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harrod domar model wikipedia jump to content main menu main menu move to sidebar hide navigation main page contents current events random article about wikipedia contact us contribute help learn to edit community portal recent changes upload file special pages search search appearance donate create account log in personal tools donate create account log in contents move to sidebar hide top 1 reception and reinterpretation 2 mathematical formalism toggle mathematical formalism subsection 2 1 definitions 2 2 derivations 3 significance 4 criticisms 5 see also 6 references 7 further reading toggle the table of contents harrod domar model 20 languages azərbaycanca deutsch español français हिन्दी magyar հայերեն italiano македонски मराठी नेपाली nederlands polski português русский svenska தமிழ் українська tiếng việt 中文 edit links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikimedia commons wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia development economics the harrod domar model is a keynesian model of economic growth it is used in development economics to explain an economy s growth rate in terms of the level of saving and of capital it suggests that there is no natural reason for an economy to have balanced growth the model was developed independently by roy f harrod in 1939 1 and evsey domar in 1946 2 although a similar model had been proposed by gustav cassel in 1924 3 the harrod domar model was the precursor to the exogenous growth model 4 neoclassical economists claimed shortcomings in the harrod domar model in particular the instability of its solution 5 and by the late 1950s started an academic dialogue that led to the development of the solow swan model 6 7 according to the harrod domar model there are three kinds of growth warranted growth actual growth and natural rate of growth warranted growth rate is the rate of growth at which the economy does not expand indefinitely or go into recession actual growth is the real rate increase in a country s gdp per year see also gross domestic product and natural gross domestic product natural growth is the growth an economy requires to maintain full employment for example if the labor force grows at 3 percent per year then to maintain full employment the economy s annual growth rate must be 3 percent reception and reinterpretation edit although harrod stressed instability and domar highlighted equilibrium growth conditions economists soon noticed the formal similarity between harrod s capital coefficient and domar s σ by the 1950s 1960s their ideas were routinely combined in development economics as the harrod domar model 8 modern scholarship emphasizes that this model is a retrospective synthesis rather than a single unified theory besomi 1998 shows that harrod s readers almost unanimously interpreted his work as a theory of economic growth despite his own emphasis on instability 9 orlando sportelli and della rossa 2021 likewise argue that harrod s writings developed across his entire career primarily addressed the instability of capitalist economies whereas domar s 1946 paper focused on the dual role of investment in productive capacity and demand 10 mathematical formalism edit definitions edit let y represent output which equals income and let k equal the capital stock s is total saving s is the savings rate and i is investment δ stands for the rate of depreciation of the capital stock the harrod domar model makes the following a priori assumptions y f k displaystyle y f k 1 output is a function of capital stock only labor is irrelevant d y d k c d y d k y k displaystyle frac dy dk c rightarrow frac dy dk frac y k 2 the marginal product of capital is constant the production function exhibits constant returns to scale this implies capital s marginal and average products are equal f 0 0 displaystyle f 0 0 3 capital is necessary for output s y s i displaystyle sy s i 4 the product of the savings rate and output equals saving which equals investment δ k i δ k displaystyle delta k i delta k 5 the change in the capital stock equals investment less the depreciation of the capital stock derivations edit derivation of output growth rate c d y d k y t 1 y t k t s y t δ k t k t c y t 1 y t s y t δ d k d y y t c s y t δ d k d y y t y t 1 y t c y t s δ d k d y y t 1 y t c s c δ d k d y y t 1 y t y t s d y d k δ d y d k d k d y y t 1 y t y t s c δ δ y y displaystyle begin aligned c frac dy dk frac y t 1 y t k t sy t delta k t k t 8pt c frac y t 1 y t sy t delta frac dk dy y t 8pt c sy t delta frac dk dy y t y t 1 y t 8pt cy t left s delta frac dk dy right y t 1 y t 8pt cs c delta frac dk dy frac y t 1 y t y t 8pt s frac dy dk delta frac dy dk frac dk dy frac y t 1 y t y t 8pt sc delta frac delta y y end aligned a derivation with calculus is as follows using dot notation for example y displaystyle dot y for the derivative of a variable with respect to time first assumptions 1 3 imply that output and capital are linearly related for readers with an economics background this proportionality implies a capital elasticity of output equal to unity these assumptions thus generate equal growth rates between the two variables that is y c k l o g y l o g c l o g k displaystyle y ck rightarrow log y log c log k since the marginal product of capital c is a constant we have d log y d t d log k d t y y