywillbe saidto be inequilibriumwhenitsproductive
capacityP equalsitsnationalincomeY. Ourfirsttaskis to discover
theconditionsunderwhichthisequilibriumcanbemaintained,ormore
precisely,therateofgrowthatwhichtheeconomymustexpandinorder
toremainina continuousstateoffullemployment.
II. THE PROBLEM OF GROWTH
The idea thatthepreservationoffullemploymentin a capitalist
economyrequiresa growingincomegoesback(inoneformoranother)
at leastto Marx.It has beenfullyrecognizedin numerousstudies
(recentlymadein Washingtonand elsewhere)ofthe magnitudeof
grossnationalproductneededto maintainfullemployment.But
thoughthevariousauthorscometodifferentnumericalresults,they
all approachtheirproblemfromthepointofviewofthesizeofthe
laborforce.Thelaborforce(man-hoursworked)anditsproductivity
aresupposedto increaseaccordingto oneformulaoranother,and if
fullemploymentis to be maintained,nationalincomemustgrowat
thecombinedrate.Forpracticalrelativelyshort-runpurposesthisisa
goodmethod,butitsanalyticalmeritsarenothigh,becauseitpresents
a theoreticallyincompletesystem:sincean increasein laborforceor
in its productivityonlyraisesproductivecapacityand doesnotby
itselfgenerateincome(similarto thatproducedby investment),the
demandsideoftheequationis missing.Noris thedifficultydisposed
ofbyMr.Kalecki'smethodaccordingtowhichcapitalshouldincrease
proportionallyto theincreaseinlaborforceanditsproductivity.4As
Mrs.Robinsonwellremarked,"Therateofincreaseinproductivityof
laborisnotsomethinggivenbyNature."6Laborproductivityisnota
functionoftechnologicalprogressin theabstract,but technological
progressembodiedincapitalgoods,andtheamountofcapitalgoodsin
3 It shouldundoubtedlybe possibleto workout a moreprecisedefinitionof
productivecapacity,but I preferto leave thematteropen,because a morepre-
cise definitionis not entirelynecessaryin thispaperand can be workedout as
andwhenneeded.
4 See his essay,"Three Waysto Full Employment"in TheEconomicsofFull
Employment,Oxford,1944,p. 47,andalso his"Full EmploymentbyStimulating
PrivateInvestment?"in OxfordEconomicPapers,March,1945,pp. 83-92.
5 See herreviewofTheEconomicsofFull Employment,EconomicJournal,Vol.
55, April,1945,p. 79.
4. CAPITAL EXPANSION, RATE OF GROWTH, AND EMPLOYMENT 139
general.Evenwithouttechnologicalprogress,capitalaccumulationin-
creaseslaborproductivity,at leastto a certainpoint,bothbecause
morecapitalis usedperworkmanineachindustryandbecausethere
is a shiftoflabortoindustriesthatusemorecapitalandcanaffordto
paya higherwage.Soiflaborproductivityisaffectedbycapitalaccum-
ulation,theformulathatthelattershouldproceedat thesamerateas
theformer(andas theincreaseinlaborforce)isnotas helpfulas itap-
pears.
ThestandardKeynesiansystemdoesnotprovideus withanytools
forderivingtheequilibriumrateofgrowth.Theproblemofgrowthis
entirelyabsentfromitbecauseoftheexplicitassumptionthatemploy-
mentisa functionofnationalincome.Thisassumptioncanbejustified
onlyovershortperiodsoftime;it willresultin seriouserrorsovera
periodofa fewyears.Clearly,a full-employmentlevelofincomeof
fiveyearsagowouldcreateconsiderableunemploymenttoday.Weshall
assumeinsteadthatemploymentis a functionoftheratioofnationalin-
cometoproductivecapacity.Whilethisapproachseemsto me to be
superiorto thatofKeynes,it shouldbe lookeduponas a secondap-
proximationratherthana finalsolution:itdoesnotallowustoseparate
unusedcapacityintoidle machinesand idle men;dependingupon
variouscircumstances,thesameratioofincometocapacitymayyield
differentfractionsoflaborforceemployed.
