Presentation on theme: "Economic Growth II: Technology, Empirics, and Policy"— Presentation transcript:
1Economic Growth II: Technology, Empirics, and Policy Chapter 9 of Macroeconomics, 8th edition, by N. Gregory MankiwECO62 Udayan Roy
2Recap: Solow-Swan, Ch. 7L and K are used to produce a final good Y = F(K, L)k = K/L and y = Y/L = f(k) are per worker capital and outputThe population is P, but a fraction u is not engaged in the production of the final good. Therefore, L = (1 – u)P.Both P and L grow at the rate n.A fraction s of Y is saved and added to capitalA fraction δ of K depreciates (wears out)
3Recap: Solow-Swan, Ch. 8In the long run, the economy reaches a steady state, with constant k and y
4Recap: Solow-Swan, Ch. 8In the long run, the economy reaches a steady state, with constant k and yLike the per-worker variables, k and y, per-capita capital and output are also constant in the long runTotal capital (K) and total output (Y) both increase at the rate n, which is the rate of growth of both the number of workers (L) and the population (P)
5Recap: Solow-Swan, Ch. 8 Variable Symbol Steady state behavior Capital per workerkConstantIncome per workery = f(k)Saving and investment per workersyConsumption per workerc = (1 – s)yLaborLGrows at rate nCapitalKIncomeY = F(K, L)Saving and investmentsYPopulationPCapital per capita(1 – u)kIncome per capita(1 – u)ySaving and investment per capita(1 – u)syConsumption per capita(1 – u)c
6The sad lesson of Solow-Swan It is an undeniable fact that our standards of living increase over timeYet, Solow-Swan cannot explain this! Why?Solow-Swan relies on capital accumulation as the only means of progressTherefore, the model’s failure to show economic progress indicates that we must introduce some means of progress other than capital accumulation
7Technological Progress Maybe Solow-Swan fails to show economic progress because there is no technological progress in itWe need to create a theory with technological progressBut how?
8Technological Progress A simple way to introduce technological progress into the Solow-Swan model is to think of technological progress as increases in our ability to multitask
9Technological Progress Imagine that both population and the number of workers are constant but that steady increases in the workers’ ability to multitask creates an economy that is equivalent to the Solow-Swan economy with steadily increasing population
10Technological Progress In such an economy, total output would be increasing—exactly as in the Solow-Swan economy with steady population growth—but without population growthThat is, under multitasking technological progress, per capita and per worker output would be steadily increasingIn this way, a simple re-interpretation of the Solow-Swan economy gives us what we were looking for—steadily increasing income per worker
11Efficiency of Labor Specifically, section 9−1 defines a new variable E is the efficiency of laborSpecify some date in the past, say 1984, and arbitrarily set E = 1 for 1984.Let’s say that technological progress has enabled each worker of 2011 to do the work of 10 workers of 1984.This implies that E = 10 in 2011.Therefore, E in any given year is the number of 1984 human workers that one human worker of the given year is equivalent too.
