Economic Growth II: Technology, Empirics, and Policy

1 / 35

# Economic Growth II: Technology, Empirics, and Policy - PowerPoint PPT Presentation

Economic Growth II: Technology, Empirics, and Policy. Chapter 9 of Macroeconomics , 8 th edition, by N. Gregory Mankiw ECO62 Udayan Roy. Recap: Solow-Swan, Ch. 7. L and K are used to produce a final good Y = F ( K , L )

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Economic Growth II: Technology, Empirics, and Policy' - makya

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Economic Growth II: Technology, Empirics, and Policy

Chapter 9 of Macroeconomics, 8thedition, by N. Gregory Mankiw

ECO62UdayanRoy

Recap: Solow-Swan, Ch. 7
• L 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 output
• The 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 capital
• A fraction δ of K depreciates (wears out)
Recap: Solow-Swan, Ch. 8
• In the long run, the economy reaches a steady state, with constant k and y
Recap: Solow-Swan, Ch. 8
• In the long run, the economy reaches a steady state, with constant k and y
• Like the per-workervariables, k and y, per-capita capital and output are also constant in the long run
• Total 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)
• It is an undeniable fact that our standards of living increase over time
• Yet, Solow-Swan cannot explain this! Why?
• Solow-Swan relies on capital accumulation as the only means of progress
• Therefore, the model’s failure to show economic progress indicates that we must introduce some means of progress other than capital accumulation
Technological Progress
• Maybe Solow-Swan fails to show economic progress because there is no technological progress in it
• We need to create a theory with technological progress
• But how?
Technological 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
Technological 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
Technological Progress
• In such an economy, total output would be increasing—exactly as in the Solow-Swan economy with steady population growth—but without population growth
• That is, under multitasking technological progress, per capita and per worker output would be steadily increasing
• In this way, a simple re-interpretation of the Solow-Swan economy gives us what we were looking for—steadily increasing income per worker
Efficiency of Labor
• Specifically, section 9−1 defines a new variable
• E is the efficiency of labor
• Specify 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.
Efficiency of Labor
• The old production function F(K,L) no longer applies to both 1984 and 2011
• Suppose K = 4 in both 1984 and 2011
• Suppose L = 10 in 1984 and L = 1 in 2011
• The old production function F(K,L) will say that output is larger in 1984
• But we know that output is the same in both years because just one worker in 2011 can do the work of 10 workers of 1984
• We need a new production function: F(K, E✕ L)
Y = 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 output
• The effective number of workers is E✕ L
Efficiency of Labor
• Assumption: the efficiency of labor grows at the constant and exogenous rate g
Production
• As 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)
From “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)
From “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” form
• sy = sf(k), is now saving (and investment) per effective worker
• Only the growth rate of effective labor is slightly different
From “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 n
• Now, 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
From “per worker” to “per effective worker”
• Recall from Chapter 8 that the break-even investment per worker was (δ + n)k
• This will have to be replaced by the break-even investment per effective worker
• We can do this by redefining k as capital per effective worker (which we have already done) and by replacing n by g + n
• Therefore, break-even investment per effective worker is now (δ + n + g)k
Dynamics: algebra

Ch. 8 No technological change

Ch. 9 Technological Progress

Dynamics: graph
• As in Ch. 8, in the long run, k and y reach a steady state at k = k* and y = y* = f(k*)
• We just saw that k is constant in the steady state
• That is, k = K/(E✕ L) is constant
• Therefore, in terms of growth rates, kg = Kg – (Eg + Lg) = Kg – (g + n) = 0
• Therefore, the economy’s total stock of capital grows at the rate Kg = g + n
• Capital per worker (K/L) grows at the rate Kg –Lg = g + n – n = g
• Therefore, the per-worker capital stock, which was constant in Chapter 8, grows at the rate g
• As each worker’s ability to multitask increases at the rate g, the capital used by a worker also increases at that rate
• y = f(k) is constant in the steady state
• That is, y = Y/(E✕ L) is constant
• Therefore, in terms of growth rates, yg = Yg – (Eg + Lg) = Yg – (g + n) = 0
• Therefore, the economy’s total output grows at the rate Yg = g + n
• Recall that this is also the growth rate of the total stock of capital, K.
• Output per worker (Y/L) grows at the rate Yg – Lg = g + n – n = g
• Therefore, the per-worker output, which was constant in Chapter 8, grows at the rate g
• Recall that this is also the growth rate of per-worker capital, K/L.
Progress, 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 state
• Per-worker output (Y/L) increases at the rate g, which is the rate of technological progress
• This is a major triumph for the Solow-Swan theory
• Table 9.1 Steady-State Growth Rates in the Solow Model With Technological Progress
• 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 formula
• Now the formula changes to
Technological Progress: where does it come from????
• But a puzzle remains …
• So far, the rate of technological progress, g, has been exogenous
• We need to ask, What does g depend on?
• We need to make g endogenous
Endogenous 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 good
• Therefore, we had L = (1 – u)P or L/P= 1 – u
• In Ch. 8 we had interpreted u as the long-run unemployment rate
• Now, we’ll reinterpret u as the fraction of the population that does scientific research
Endogenous 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 increases
• This assumption is represented by the technology function g(u)
• Example: g(u) = g0 + guu
Endogenous 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
Productivity Slowdown
• There was a worldwide slowdown in economic growth during 1972-1995. Why?
Growth Accounting
• Table 9.3 Accounting for Economic Growth in the United States