The Production FunctionGrowth ModelsThe Production FunctionGrowth ModelsGrowth TheoryElias YannopoulosSeptember 19, 2012Elias Yannopoulos Growth TheoryThe Production FunctionGrowth ModelsThe Production FunctionProduction function - the relationship between inputs andoutputY = F (Inputs)Y = F (Labor , Land, Capital)Ex: Robinson Crusoe (deserted island)Crusoe’s output is coconuts, which he gets by climbing thetrees that contain themAlso Crusoe posses the technology of ladders and can get thematerials to make themThe ladders make it much easier to climb the trees, but arenot easy to make because the materials have to be gatheredSample Production function, on boardInvestment is costly, eventually there is no longer a reason tobuild more laddersElias Yannopoulos Growth TheoryThe Production FunctionGrowth ModelsProduction Function ConceptsLaw of diminishing marginal productivity - increasing oneinput, keeping all others constant, will lead to ever decreasinggains in outputCrusoe and the ladders, also hours spent getting coconutsConstant Returns to Scale - increasing all inputs by thesame percentage, output will increase by that percentageIncreasing Returns to Scale - increasing all inputs by thesame percentage, output will increase by more than thatpercentageDecreasing Returns to Scale - increasing all inputs by thesame percentage, output will increase by less than thatpercentageMathematical demonstrationElias Yannopoulos Growth TheoryThe Production FunctionGrowth ModelsEconomic ModelsEconomic Model - a theoretical construct that representseconomic processes by a set of variables and a set of logicaland/or quantitative relationships between themAn economic model is a set of agents (variables) and a set ofrules (relationships)Like the MatrixEconomists use models to simplify the complexity economies,while attempting to stay close to real world observationsIn a growth model we are trying to determine what variableshelp/hinder growth and their relationshipsElias Yannopoulos Growth TheoryThe Production FunctionGrowth ModelsThe First Solow Growth ModelNamed for economist Robert SolowThe model focuses on capital accumulationRemember the production functionY = F (Labor , Land, Capital)Why capital?Remember the production functionY = F (Labor, Land , Capital)Land is assumed fixed, imagine the US once we have achievedManifest DestinyDiminishing marginal productivity of labor implies a ceiling togrowth from population increasesAlso, two empirical observationsThe wealthy have more capital goodsInvestment and growth are correlatedElias Yannopoulos Growth TheoryThe Production FunctionGrowth ModelsSolow I Cont.The thrust of the model is that increasing capital(investment) leads to growthBut remember law of diminishing marginal productivityapplies to capital as wellEx production functionThis model gives two important implicationsSteady State - A state where properties are unchanging intimeFor the Solow model that means that there is no change incapitalThere is no net investment (Remember! Net investment =investment - depreciation)⇒ No Growth!!Elias Yannopoulos Growth TheoryThe Production FunctionGrowth ModelsSolow I Cont. Cont.The second implication is ConvergenceConvergence is the idea that nations with the sameinstitutions will gravitate towards the same per capita incomeEventually the rich stop growing and the poor catch upThere are greater returns to investment in poor nationsSteady state ⇒ convergenceOne major problem, growth rates of the rich countries did notdecrease they increasedElias Yannopoulos Growth TheoryThe Production FunctionGrowth ModelsThe Second Solow ModelSource of new growth is technologyNew capital is more productive than old capital because it ismade with better technologyModified production functionY = A × F (Labor , Land, Capital)In Solow’s model technology is exogenous, not by the actionsof agents in the economyExogenous - introduced from or produced outside theorganism or systemThe model treats technological changes as random shocksuncontrolled by the economySolow II still implies convergence, technology can move acrossbordersElias Yannopoulos Growth TheoryThe Production FunctionGrowth ModelsPolicy ImplicationsSpecifically this policy was aimed at increasing growth in thenewly independent nations of AfricaThe prescription is to give them investment goods, or aid tobe used for investmentThe result was that the rich got richer and the poor stayedpoorThe problem was in the original empirical observationsCorrelation doesn’t prove causationElias Yannopoulos Growth
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