Lecture 1: Economic GrowthVladimir Asriyan and John MondragonUC BerkeleyAugust 31, 2011Vladimir Asriyan and John Mondragon Lecture 1: Economic GrowthGoal: Build a model of economic growth. Use it to discussdifferences in income and growth rates.Robert Solow, “A Contribution to the Theory of EconomicGrowth” (1956)These slides follow Jones (2002) closely.Vladimir Asriyan and John Mondragon Lecture 1: Economic GrowthProduction Function: how inputs become outputsIY : Output (cars, movies, BBQ,...)IK : Capital (bulldozers, factory buildings, computers,...)IL: Labor (engineers, servers, teachers,...)Y =KαL1−α,0 ≤ α ≤ 1Constant returns to scale:aY = (aK )α(aL)1−αVladimir Asriyan and John Mondragon Lecture 1: Economic GrowthWe want to deal with per capita or per worker variables.y =YLThis gives us the per worker production functiony =KαL1−αL= kαDiminishing returns to capital per worker.Vladimir Asriyan and John Mondragon Lecture 1: Economic GrowthCapital AccumulationAgents invest/save some of their income:˙K|{z}Change in capital= sY|{z}savings− dK|{z}depreciation(1)Notice that savings and depreciation are constant.Vladimir Asriyan and John Mondragon Lecture 1: Economic GrowthL grows at rate n:˙LL= nDefine capital per worker k:k ≡KL⇒log(k) = log(K ) − log(L) ⇒˙kk=˙KK−˙LL.Now we can derive the evolution of capital per worker.Vladimir Asriyan and John Mondragon Lecture 1: Economic Growth˙kk=˙KK−˙LL=sY − dKK− n=sY /LK /L− d − n⇒˙k = sy − (d + n)kNow we can solve the model for the steady state˙k = 0.Vladimir Asriyan and John Mondragon Lecture 1: Economic GrowthAnalytically:k∗=sn + d11−αThe production function y = kαimpliesy∗=sn + dα1−αHigher savings implies higher income per worker.Vladimir Asriyan and John Mondragon Lecture 1: Economic GrowthSolow DiagramVladimir Asriyan and John Mondragon Lecture 1: Economic GrowthTransition DynamicsVladimir Asriyan and John Mondragon Lecture 1: Economic GrowthConsumption and Income DynamicsVladimir Asriyan and John Mondragon Lecture 1: Economic GrowthIncrease in SavingsVladimir Asriyan and John Mondragon Lecture 1: Economic GrowthConsumption and Savings (n = .01, d = .05, α = .3)c = (1 − s)yVladimir Asriyan and John Mondragon Lecture 1: Economic GrowthIncrease in PopulationVladimir Asriyan and John Mondragon Lecture 1: Economic GrowthTaking StockSolow model predicts:ICountries that save more are wealthier.Vladimir Asriyan and John Mondragon Lecture 1: Economic GrowthInvestmentVladimir Asriyan and John Mondragon Lecture 1: Economic GrowthTaking StockSolow model predicts:ICountries that save more are wealthier.ICountries with higher population growth rates are poorer(capital widening).Vladimir Asriyan and John Mondragon Lecture 1: Economic GrowthPopulationVladimir Asriyan and John Mondragon Lecture 1: Economic GrowthTaking StockSolow model predicts:ICountries that save more are wealthier.ICountries with higher population growth rates are poorer(capital widening).INo long run growth per capita!What can we do to fix this prediction?Technology.Vladimir Asriyan and John Mondragon Lecture 1: Economic GrowthTaking StockSolow model predicts:ICountries that save more are wealthier.ICountries with higher population growth rates are poorer(capital widening).INo long run growth per capita!What can we do to fix this prediction?Technology.Vladimir Asriyan and John Mondragon Lecture 1: Economic GrowthTechnologyAssume growth in technology A:˙AA= gChange the production function:Y = Kα(AL)1−αHarrod-neutral technology. Efficiency of labor increases. Thistechnology is exogenous.Vladimir Asriyan and John Mondragon Lecture 1: Economic GrowthCapital accumulation equation is unchanged:˙KK= sYK− dOutput per worker:y = kαA1−α˙yy= α˙kk+ (1 − α)˙AAVladimir Asriyan and John Mondragon Lecture 1: Economic GrowthBalanced Growth PathWe want to look at a situation where growth rates are constant.ICapital accumulation tells us that the growth rate of capital isconstant only when Y /K is constant.IThis means output Y and capital K must grow at the samerate.IWhich implies that y and k also grow at the same rate.Let gy= gkbe the growth rate for capital and output.˙yy= α˙kk+ (1 − α)˙AAgy− αgk= (1 − α)g(1 − α)gy= (1 − α)ggy= gOutput and capital grow at the rate of technological progress.Vladimir Asriyan and John Mondragon Lecture 1: Economic GrowthDefine˜k ≡ K/AL ≡ k/A. This is the capital - technology ratio.˜y =˜kαCapital accumulation (you should construct it as an exercise):˙˜k = s˜y − (n + g + d)˜kWe can solve for˜k as before and find steady state output perworker y∗:y∗= Asn + g + dα1−αNow we have growth in output per worker.What happens now when we increase the savings rate?Vladimir Asriyan and John Mondragon Lecture 1: Economic GrowthIncrease in Savings RateVladimir Asriyan and John Mondragon Lecture 1: Economic GrowthIncrease in Savings RateVladimir Asriyan and John Mondragon Lecture 1: Economic GrowthUnresolved issues:IWhat is technology and where does it come from? (SeeRomer paper.)ICan technology really explain all differences? (See Lucaspaper.)IWhat factors are missing?Additional reading:I“Introduction to Economic Growth” by Charles I. JonesI“Advanced Macroeconomics” by David RomerIHall and Jones, “Why Do Some Countries Produce So MuchMore Output per Worker than Others?” (1999)ILucas, “Why Doesn’t Capital Flow from Rich to PoorerCountries?” (1990)IRomer, “Endogenous Technological Change” (1990)Vladimir Asriyan and John Mondragon Lecture 1: Economic