12Efficiency of LaborThe old production function F(K,L) no longer applies to both 1984 and 2011Suppose K = 4 in both 1984 and 2011Suppose L = 10 in 1984 and L = 1 in 2011The old production function F(K,L) will say that output is larger in 1984But we know that output is the same in both years because just one worker in 2011 can do the work of 10 workers of 1984We need a new production function: F(K, E ✕ L)
13Y = F(K, E ✕ L)In other words, although the number of human workers is 10 in 1984 and 1 in 2011, the effective number of workers is 10 in both years,and that’s what matters in determining the level of outputThe effective number of workers is E ✕ L
14Efficiency of LaborAssumption: the efficiency of labor grows at the constant and exogenous rate g
15ProductionAs the production of the final good no longer depends only on the number of workers, but instead depends on the effective number of workers, …… we replace the production function Y = F(K, L) by the new production function Y = F(K, E ✕ L)
16From “per worker” to “per effective worker” Similarly, we will now redefine k, which used to be capital per worker (K/L), as capital per effective worker: k = K/(E ✕ L)Likewise, we will now redefine y, which used to be output per worker (Y/L), as output per effective worker: y = Y/(E ✕ L)
17From “per worker” to “per effective worker” As a result of the redefinition of k and y, we still have y = f(k), except that the definitions of y and k are now in “per effective worker” formsy = sf(k), is now saving (and investment) per effective workerOnly the growth rate of effective labor is slightly different
18From “per worker” to “per effective worker” In Chapter 8, what mattered in production was L, the number of workers, and the growth rate of L was nNow, however, what matters in production is E ✕ L, the effective number of workers, and the growth rate of E ✕ L = growth rate of E + growth rate of L = g + n
19From “per worker” to “per effective worker” Recall from Chapter 8 that the break-even investment per worker was (δ + n)kThis will have to be replaced by the break-even investment per effective workerWe can do this by redefining k as capital per effective worker (which we have already done) and by replacing n by g + nTherefore, break-even investment per effective worker is now (δ + n + g)k
21Dynamics: graphAs in Ch. 8, in the long run, k and y reach a steady state at k = k* and y = y* = f(k*)
22Describing the Steady State We just saw that k is constant in the steady stateThat is, k = K/(E ✕ L) is constantTherefore, in terms of growth rates, kg = Kg – (Eg + Lg) = Kg – (g + n) = 0Therefore, the economy’s total stock of capital grows at the rate Kg = g + n
23Describing the Steady State Capital per worker (K/L) grows at the rate Kg –Lg = g + n – n = gTherefore, the per-worker capital stock, which was constant in Chapter 8, grows at the rate gAs each worker’s ability to multitask increases at the rate g, the capital used by a worker also increases at that rate
24Describing the Steady State y = f(k) is constant in the steady stateThat is, y = Y/(E ✕ L) is constantTherefore, in terms of growth rates, yg = Yg – (Eg + Lg) = Yg – (g + n) = 0Therefore, the economy’s total output grows at the rate Yg = g + nRecall that this is also the growth rate of the total stock of capital, K.
25Describing the Steady State Output per worker (Y/L) grows at the rate Yg – Lg = g + n – n = gTherefore, the per-worker output, which was constant in Chapter 8, grows at the rate gRecall that this is also the growth rate of per-worker capital, K/L.
26Progress, finally!We have just seen that if we introduce technological progress in the Solow-Swan theory of long-run growth, then in the economy’s steady statePer-worker output (Y/L) increases at the rate g, which is the rate of technological progressThis is a major triumph for the Solow-Swan theory
27Solow-Swan Steady State Table Steady-State Growth Rates in the Solow Model With Technological Progress
28Solow-Swan Steady State Remember from Chapter 8 that, when the production function follows the Cobb-Douglas form, the steady state value of k = k* was given by the formulaNow the formula changes to
29Technological Progress: where does it come from???? But a puzzle remains …So far, the rate of technological progress, g, has been exogenousWe need to ask, What does g depend on?We need to make g endogenous
30Endogenous Technological Progress Remember that in Chapter 8 we had distinguished between the population (P) and the number of workers (L)We had defined the exogenous variable u as the fraction of the population that does not produce the final goodTherefore, we had L = (1 – u)P or L/P = 1 – uIn Ch. 8 we had interpreted u as the long-run unemployment rateNow, we’ll reinterpret u as the fraction of the population that does scientific research
31Endogenous Technological Progress Once u is seen as the fraction of the population that is engaged in scientific research, it makes sense to assume that …Assumption: the rate of technological progress increases if and only if u increasesThis assumption is represented by the technology function g(u)Example: g(u) = g0 + guu
32Endogenous Technological Progress We now have a theory that gives an answer to the following question: Why is growth in living standards slow in some cases and fast in others?Growth in per-worker output is fast when u is high.That is, our standards of living grow rapidly when we invest more heavily in scientific research