k k displaystyle frac d log y dt frac d log k dt rightarrow frac dot y y frac dot k k next with assumptions 4 and 5 we can find capital s growth rate as k k i k δ s y k δ displaystyle frac dot k k frac i k delta s frac y k delta y y s c δ displaystyle rightarrow frac dot y y sc delta in summation the savings rate times the marginal product of capital minus the depreciation rate equals the output growth rate increasing the savings rate increasing the marginal product of capital or decreasing the depreciation rate will increase the growth rate of output these are the means to achieve growth in the harrod domar model significance edit domar proposed the model in the aftermath of the great depression intending to model economies in the short run during a period where there is high enough unemployment such that any additional machine may be fully utilized by labor consequently production can be modelled as a function of capital only 11 although the harrod domar model was initially created to help analyse the business cycle it was later adapted to explain economic growth its implications were that growth depends on the quantity of labour and capital more investment leads to capital accumulation which generates economic growth the model carries implications for less economically developed countries where labour is in plentiful supply in these countries but physical capital is not slowing down economic progress ldcs do not have sufficiently high incomes to enable sufficient rates of saving therefore accumulation of physical capital stock through investment is low the model implies that economic growth depends on policies to increase investment by increasing saving and using that investment more efficiently through technological advances the model concludes that an economy does not naturally find full employment and stable growth rates criticisms edit the main criticism of the model is the level of assumption one being that there is no reason for growth to be sufficient to maintain full employment this is based on the belief that the relative price of labour and capital is fixed and that they are used in equal proportions the model also assumes that savings rates are constant which may not be true and assumes that the marginal returns to capital are constant furthermore the model has been criticized for the assumption that productive capacity is proportional to capital stock which domar later stated was not a realistic assumption 12 see also edit economic growth feldman mahalanobis model solow swan model references edit harrod roy f 1939 an essay in dynamic theory the economic journal 49 193 14 33 doi 10 2307 2225181 jstor 2225181 domar evsey 1946 capital expansion rate of growth and employment econometrica 14 2 137 147 doi 10 2307 1905364 jstor 1905364 cassel gustav 1967 1924 capital and income in the money economy the theory of social economy pdf new york augustus m kelley pp 51 63 hagemann harald 2009 solow s 1956 contribution in the context of the harrod domar model history of political economy 41 suppl 1 67 87 doi 10 1215 00182702 2009 017 scarfe brian l 1977 the harrod model and the knife edge problem cycles growth and inflation a survey of contemporary macrodynamics new york mcgraw hill pp 63 66 isbn 0 07 055039 5 sato ryuzo 1964 the harrod domar model vs the neo classical growth model the economic journal 74 294 380 387 doi 10 2307 2228485 jstor 2228485 solow robert m 1994 perspectives on growth theory journal of economic perspectives 8 1 45 54 doi 10 1257 jep 8 1 45 jstor 2138150 schelling t c 1947 capital growth and equilibrium american economic review 37 5 864 876 besomi d 1998 failing to win consent harrod s dynamics in the eyes of his readers palgrave macmillan uk orlando giuseppe sportelli mario della rossa fabio february 2021 the harrod model in orlando giuseppe pisarchik alexander n stoop ruedi eds nonlinearities in economics cham switzerland springer international publishing pp 177 189 doi 10 1007 978 3 030 70982 2_13 isbn 978 3 030 70982 2 via springerlink easterly william 1999 11 30 the ghost of financing gap how the harrod domar growth model still haunts development economics pdf policy research working papers doi 10 1596 1813 9450 1807 issn 1813 9450 s2cid 13515227 easterly william 1997 ghost of the financing gap how the harrod domar model still haunts development economics pdf world bank development research group further reading edit ackley gardner 1961 economic growth the problem of capital accumulation macroeconomic theory new york macmillan pp 505 535 baumol william j 1970 mr harrod s model economic dynamics third ed london macmillan pp 37 55 isbn 0 02 306660 1 brems hans 1967 the one country harrod domar model of growth quantitative economic theory a synthetic approach new york wiley pp 426 435 cochrane james l gubins samuel kiker b f 1974 economic growth i macroeconomics analysis and policy glenview scott foresman and co pp 328 353 isbn 0 673 07639 3 gapinski james h 1982 celebrated paradigms of economic growth macroeconomic theory statics dynamics and policy mcgraw hill pp 251 285 isbn 0 07 022765 9 keiser norman f 1975 an introduction to growth theory macroeconomics second ed new york random house pp 386 399 isbn 0 394 31922 2 lindauer john 1976 macroeconomics third ed new york wiley pp 325 332 isbn 0 471 53572 9 v t e 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