The starting point of Solow Model Solow considered the following production function: Y = F(K, L) = KaL1-a, 0 In the long run, when t=T, KT = KT+1 = K* (E on slide 6), the economy converges to a constant state of capital. > At point E, the economic growth rate will be zero. > However, r In reality, the economies of many countries keep growing over a run long > capital accumulation alone can not explain sustainable economic growth. > The question is: what are the other factors that can be decisive? } 8 lecture 6 Growth Model {2) First, let's take a look at the saving rate - Now we assume that the government is trying to increase the saving rate of the households. - When sT, the original 51'; curve will move to the blue one. Thus the new 16* will rise. - However, at point E', the growth rate will turn zero again. It shows only the change of the steady state. b 9 lecture 15 Growth Model {2) k* k** k Second, let's focus on the population growth b By far, we have assumed that population is constant. But what if we relax the assumption? > Now we assume that the population grows at an annual } l0 lecture 6 Growth Model (2) Active learning (1) r The original process of capital accumulation is : Kt+1 - Kt = 5Y1: th l kt+1(1 + n) kt = 3% dkt Question: how can you make the transformation above? (Hint: use the condition on the previous slide) } I | lecture 6 Growth Model {2) Capital accumulation with 11 kt+1(1 + n) kt = 3% dkt kt+1 kt = 53': _ dkt _ nkt+1 I .r l_l Change of k from I to t+f Positive power Negative power b nkt+1 can be explained as the necessary investment to meet the needs of population growth. > At the steady state, k will converge to k*that satises 0 = s(k)'(d + 10!: } l2 lecture 15 Growth Model {2) Capital accumulation with n (d + n)k s (k) a K* K 13 lecture 6 Growth Model (2)The relation between H and g (economic growth rate) - When population growths, investment is also increased to make ends meet>dk moves y upwards by n units. - As a result, the new unit product of labor will drop. (why?) - As a result, After reaching E', the economic growth rate will become zero again. k** k* k } I4 lecture 6 Growth Model (2) Third: how does technology progress matter? > If we take into account the level of technology (A) outside the production function, can it explain the long term economic growth? Y=A-F(K, L, H, N): A'(K\"L1'\") } I8 lecture 6 Growth Model (2) \fIf we draw a graph of Y = KLl-a > What can we say about the Y curve on the right? K *We assume that labor is constant. } I5 |ecture5 Groww Model Concerning the function K 0[Ll'3" > If we increase each input by UL times: =F(%1)= When goods market is balanced: I = S = 31' ' S : rate of saving, which measures the ratio of saving amount with respect to GDP. } 20 lecture5 Groww Model Using some algebra Kt+1 - Kt = It - dKt It = St = SYt Kt+1 - Kt = SYt - dkt And Y = F(K, L) = K L1-a 21 lecture 5 Growth ModelNext we try to simplify the model If we increase each input to 1/L times: L Z F (G . 1) - Assume that K y, = k , y = ka 4 lecture 6 Growth Model (2)The accumulation process of capital > Since capital is the main element of economic growth, we assume that: Kt'l'l Kt:It _ th= AK ;'_l -._|,_| |_'_4 capital change invest depreciation from t to Hi ment ' d : rate of depreciation } 5 lecture 6 Growth Model {2)