BecauseinvestmentintheKeynesiansystemis merelyan instru-
mentforgeneratingincome,thesystemdoesnottakeintoaccount
theextremelyessential,elementary,andwell-knownfactthatinvest-
mentalso increasesproductivecapacity.6Thisdual characterofthe
investmentprocessmakesthe approachto the equilibriumrate of
growthfromtheinvestment(capital)pointofviewmorepromising:if
investmentbothincreasesproductivecapacityandgeneratesincome,
itprovidesuswithbothsidesoftheequationthesolutionofwhichmay
yieldtherequiredrateofgrowth.
Let investmentproceedat therateI peryear,andlettheratioof
thepotentialnetvalueadded(afterdepreciation),i.e.,oftheproduc-
tivecapacityofthenewprojectsto capitalinvestedin them,i.e.,to
I, beindicatedbys.?Thenetannualpotentialoutputoftheseprojects
willthenbeequaltoIs. Buttheproductivecapacityofthewholeecon-
6 Whethereverydollarinvestedincreasesproductivecapaoityis essentiallya
matterofdefinition.It can safelybe said thatinvestmenttakenas a wholecer-
tainlydoes. To makethisstatementholdin regardto residentialhousing,im-
putedrentshouldbe includedin thenationalincome.See also note 19.
7 The use oftheword"project"doesnotimplythatinvestmentis donebythe
government,orthatitis alwaysmadeinnewundertakings.I am using"project"
(intheabsenceofa betterterm)becauseinvestmentcan meantheact ofinvest-
ingand theresultoftheact.
5. 140 EVSEY D. DOMAR
omymayincreasebya smalleramount,becausetheoperationofthese
newprojectsmayinvolvea transferoflabor(andotherfactors)from
otherplants,whoseproductivecapacityisthereforereduced.8Weshall
definea-,the potentialsocial averageinvestmentproductivityas
dP
dt
(1)
Thefollowingcharacteristicsofo-shouldbe noted:
1. Itsusedoesnotimplythatotherfactorsofproductionandtech-
nologyremainconstant.On thecontrary,itsmagnitudedependsto a
verygreatextentontechnologicalprogress.It wouldbe morecorrect
tosaythato-referstoanincreaseincapacitywhichaccompaniesrather
thanonewhichis causedbyinvestment.
2. o-referstotheincreaseinpotentialcapacity.Whetherornotthis
potentialincreaseresultsin a largerincomedependson thebehavior
ofmoneyexpenditures.
3. o-is concernedwiththeincreasein productivecapacityofthe
wholesociety,andnotwiththerateofreturnderivedorexpectedfrom
investment.Thereforeo-isnotaffecteddirectlybychangesindistribu-
tionofincome.
4. s isthemaximumthata-canattain.Thedifferencebetweenthem
willdependon themagnitudeoftherateofinvestmenton theone
hand,andthegrowthofotherfactors,suchas labor,naturalresources,
andtechnologicalprogressontheother.A misdirectionofinvestment
willalsoproducea differencebetweens ando-.
Weshallmaketheheroicassumptionthats anda areconstant.
From(1) itfollowsthat
(2) dP I.
dt -
It is importantto notethat,witha giveno-,dP/dtis a functionof
I, and notofdI/dt.WhetherdI/dtis positiveornegative,dP/dtis
alwayspositivesolongas a andI arepositive.
Expression(2) showingtheincreaseinproductivecapacityis essen-
tiallythesupplysideofoursystem.Onthedemandsidewehavethe
multipliertheory,too familiarto needanycomment,exceptforan
emphasisontheobviousbutoftenforgottenfactthatwithanygiven
marginalpropensityto save, dY/dtis a functionnotofI, butofdI/dt.
Indicatingthemarginalpropensitytosavebya, andassumingittobe
constant,9wehavethesimplerelationshipthat
8 I am disregardingthe externaleconomiesand diseconomiesof the older
plantsdue to theoperationofthenewprojects.
' Overtheperiod1879-1941theaveragepropensitytosave (ratioofnetcapital
6. CAPITAL EXPANSION, RATE OF GROWTH, AND EMPLOYMENT 141
dY dI 1
(3)=__
dt dt a
Let theeconomybeinan equilibriumpositionso that10
(4) Po = Yo.
