1Chapter Eight

CHAPTER 8

Economic Growth II: Technology,

Empirics and Policy

®

A PowerPointTutorial

To Accompany

MACROECONOMICS, 7th. Edition

N. Gregory MankiwTutorial written by:

Mannig J. SimidianB.A. in Economics with Distinction, Duke University

M.P.A., Harvard University Kennedy School of Government

M.B.A., Massachusetts Institute of Technology (MIT) Sloan School of Management

2Chapter Eight

The Solow model does not explain technological progress but,instead, takes it as given and shows how it interacts with othervariables in the process of economic growth.

The Solow model does not explain technological progress but,instead, takes it as given and shows how it interacts with othervariables in the process of economic growth.

3Chapter Eight

To examine how a nation’s public policies can influence the leveland growth of the citizens’ standard of living, we must ask fivequestions.

1) Should our society save more or less?2) How can policy influence the rate of saving?3) Are there some types of investment that policy should encourage?4) What institutions ensure that the economy’s resources are putto their best use?5) How can policy increase the rate of technological progress?

The Solow model provides the theoretical framework within whichwe consider these issues.

4Chapter Eight

To incorporate technological progress, the Production Function is now written as:

Y = F (K, L × E)

The term L × E measures the number of workers. This takes into account the number of workers L and the efficiency of each worker, E. It states that total output Ydepends on capital K and workers L × E. The essence of this model is that increases in E(efficiency) are analogous to increases in L (number of workers). In

other words, a single worker (if twice as productive)can be thought of as two workers. L × E doubles and the economy

benefits from the increased production of goods and services.

5Chapter Eight Capitalper worker, k

kkkk*

The Steady State

Investment, sf(kkkk)

((((δ + δ + δ + δ + n + g)kkkk

Technological progress causes E to grow at the rate g, and L grows at rate n so the number of workers L × E is growing at rate n + g.

Now, the change in the capital stock per worker is: ∆k = i –(δ+n +g)k,where i is equal to s f(k).

Technological progress causes E to grow at the rate g, and L grows at rate n so the number of workers L × E is growing at rate n + g.

Now, the change in the capital stock per worker is: ∆k = i –(δ+n +g)k,where i is equal to s f(k).

Note: k = K/LE and y=Y/(L × Ε).So, y = f(k) is now different.

Also, when the g term is added,gk is needed to provided capital

to new “effective workers”created by technological progress.

Note: k = K/LE and y=Y/(L × Ε).So, y = f(k) is now different.

Also, when the g term is added,gk is needed to provided capital

to new “effective workers”created by technological progress.

sf(kkkk)

6Chapter Eight

Labor-augmenting technological progress at rate g affects the Solowgrowth 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.

Important…Important…

7Chapter Eight

Capital per effective worker is constant in the steady state. Because 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.

Capital per effective worker is constant in the steady state. Because 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.

8Chapter Eight

Steady-state consumption is maximized if MPK = δ + n + g,

rearranging, MPK - δ = n + g.

That is, at the Golden Rulelevel of capital, the net marginal product of capital, MPK - δ, 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 they would at the Golden Rulesteady state.

The introduction of technological progress also modifies the criterion for the Golden Rule. The Golden Rulelevel 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*) - (δ + n + g) k*c*= f (k*) - (δ + n + g) k*

9Chapter Eight

Capital per effective worker k = K/(E × L) 0Output per effective worker y = Y/ (E × L) = f(k) 0Output per worker Y/L = y × Ε gTotal output Y = y × (Ε × L) n + g

10Chapter Eight

So far we have introduced technological progress into theSolow model to explain sustained growth in standards of living.Let’s now discuss what happens when theory meets facts.

11Chapter Eight

According to the Solow model, technological progress causesthe values of many variables to rise together in the steady stateThis property is called balanced growth.

In the steady state, output per worker, Y/L,and capital stock per worker, K/L, both grow at rate g, which is the rate of technologicalprogress. This is consistent with U.S. data in that g has been about 2 percent consistently over the past 50 years.

Technological progress also affects factor prices. The real wagegrows at the rate of technological progress, but the real rentalprice of capital remains constant over time. Again, over the last50 years, the real wage has increased by 2 percent and has increased byabout the same as real GDP. Yet, the real rental price of capital (realcapital income divided by the capital stock) has been about the same.

12Chapter Eight

The property of catch-up is called convergence. If thereis not convergence, countries that start off poor are

likely to remain poor.The Solow model makes predictions about when

convergence should occur. According to the model,whether two economies will converge depends on why

they differ in the first place (i.e., savings rates, population growth rates, and human capital accumulation).

