Endogenous Technological Change Daron Acemoglu 经济增长导论课件.pdf

14.452 Economic Growth: Lectures 9 and 10, Endogenous Technological ChangeDaron AcemogluMITNovember 24 and December 1, 2009.Daron Acemoglu (MIT)Economic Growth Lectures 9 and 10November 24 and December 1, 2009.1/ 60Endogenous Technological ChangeExpanding Variety ModelsIntroductionThe key to understanding technology is that RAn increase in N(t)raises the productivity of labor and when N(t) increases at a constant rate so will output per capita.Daron Acemoglu (MIT)Economic Growth Lectures 9 and 10November 24 and December 1, 2009.15/ 60Baseline Expending Varieties ModelThe Lab Equipment ModelCharacterization of Equilibrium IVEquilibrium wages:w(t) =β 1?βN(t).(13)Free entryηV(ν,t)?1, Z(ν,t) ?0 and(14) (ηV(ν,t) ?1)Z(ν,t)=0, for all ν and t,where V(ν,t)is given by (7).For relevant parameter values with positive entry and economic growth: ηV(ν,t) =1.Daron Acemoglu (MIT)Economic Growth Lectures 9 and 10November 24 and December 1, 2009.16/ 60Baseline Expending Varieties ModelThe Lab Equipment ModelCharacterization of Equilibrium VSince each monopolist ν2 [0,N(t)]produces machines given by (10), and there are a total of N(t)monopolists, the total expenditure on machines is X(t) =N(t)L.(15)Finally, the representative household’ s problem is standard and implies the usual Euler equation:˙C(t) C(t)=1 θ(r(t) ?ρ)(16)and the transversality conditionlimt!∞? exp? ?Zt0r(s)ds? N(t)V(t)? =0.(17)Daron Acemoglu (MIT)Economic Growth Lectures 9 and 10November 24 and December 1, 2009.17/ 60Baseline Expending Varieties ModelThe Lab Equipment ModelEquilibrium and Balanced Growth Path IWe can now de…ne an equilibrium more formally as time paths[C(t),X(t),Z(t),N(t)]∞t=0, such that (3), (15), (16), (17) and(14) are satis…ed; [px(ν,t),x(ν,t)]∞ν2N(t),t=0that satisfy (9) and (10), [r(t),w(t)]∞t=0such that (13) and (16) hold.We de…ne a balanced growth path (BGP) as an equilibrium path where C(t),X(t),Z(t)and N(t)grow at a constant rate. Such an equilibrium can alternatively be referred to as a “steady state”, since it is a steady state in transformed variables.Daron Acemoglu (MIT)Economic Growth Lectures 9 and 10November 24 and December 1, 2009.18/ 60Baseline Expending Varieties ModelThe Lab Equipment ModelBalanced Growth Path IA balanced growth path (BGP) requires that consumption grows at a constant rate, say gC. This is only possible from (16) ifr(t) =r?for all tSince pro…ts at each date are given by (11) and since the interest rate is constant,˙V(t) =0 andV?=βL r?.(18)Daron Acemoglu (MIT)Economic Growth Lectures 9 and 10November 24 and December 1, 2009.19/ 60Baseline Expending Varieties ModelThe Lab Equipment ModelBalanced Growth Path IILet us next suppose that the (free entry) condition (14) holds as an equality, in which case we also haveηβL r?=1This equation pins down the steady-state interest rate, r?, as:r?=ηβLThe consumer Euler equation, (16), then implies that the rate of growth of consumption must be given byg?C=˙C(t) C(t)=1 θ(r??ρ).(19)Daron Acemoglu (MIT)Economic Growth Lectures 9 and 10November 24 and December 1, 2009.20/ 60Baseline Expending Varieties ModelThe Lab Equipment ModelBalanced Growth Path IIINote the current-value Hamiltonian for the consumer’ s maximization problem is concave, thus this condition, together with the transversality condition, characterizes the optimal consumption plans of the consumer.In BGP, consumption grows at the same rate as total outputg?=g?C.Therefore, given r?, the long-run growth rate of the economy is:g?=1 θ(ηβL?ρ)(20)Suppose that ηβL>ρ and(1?θ)ηβL0 and that the transversality condition is satis…ed.Daron Acemoglu (MIT)Economic Growth Lectures 9 and 10November 24 and December 1, 2009.21/ 60Baseline Expending Varieties ModelThe Lab Equipment ModelBalanced Growth Path IVProposition Suppose that condition (21) holds. Then, in the above-described lab equipment expanding input variety model, there exists a unique balanced growth path in which technology, output and consumption all grow at the same rate, g?, given by (20)..An important feature of this class models is the presence of the scale e¤ect: the larger is L, the greater is the growth rate.Daron Acemoglu (MIT)Economic Growth Lectures 9 and 10November 24 and December 1, 2009.22/ 60Baseline Expending Varieties ModelThe Lab Equipment ModelTransitional Dynamics IThere are no transitional dynamics in this model.Substituting for pro…ts in the value function for each monopolist, this gives r(t)V(ν,t) ?˙V(ν,t) =βL.The key observation is that positive growth at any point implies that ηV(ν,t) =1 for all t. In other words, if ηV(ν,t0) =1 for some t0, then ηV(ν,t) =1 for all t.Now di¤erentiating ηV(ν,t) =1 with respect to time yields ˙V(ν,t) =0, which is only consistent with r(t) =r?for all t, thusr(t) =ηβL for all t.Daron Acemoglu (MIT)Economic Growth Lectures 9 and 10November 24 and December 1, 2009.23/ 60Baseline Expending Varieties ModelThe Lab Equipment ModelTransitional Dynamics IIProposition Suppose that condition (21) holds. In the above-desc。