GR5215 RonMiller Fall2021 Assignment2;dueThursdayOctober7inclass 1) Assume that the rate of exogenous technological progress is constant in the Solow model, but assume that the production...

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GR5215 RonMiller Fall2021 Assignment2;dueThursdayOctober7inclass 1) Assume that the rate of exogenous technological progress is constant in the Solow model, but assume that the production function is Y = F [B(t)K ,A(t)L], where B(t)=ezt and A(T)=ext , with z ≥ 0 and x ≥ 0. Show that if z > 0 and a steady state exists, the production function must take the Cobb–Douglas form. 2) Transitional dynamics in the Solow model. Simulate a discrete time version of the Solow model, where the unit of time is one year. Assume a Cobb-Douglas production function: Population grows at 2% per year, annual depreciation is 3%, and the savings rate is 25%. There is no technological change. To start with assume α = 0.33. a) Solve for the steady-state capital-labor ratio. (You can do this from the continuous time equations we examined in class.) b) Simulate the model starting from L0=1 (that’s just a normalization) and K0 = 0.05 of the steady state K/L ratio. (You can use any software you want to do the simulation. Excel will do.) Include the simulation results in your answer. About how many years does it take to reach steady-state? (It won’t get there exactly – state how you have defined convergence.) c) Repeat the simulation with α = 0.7. Now how long does convergence take? 3)Considerthetwo-periodconsumptionproblemwithexogenousincomeandgiven interestrater.Supposethatthegovernmenttaxesinterestincomeattherateτ.The government’srevenuewillbezeroinperiod1andτr(Y1–C1)inperiod2. a)Writeouttheindividual’sbudgetconstraint. Nowsupposethegovernmenteliminatesthetaxationofinterestincome andinsteadinstituteslump-sumtaxesofamountsT1andT2inthetwoperiods. b)Writeouttheindividual’sbudgetconstraintunderthisalternatetaxregime. c)Whatconditionmustthenewtaxessatisfysothatthechangedoesnotaffectthe presentvalueofgovernmentrevenue? d)Ifthenewtaxessatisfytheconditioninpart(c)istheoldconsumption bundle,notaffordable,justaffordable,oraffordablewithroomto spare? e)Ifthenewtaxessatisfytheconditioninpart(c)doesfirst-periodconsumption rise,fall,orstaythesame? 4)a)WritedownaversionoftheSolowgrowthmodelinwhichthelaborforceisa fraction!ofthepopulation.Forsimplicity,assumenopopulationgrowth.Write downtheequationforsteadystateundertheassumptionthat!=!#,aconstant. DoesthischangehaveanysubstantiveeffectontheSolowmodel? Y = AK αL1−α GR5215 RonMiller Fall2021 b)Suppose!growsataconstantrate,!$.Howdoesthissteadyincreaseaffectthe growthrateofpercapitaincome?Solveforthesteadystateinthismodel. c)Brieflyexplainhowyouranswertopart(b)mayhelpexplainhighgrowthratesin somedevelopingcountries.Whyisthissourceofgrowthnecessarilytemporary? Graphicallydepictthetransitionfromapositive!$tozerolaborforceparticipation growth.