To retaintheequilibriumposition,wemusthave
dP dY
dt dt
Substituting(2) and (3) into(5) weobtainourfundamentalequation
dl 1
(X6) I - -,
dt a
thesolutionofwhichgives
(7) I = Ioeaat.
ao-istheequilibriumrateofgrowth.So longas it remainsconstant,
themaintenanceoffull employmentrequiresinvestmenttogrowat a con-
stantcompound-interestrate.
If,as a crudeestimate,a is takenat 12percentand a-at some30
percent,theequilibriumrateofgrowthwillbe some3.6 percentper
year.lOa
The readerwillnowseethattheassumptionofconstanta andafis
notentirelynecessary,andthatthewholeproblemcanbe workedout
withvariablea and a.
formationto nationalincome)was fairlyconstantand approximatelyequal to
some 12 per cent. See Simon Kuznets,National ProductSince 1869, National
BureauofEconomicResearch(mimeographed,1945) p. II-89 and theSurveyof
CurrentBusiness,Vol. 22, May, 1942,and Vol. 24, April,1944.In a problemof
cyclicalcharacter,an assumptionofa constantpropensityto save wouldbe very
bad. Sinceweareinterestedherein a secularproblemofcontinuousfullemploy-
ment,thisassumptionis nottoo dangerous.
10 The problemcan be also workedout forthecase whenPO> YO.
lOa Afterthispaperwas sentto the printer,I founda veryinterestingarticle
by E. H. Stern,"Capital Requirementsin ProgressiveEconomies,"Economica,
Vol. 12, August,1945,pp. 163-171,in whichtherelationbetweencapital and
outputintheU. S. during1879-1929isexpressed(inbillionsofdollars)as capital
=3.274 income-3.55. My estimatesgave roughlysimilarresults.This would
place s around30 percent,thoughthisfigureshouldbe raisedto accountforthe
underutilizationofcapitalduringa partofthatperiod.It is also notclearhow
thejunkingprocess(see p. 144) wasreflectedinthesefigures.
The averagerateofgrowthofrealnationalincomeovertheperiod1879-1941
was some3.3 percent.See Table V, p. 818,and AppendixB, pp. 826-827,in my
paper,"The 'Burden'oftheDebt andtheNationalIncome,"AmericanEconomic
Review,Vol. 34, December,1944.
7. 142 EVSEY D. DOMAR
III. THE EFFECTS OF GROWTH
Ournextproblemis toexplorewhathappenswheninvestmentdoes
growat someconstantpercentagerater,which,however,isnotneces-
sarilyequaltotheequilibriumrateac-.It willbenecessarytointroduce
two additionalconcepts:averagepropensityto save IIY and the
averageratioofproductivecapacityto capitalP/K. To simplifythe
problem,weshallassumethat
1. IIY= a, so thataveragepropensityto saveisequaltomarginal.
2. P/K=s, i.e.,theratioofproductivecapacityto capitalforthe
wholeeconomyis equalto thatofthenewinvestmentprojects.
We shall considerfirstthe special simple case a-=s, and then the
moregeneralcase when -<8s.11
Case 1: a-=s. SinceI = oert,capital,beingthesumofall netinvest-
ments,equals
rt 10
(8) K =Ko + IoJ ertdt= Ko +- (ert-1).
O ~~~~r
As tbecomeslarge,K willapproachtheexpression
(9) - ert,
r
so thatcapitalwillalsogrowat a rateapproachingr.
As Y= (l/a)Ioert,theratioofincometocapitalis
1
- Ioert
Y a
(10) .
Ko +-(ert-1)
r
and
y r C
lim- = -
t(11 goo K a
Thusso longas r and a remainconstant(or changein thesame
proportion)no "deepening"of capital takes place. This, roughly
speaking,wasthesituationintheUnitedStatesoverthelastseventy
yearsorso priortothiswar.
11It is also possiblethat,owingto capital-savinginventionsinexistingplants,
a>s. Formallythis case can be excludedby fallingback on the definitionof
depreciationgivenin note2. This,however,is not a veryhappysolution,but
theapproachusedin thispaperwillhardlyoffera betterone. I think,however,
thata inoursocietyis sufficientlyhighto makeof>s ina continuousstateoffull
employmentmorean exceptionthana rule.