13Chapter Eight

Differences in income are a result of either:

1) Factors of production such as the quantities of physical and humancapital2) Efficiency with which economies use their factors of production

Put simply, workers in a poor country either don’t have the tools and skills, or they are not putting their tools and skills to the best use.

14Chapter Eight

In terms of the Solow model, the central question is whetherthe large gap between the rich and poor is explained bydifferences in capital accumulation, or differences in theproduction function.

15Chapter Eight

The savings rate determines the steady-state levels of capital andoutput. One particular saving rate produces the Golden Rule steadystate, which maximizes consumption per worker. Let’s use theGolden Rule to analyze the U.S. saving rate.

Marginal product of capital net of depreciation

(MPK –δ)

Growth rate of total output(n + g)

Recall that at the Golden Rule steady state, (MPK –δ) = (n + g)

16Chapter Eight

Amount of capital in the Golden Rule steady state

If the economy is operating with less capital than in the Golden Rule steady state, then (MPK –δ > n + g)

If the economy is operating with more capital than in the

Golden Rule steady state, then (MPK –δ < n + g)

17Chapter Eight

Marginal product of capital net of depreciation

(MPK –δ)

Marginal product of capital net of depreciation

(MPK –δ)

Growth rate of total output(n + g)

Growth rate of total output(n + g)

To make this comparison for the U.S. economy, we need to estimatethe growth rate of output (n + g) and an estimate of the net marginalproduct of capital (MPK –δ). U.S. GDP grows at about 3 percent per year, so, n + g = 0.03. We can estimate the net marginal product of capital from the following facts:

18Chapter Eight

We solve for the rate of depreciation δ by dividing equation 2 by equation 1:

δk/k= (0.1y)/(2.5y)δ = 0.04

And we solve for the marginal product of capital (MPK)by dividing equation 3 by equation 1:

(MPK × k)/k= (0.3y)/(2.5y)MPK = 0.12

1) The capital stock is about 2.5 times one year’s GDP, or k = 2.5y2) Depreciation of capital is about 10 percent of GDP, or dk= 0.1y3) Capital income is about 30 percent of GDP, or MPK × k = 0.3y

Thus, about 4 percent of the capital stock depreciates each year, and the marginal product of capital is about 12 percent per year. The netmarginal product of capital, MPK – d,is about 8 percent per year.

19Chapter Eight

We can now see that the returns to capital (MPK – δ = 8 percent per year) is well in excess of the economy’s growth rate (n + g = 3 percent per year).

This indicates that the capital stock in the U.S. economy is wellbelow the Golden Rule-level. In other words, if the United States saved and invested a higher fraction of its income, it would grow faster andeventually reach a steady state with higher consumption.

20Chapter Eight

Public saving is the difference between what the government receives in tax revenue minus what it spends.

When spending > revenue, it is a budget deficit �

When spending < revenue, it is a budget surplus ☺

Private saving is the saving done by households and firms.

21Chapter Eight

• In 2009, one of President Barack Obama’s first economic proposals was to increase spending on public infrastructure such as new roads, bridges, and transit systems.

• This policy was partly motivated by a desire to increase short-run aggregate demand and partly to provide public capital and enhance long-run economic growth.

22Chapter Eight

Nations may have different levels of productivity in part becausethey have different institutions that govern the allocation of theirscarce resources.

For example, a nation’s legal tradition is an institution. Otherexamples are the quality of the government itself and the level ofcorruption that exists within the political infrastructure.

23Chapter Eight

The Solow model shows that sustained growth in income per workermust come from technological progress. The Solow model, however,takes technological progress as exogenous, and therefore does notexplain it.

24Chapter Eight

??

The Endogenous Growth Theory rejects Solow’s basic assumption of exogenous technological change.

25Chapter Eight

Start 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 is the key difference between this endogenous growth model and theSolow model.

Let’s describe capital accumulation with an equation similar to thosewe’ve been using: ∆K = sY - δK. This equation states that the changein the capital stock (∆K) equals investment (sY)minus depreciation(δK). We combine this equation with the production function, dosome rearranging, and we get: ∆Y/Y = ∆K/K = sA – δ.

26Chapter Eight

∆Y/Y = ∆K/K = sA - δ

This equation shows what determines the growth rate of output ∆Y/Y.Notice that as long as sA > δ, 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.

27Chapter Eight

Creative Destruction

Schumpeter suggested that the economy’s progress come througha process a creative destruction. According to Schumpeter, thedriving force behind progress is the entrepreneur with an ideafor a new product, a new way to produce an old product, orsome other innovation.

28Chapter Eight

Efficiency of laborLabor-augmenting technological progressEndogenous growth theory

Efficiency of laborLabor-augmenting technological progressEndogenous growth theory