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Lord Harrod and Mr. DomarKeynesian based modelsSaving ratesCapital/Output ratio orCapital ProductivityCapital stockGDPPersonal ConsumptionGross SavingsGross InvestmentNet Investment, or CapitalAccumulationDepreciationDynamic modelsIn growth models, we will encounter thefollowing terms:
What is a Keynesian Growth Model?Keynes’ model and Keynesian models weredeveloped to explains business cycles» A short run phenomenaAs such they attribute a major role to aggregateexpenditures (demand side)Regarding the supply side, they assume that thereis unemployment: production responds fast toincreases in aggregate demand because capitaland labor is unemployed.
Aggregate Demand, AD– AD = C + I + G + X-M– C, Consumption expenditures– I, Investment expenditures– G, Government expenditures– X-M, Foreigners’ ExpendituresAggregate Supply– AS < ASfe– Aggregate Supply, at full employmentMacroeconomic Equilibrium– AS = AD– Or– S = I
A Keynesian ModelA Keynesian growth model takes a long runperspective.– Aggregate demand (or savings=investment)still is important, but– It also includes the aggregate supply» Investment has two impacts:On expenditures (in the short run)On capital stock (in the long run)
Trends and business cyclesRealGDPYearsOne business cycleTrend
Main PropositionsEconomic growth can be accelerated by– changing the saving rate– improving technology.Saving rates and technology can bechanged– government interventions withoutconsideration to prices
v= K/Y ora=Y/KCapitalCapital/OutputRatio or ProductivityGDPsSaving RateCSdDepreciationRateDInIgProduction functionHarrod-Domar Growth ModelA Flow chart model
Factors Explaining the growth rateAccording to Harrod-Domar modelgsadSaving rateCapital productivityCapital depreciationRate ofEconomicGrowthExplained variable Explanatory Variables++_
Arithmetic specificationWithout Depreciationa=dY/dKY=K.aS=Y.s s=dS/dYIKdKIf we know the initialcapital stock K; and weknow a, (how muchoutput increases whencapital increases 1 unit)then we know what willtotal output Y be.If we know output Y,and we know s, which isthe saving rate, then weknow total savings S.IfweknowtotalsavingsS,weknowhowmuchwecaninvest(I)innewcapital(dK)If we know dK anda, we know growthof output dYdY
Numerical specificationWithout Depreciationa=.20Y=1S=.10 s=.10.10K=5dK=.10If we know the initialcapital stock K=5; andwe know its productivitya=.20 then we knowtotal output Y=1If we know output Y=1and we know the savingrate s=.10, then we knowtotal savings S=.10IfweknowtotalsavingsS=.10weknowthatwecaninvestI=.10innewcapital(dK=.10)If we know dK=.10and a=.20, we knowgrowth of outputdY=0.02=2%dY=.02=2%Or …dY = s.aBy approximation:dY/Y=s.a/Yg=s.aSince Y=1
Economic growth formulaAccording to Harrod-Domar the rate of economic growthis defined by the formula:g = s.a – dthat is, if s=10% and a=0.20 and d =1%, theng=0.10*0.20 - 0.01 = 0.02 -0.01 = 0.01 = 1%What happens if the rate of saving (s) increases to 20% ?What happens if the productivity of capital (a) increases to 0.40?What happens if the depreciation (d) rate is 2% ?
.Conventional Keynes’ ModelSpecificationSaving function (demand side)S = s.Y where s is the average propensity to save or average savingrate.In the conventional short run Keynesian model investment (I) is given.I = IaIn equilibriumS = ISolving the models.Y = IaY = 1/s.Ia = m.Ia where m is the investment multiplierMathematical derivation of Harrod-Domar model
In this model national GDP increases because the autonomous demand (I)increases. It is assumed that aggregate supply responds as to producewhat is demanded. But, what will happen if the economy was at fullemployment? The only way for production to increase will be an increasein the capital stock. With more capital (and labor) the economy willproduce more GDP.
Mathematical derivation of Harrod-Domar model (2)Keynes’ Model Expanded to Consider GrowthHarrod and Domar explained how the aggregate supply expands.For them, investment has two effects, one on the aggregate demandside (businesses expend more) and another in the aggregate supplyside (more investment increases capital stock and therebybusinesses produce more the next period).We, therefore, need to add a production function:Y = a.K production functionWhere a is the productivity of capital: ∆Y/ ∆K, which is constantNow we can determine how a change in capital changes income.∆Y = a.∆K
Mathematical derivation of Harrod-Domar model (3)What we need to know is how capital changes. It changes bybusinesses, and government investment:∆K = IaWe are assuming that capital doesn’t ware out, i.e. there is notdepreciation.Returning to the equilibrium condition (S=I) we solve the model againfor the long run cases.Y = Ia = ∆K, but we know that ∆K = ∆Y/a, thens.Y = ∆Y/as.a = ∆Y/YCalling ∆Y/Y = g : rate of GNP growth
Mathematical derivation of Harrod-Domar model IVg = s.aIf we recognize that capital depreciates:g = s.a – dWhere d is the depreciation rate per year.Notice that in this model the rate ofgrowth (g) is constant. Why?
Harrod’s way:K = v.Y where v = 1/ag = s/vAnd with depreciationg = s/v - d
Production functionKNGDP1GDP2> GDP1ProductionfunctionGDPKGDPProductivity rateTo growth model
Assumptions– Labor/capital proportions are fixed– Saving rate is givenKNGDP1GDP2> GDP1SSIncome = GDPProductionfunctionSavingfunctionGDPKGDPSaving rateProductivity rateTo growth model