8. CAPITAL EXPANSION, RATE OF GROWTH, AND EMPLOYMENT 143
SubstitutingK = P/s into(11) weobtain
Y r
(12) lim-=
t-*O P aS
Sinceinthepresentcaseo=s,
Y r
(13) lim-=-*
t- o P ao
Theexpression
r
(14) 0 =-
maybe calledthecoefficientofutilization.Whentheeconomygrows
at theequilibriumrate,sothatr= ao-,0= 100percentandproductive
capacityisfullyutilized.Butas rfallsbelowao-,a fractionofcapacity
(1-0) isgraduallyleftunused.12Thusthefailureoftheeconomytogrow
attherequiredratecreatesunusedcapacityandunemployment.
Case2: o-<s. As investmentproceedsat therateI, newprojects
witha productivecapacityofIs arebuilt.Sincetheproductivecapac-
ityofthewholeeconomyincreasesonlybyIo, it followsthatsome-
wherein theeconomy(notexcludingthenewprojects)productive
capacityis reducedby I(s - o). Thereforeeveryyearan amountof
capitalequal to I(s - o-)/sbecomesuseless.
Theproblemcannowbe approachedfromtwopointsofview.The
amountsI(s-o)/s, can be lookeduponas capitallosses,whichare
nottakenintoaccountincalculatingincomeandinvestment.13In this
case,I stillindicatestherateofnetinvestment,andallothersymbols
retaintheiroldmeaning,exceptthatcapitalhastoberedefinedas the
integralof investmentminuscapitallosses:everyyear chunksof
capital(overandabovedepreciation)arewrittenoffandjunked.The
annualadditionto capitalwillthenbe
dK I(s-) Of
(15) ~ ~ =I- - = I-,
dt s s
and
(16) K = Ko + Io-f ertdt= Ko + Io -(e't - 1).
s sr
1 It shouldbe notedthatifr,a, and o areconstant,0is also a constant.Even
thoughthe economyfailsto growat the requiredrate,the relativedisparity
betweenits capacity and incomedoes not become wider,because its capital
also growsnotat theao but at ther rate.
18 These lossesare notnecessarilylossesin theaccountingsense.See note 14.
9. 144 EVSEY D. DOMAR
Also,
Y r s
(17) lim- = -.-,
)K a a
and
Y r
(18) lim-=-,
t c P ao
whichis exactlythesameresultwehadin (13).
ThesecondapproachconsistsintreatingtheamountsI(s - o)/s not
as capitallossesbutas a specialallowanceforobsolescence.Netinvest-
mentwouldthenhavetobe definednotas I, butas IoIs. Othersym-
bolswouldhaveto be redefinedaccordingly,and thewholeproblem
couldthenbe reworkedoutinthesamewayas onpp. 142-143.
In a sensethe choicebetweenthesetwomethodsis a matterof
bookkeeping;dependinguponthecharacteroftheproblemin hand,
oneortheothercanbeused,thoughI suspectthatthesecondmethod
can easilybecomemisleading.The natureoftheprocesswillbe the
samewhichevermethodisused.Thefactisthat,owingtoa difference
betweens and o-,theconstructionofnewinvestmentprojectsmakes
certainassets(notexcludingthenewprojectsthemselves)useless,be-
causeunderthenewconditionsbroughtaboutbychangesindemand,
ora riseinthewagerates,orboth,theproductsoftheseassetscannot
be sold.'4Asstatedonp. 140thedifferencebetweens and o-is created
eitherbymisdirectionofinvestmentorbythelackofbalancebetween
thepropensityto saveontheonehand,andthegrowthoflabor,dis-
coveryofnaturalresources,and technologicalprogresson theother.
So longas mistakesaremadeorthislackofbalanceexists,thejunking
processisinevitable.
Froma socialpointofview,thejunkingprocessis notnecessarily
undesirable.In thiscountry,wheresavinginvolveslittlehardship,it
maybe perfectlyjustified.But it maypresenta seriousobstacleto
theachievementoffullemployment,becausethe ownersof capital
assetsheadedforthejunkpilewilltrytoavoidthelosses.So longas
theyconfinethemselvesto changesin theiraccountingpractices,no
specialconsequenceswillfollow.But it is morelikelythattheywill
tryto accumulatelargerreserveseitherby reducingtheirowncon-
14 To be strictlytrue,the statementin the text would requireconsiderable
divisibilityofcapital assets. In the absenceofsuch divisibility,the expression
"junking"shouldnotbe takentoo literally.
