Worth: Mankiw Economics 5e 210 PART I11 Growth Theory: The Economy in the Very Long Run k, at which capital per effective worker and output per effective worker are constant. As before, this steady state represents the long-run equilibrium of th e econom The Effects of Technological Progress able 8-1 shows how four key variables behave in the steady state with technolog ical progress As we have just seen, capital per effective worker k is constant in the steady state. Because y=f(k), output per effective worker is also constant Remem- ber,though, that the efficiency of each actual worker is growing at rate g. Hence, output per worker(Y/L=yXE)also grows at rate g Total output Y=yX(EX LI With the addition of technological progress, our model can finally explain the sustained increases in standards of living that we observe. That is, we have shown that technological progress can lead to sustained growth in output per worker. B contrast, a high rate of saving leads to a high rate of growth only until the steady state is reached. Once the economy is in steady state, the rate of growth of output per worker depends only on the rate of technological progress. Acording to the Solow model, only technological progress can explain persistently rising living standards The introduction of technological progress also modifies the criterion for the Golden Rule. The Golden Rule level of capital is now defined as the steady state chat maximizes consumption per effective worker. Following the same argu ments that we have used before, we can show that steady-state consumption per effective worker is *=f(k*)-(6+n+g)k Steady-state consumption is maximized if MPk=δ+n+g, MPK-6=n+ That is, at the Golden Rule level of capital, the net marginal product of capital, MPK-6, equals the rate of growth of total output, n g. Because actual Steady-State Growth Rates in the Solow Model With Technological Progress Variable Symbol eady-State Growth Rate Output per effective worker y=Y/(EXL)=f(k) Output pe g g User JoENA: Job EFFo1424: 6264_ ch08: Pg 210: 27099#/eps at 100sl ed,Feb13,20029:584MUser JOEWA:Job EFF01424:6264_ch08:Pg 210:27099#/eps at 100% *27099* Wed, Feb 13, 2002 9:58 AM k*, at which capital per effective worker and output per effective worker are constant. As before, this steady state represents the long-run equilibrium of the economy. The Effects of Technological Progress Table 8-1 shows how four key variables behave in the steady state with technolog￾ical progress.As we have just seen, capital per effective worker k is constant in the steady state. Because y = f(k), output per effective worker is also constant. Remem￾ber, though, that the efficiency of each actual worker is growing at rate g. Hence, output per worker (Y/L = y × E) also grows at rate g.Total output [Y = y × (E × L)] grows at rate n + g. With the addition of technological progress, our model can finally explain the sustained increases in standards of living that we observe.That is, we have shown that technological progress can lead to sustained growth in output per worker. By contrast, a high rate of saving leads to a high rate of growth only until the steady state is reached. Once the economy is in steady state, the rate of growth of output per worker depends only on the rate of technological progress. According to the Solow model, only technological progress can explain persistently rising living standards. The introduction of technological progress also modifies the criterion for the Golden Rule.The Golden Rule level of capital is now defined as the steady state that maximizes consumption per effective worker. Following the same argu￾ments that we have used before, we can show that steady-state consumption per effective worker is c* = f(k*) − ( d + n + g)k*. Steady-state consumption is maximized if MPK = d + n + g, or MPK − d = n + g. That is, at the Golden Rule level of capital, the net marginal product of capital, MPK − d , equals the rate of growth of total output, n + g. Because actual 210 | PART III Growth Theory: The Economy in the Very Long Run Variable Symbol Steady-State Growth Rate Capital per effective worker k = K/(E × L) 0 Output per effective worker y = Y/(E × L) = f(k) 0 Output per worker Y/L = y × E g Total output Y = y × (E × L) n + g Steady-State Growth Rates in the Solow Model With Technological Progress table 8-1