3Adding the Efficiency of Labor "E" The Production Function is now written as:Y = F (K, L E)The term L E measures the number of effective workers.This takes into account the number of workers L and the efficiency of each worker E. Increases in E are like increases in L.
4Labor-Augmenting Technological Progress Technological progress causes E to grow at the rate g, and L grows at rate n so the number of effective workers L E is growing at rate n + g.Now, the change in the capital stock per worker is:Dk = i –(d+n +g)k, where i is equal to s f(k)sf(k)(d + n + g)kThe Steady StateNote: k = K/LE and y=Y/(L E).So, y=f(k) is now different.Also, when the g term is added,gk is needed to provided capitalto new “effective workers”created by technological progress.Investment,sf(k)k*Capitalper worker, k
5Labor-augmenting technological progress at rate g affects the Solow growth model in much the same way as did population growth at raten. Now that k is defined as the amount of capital per effective worker,increases in the number of effective workers because of technologicalprogress tend to decrease k. In the steady state, investment sf(k)exactly offsets the reductions in k because of depreciation, populationgrowth, and technological progress.
6The Effects of Technological Progress Capital per effective worker is constant in the steady state. y = f(k) output per effective worker is also constant. But the efficiency of each actual worker is growing at rate g. So, output per worker, (Y/L = y E) also grows at rate g. Total output Y = y (E L) grows at rate n + g.Only technological progress canexplain long run increases in living standards.
7The 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. So, 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,rearranging, 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 economies experience both population growth and technological progress, we must use this criterion to evaluate whether they have more or less capital than at the Golden Rule steady state.
9poor countries should grow faster on average than rich countries. Convergence HypothesisAn important prediction of the neoclassical model is this:Among countries that have the same steady state,the convergence hypothesis should hold:poor countries should grow faster onaverage than rich countries.
10Beyond the Solow Model: Endogenous Growth Theory The Endogenous Growth Theory rejectsSolow’s basic assumption of exogenous technological change.
11The Basic ModelStart with a simple production function: Y = AK, where Y is output,K is the capital stock, and A is a constant measuring the amount ofoutput produced for each unit of capital (noticing this productionfunction does not have diminishing returns to capital). One extra unitof capital produces A extra units of output regardless of how muchcapital there is. This absence of diminishing returns to capital isthe key difference between this endogenous growth model and theSolow model.Let’s describe capital accumulation with an equation similar to thosewe’ve been using: DK = sY - dK. This equation states that the changein the capital stock (DK) equals investment (sY) minus depreciation(dK). We combine this equation with the production function, dosome rearranging, and we get: DY/Y = DK/K = sA - d
12DY/Y = DK/K = sA - dThis equation shows what determines the growth rate of output DY/Y.Notice that as long as sA > d, the economy’s income grows forever,even without the assumption of exogenous technological progress.In the Solow model, saving leads to growth temporarily, but diminishingreturns to capital eventually force the economy to approach a steadystate in which growth depends only on exogenous technological progress.By contrast, in this endogenous growth model, saving and investment canlead to persistent growth.
13Key Concepts of Ch. 8 Efficiency of labor Labor-augmenting technological progressEndogenous growth theory