The factthattheseassetsmaystillbe operatedto someextentor thattheir
productsare sold at lowerpricesor that boththeseconditionsexist,does not
invalidateourargument,becauseo, beingexpressedin realterms,willbe higher
thanit wouldbe iftheassetswereleftcompletelyunused.
10. CAPITAL EXPANSION, RATE OF GROWTH, AND EMPLOYMENT 145
sumptionorby charginghigherprices(orpayinglowerwages).As a
result,thetotalpropensityto savemayrise.Thiswillbe exactlythe
oppositemeasurefromwhatis neededto avoidthejunkingprocess,
andwillofcourseleadtogreatertrouble,thoughI amnotpreparedto
say to whatextentcapitalownerswillsucceedin passingon these
losses.
In so faras theyareable to controlnewinvestment,theywilltry
toavoidlossesbypostponingit.Consequently,therateofgrowthmay
wellbe depressedbelowtherequiredao-,andunusedcapacitywillde-
velop.Ourpresentmodeldoesnotallowustoseparateunusedcapacity
intoidlecapitalandidlemen,thoughmostlikelybothwillbepresent.'"
Becauseofhumanitarianconsiderations,wearemoreconcernedwith
unemployedmen.But unemployedcapitalis extremelyimportant,because
its presenceinhibitsnewinvestment.'6It presentsa gravedangerto a
full-employmentequilibriumina capitalistsociety.
IV. GUARANTEED GROWTH OF INCOME
In theprecedingsectionsitwasshownthata stateoffullemploy-
mentcanbe maintainedifinvestmentandincomegrowat an annual
rateao. The questionnowarisesas towhatextenttheargumentcan
bereversed:supposeincomeisguaranteedtogrowat theao rate;will
thatcallforthsufficientinvestmenttogeneratetheneededincome?
We areconcernedherewitha situationwherespontaneousinvest-
ment(i.e.,investmentmadeinresponsetochangesintechnique,shifts
inconsumers'preferences,discoveryofnewresources,etc.)isnotsuffi-
cient,andthereforea certainamountofinducedinvestment(madein
responseto a riseinincome)is alsorequired."To simplifytheargu-
ment,letus assumethatspontaneousinvestmentisabsentaltogether.
It shouldalsobe madeclearthattheproblemis treatedfroma theo-
reticalpointofview,withoutconsideringthenumerouspracticalques-
tionsthattheincomeguaranteewouldraise.
Ifan economystartsfroman equilibriumposition,an expectedrise
inincomeofYao willrequireaninvestmentequalto Yao/s.Asbefore,
twocaseshavetobe considered.
15 The presenceofunemployedmenmaybe obscuredby inefficientutilization
oflabor,as in agriculture.
16 It istruethata givencapitalownermayoftenhave a hardtimedistinguish-
ing betweencapital idlebecauseofa<s, and capital idle becauseofr< aa. The
firstkindofidleness,however,is relativelypermanent,and cannotbe corrected
by greaterexpenditures,whilethe secondis temporary(it is hoped) and is due
to poorfiscaland monetarypolicies.
17 Cf. AlvinH. Hansen, Fiscal Policyand BusinessCycles,New York, 1944,
Part Three,and particularlyp. 297.
11. 146 EVSEY D. DOMAR
1. If a is equal or reasonablycloseto s, theresultingamountof
investmentofYa willequalthevolumeofsavingsthatwillbe made
at thatlevelofincome,and equilibriumwillbe maintained.18Thusa
mereguaranteeofa risein income(iftakenseriouslyby the investors)
willactuallygenerateenoughinvestmentandincometomaketheguarantee
goodwithoutnecessarilyresortingtoa governmentdeficit.
2. Ifu-is appreciablybelows,investmentwillprobablyfallshortof
savingsandequilibriumwillbedestroyed.Thedifficultyarisesbecause
a full-employmentrateofinvestmentinthefaceofa u<s makesthe
junkingprocess(discussedon pp. 143-145)inevitable,whilea mere
guaranteeofa riseinincome,as a generalrule,lackstheinstrument
toforcethecapitalownerstodiscardtheirequipment.Theywillsimply
investYao-IsinsteadofYa. Onlyifintheeconomyas a wholethere
is a considerablenumberofproductsthedemandforwhichis highly
elasticwithrespecttoincome,andthereforea goodnumberofothers
thedemandforwhichisnegativelyelasticwithrespecttoincome,will
a largeramountthanYaorIsbe investedanda correspondingamount
ofcapitaljunked.Ofcourse,iftheriseinincomeis accompaniedby
shiftsin consumers'preferences,the appearanceof new products,
aggressivecompetition,andotherchanges,thejunkingprocesswillbe
speededup,butifthesechangesdo takeplacetheymaygiveriseto
spontaneousinvestmentoftheirownandtheguaranteedriseinincome
willnotbe important.Still,theassuranceofa highandrisingincome
is undoubtedlyoneofthebestmethodsforencouraginginvestment.
Asexplainedbefore,a substantialdifferencebetweens andufsimply
indicatesthatwiththeavailablelaborforceandthecurrentprogress
oftechnology,themaintenanceoffullemploymentundera givena
requirestheaccumulationofcapitalata fasterratethanitcanbeused.
As a ge.neralrule,thisappliesequallywelltobothprivateandpublic
investment,thoughtheremaybe specialcases when,owingto the
developmentofparticularconsumers'preferences(e.g.,forvacations),
orto technologicalreasons(e.g.,needforpower),orto institutional
conditions(as in urbanredevelopment),considerableneedforpublic
investmentstillexists.'9
18 Thereis a slighterrorin the magnitudesin the textbecause ofthe use of
discontinuousfunctions.
19As soonas thegovernmententersthepicturewe findourselvesin a maze of
definitionalproblems.Fromthe pointofviewofthispaper,savingand invest-
mentshouldbe understoodin referenceto the wholeeconomy,includingthe
government,and notto itsprivatesectoronly.But whichgovernmentexpendi-
turesshouldbe regardedas investment?The difficultyis presentin theprivate
sectoras well,exceptthattherewe can take refugein formaldefinitions,which
cannot be well applied to government.I leave the questionopen. Certainly,
investmentneednotbe limitedto inventories,steel,and concrete.
12. CAPITAL EXPANSION, RATE OF GROWTH, AND EMPLOYMENT 147
I am notpreparedto saywhetherwe alreadyare orshallsoonbe
facedwitha seriousdifferencebetweens and o-,thoughI doubtthat
itwasan importantprobleminthepast,exceptperhapsfortheshort
boomyears.Myownguessisthatweshallbemoreconcernedwiththe
disparitybetweenao-andr,thatis withthefailureofincometogrow
at therequiredrate.
If,however,thedifferencebetweena-ands becomesseriousandin-
hibitsinvestment,orifthejunkingprocessproceedsat a fasterrate
thanis deemedsociallydesirable,thesocietywillhaveat itsdisposal
twomethodsnotmutuallyexclusive:(1) thereductionofthepro-
pensitytosave,or(2) thespeedingupoftechnologicalprogress.I hope
thatthemainemphasiswillbe placedonthelatter.
Thispaperattemptedto analyzetherelationbetweeninvestment,
rateofgrowth,and employment.The analysiswas carriedout on a
veryabstractandsimplifiedlevel-a procedurewhichmaybejustified
at thebeginningofan investigation,butwhichmustbe correctedlater
on.In general,thereis no sucha thingas an absolutelygoodorbad
assumption:whatmaybe safein onekindofa problemcanbecome
fatalinanother.Oftheseveralassumptionsmadehere,thatregarding
depreciationis likelyto causethegreatestdifficulties,butit is byno
meanstheonlyone.I hopeto developthewholesubjectfurtherat a
laterdate.
The centralthemeofthepaperwas therateofgrowth,a concept
whichhas beenlittleused in economictheory,and in whichI put
muchfaithas an extremelyusefulinstrumentofeconomicanalysis.
Onedoesnothaveto be a Keynesianto believethatemploymentis
somehowdependentonnationalincome,andthatnationalincomehas
somethingtodowithinvestment.Butas soonas investmentcomesin,
growthcannotbe leftout,becauseforan individualfirminvestment
maymeanmorecapitalandlesslabor,butfortheeconomyas a whole
(as a generalcase)investmentmeansmorecapitalandnotlesslabor.If
botharetobeprofitablyemployed,a growthofincomemusttakeplace.
Washington,D. C.