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8.3. Population Growth

Population growth has a negative effect on the level of capital per worker in the
steady-state.

The basic Solow model predicts that capital accumulation by itself is not able to
explain sustained long term economic growth. By itself, it can only explain growth
towards the steady-state in cases of low levels of capital, such as the examples of
Japan and Germany show after WWII. There are at least two other elements that
produce growth that must be added to the model. The first is population growth,
which is added here, and the second is technological progress, added in chapter 9.
We introduce the labour force growth rate n. if n = 0.01, this means that the labour
force grows by 1 percent every year.

The Steady State with Population Growth
To reiterate, k is the level of capital per labour. If the labour force grows, then this will
slow down the growth of capital per labour, so that the function of capital
accumulation must be adjusted:

Δk = i – (δ + n)k

We see that the rate of population growth effectively functions the same as the rate
of depreciation in its effect on capital accumulation per labour. The study state
consumption now becomes:

c* = f(k*) – (δ+n)k*

And the k*gold is now the k* at which MPK = δ + n

The effect of an increase in the rate of population growth can be seen here:

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This is an important effect for policymakers, because it means that in order to
increase the steady state level of income per labour in poor countries, population
growth must be decreased.

Alternative Perspectives on Population Growth
The Solow growth model does not capture all the effects of population growth. Two
of those effects are captured by the Malthusian model and the Kremerian model
respectively.

 The Malthusian model. According to Malthus, population growth would increase
until the income per worker equals that, just enough to keep him alive. So he
predicted that no real economic growth per worker could be maintained in the
long run, because population growth would always compensate it. This has
turned out not to be realistic, because population growth has been broken by
modern birth control, and because Malthus underestimated the possibilities of
technological advances on food production.

 The Kremerian model. According to this model, a large population means more
people who can become scientists, inventors and engineers to contribute to
technological progress, so that high population growth coincides with high
levels of economic growth.

8.4. Conclusion

The currently developed model can explain some aspects of growth, such as why
countries with high saving rates tend to have higher levels of income, and the fast
growth of Japan and Germany after the war, but it does not explain sustained long
term economic growth. To this we must include technological progress, which is
done in the next chapter.

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9. Economic Growth II: Technology,
Empirics, and Policy

In this chapter we introduce technological progress in the model, and we apply the
model to empirical problems.

9.1. Technological Progress in the Solow Model

Here we introduce technological progress in the Solow model.

The Efficiency of Labour
Technological progress is included in the model by the new variable E, efficiency of
labour. It reflects the knowledge and capabilities of production methods. New
available technologies and methods of production increase the efficiency of labour.
The new production function becomes:

Y = F(K,EL)

In this model, E increases at a constant rate g. This way of incorporating technology in
the model is called labour-augmenting technological progress, because it changes the
effect of labour in production. It could also have been capital augmenting, or both
capital and labour augmenting, but this is not done in this book.

The Steady State With Technological Progress.
In the previous chapter, we measured variables as “per worker”. We now redefine
these variables as “per effective worker”. This means that k=K/EL now and is called
capital per effective worker. Similarly, y= Y/EL, output per effective worker. This
means that the capital accumulation equation now becomes:

Δk = sf(k) – (δ + n+ g)k

So (δ + n+ g)k becomes the new break-even level of investment.

In a similar way as in the previous chapter when introducing population growth,
technological progress alters the steady state level of consumption per effective
worker, and the level of capital at which the steady state level of consumption is
maximized (golden rule level of capital k*gold)

c* = f(k*) – (δ+n+g)k*
MPK = δ + n

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According to the Solow growth model, only technological progress can consistently
increase the standard of living over time. That is the level of consumption per worker.

9.2. From Growth Theory to Growth Empirics

The Solow model is applied to make empirical predictions and comparisons with
evidence.

Balanced Growth
Growth of output per worker and capital stock per worker in the steady state is
caused by technological progress and is called balanced growth. IT predicts that there
is sustained economic growth at the rate of technological progress, and we
approximately see this in the real world.

Convergence
The Solow model predicts that convergence should occur if two economies have a
different capital stock but the same level of technological progress. We also see this
in the examples of Germany and Japan, which had about the same technological
progress as the rest of the western world, but destroyed capital stocks. They quickly
converged to the rest of the western world. However it predicts that convergence
should not occur with countries with different technological progress, and this is
indeed the case, as Africa and the West for example, have not converged yet. In this
case we speak of conditional convergence: countries converge to their own steady-
state, but countries do not have the same steady-state level of output.

Factor Accumulation versus Production Efficiency
An important question is the source of differences in income. It can come from either
1) differences in the factors of production such as physical or human capital, or 2)
differences in the efficiency with which the economies use their factors of
production, that is differences in the production function. On empirical inspection, it
turns out that high levels of the factors of production are correlated with high
efficiency of the use of those factors.

9.3. Policies to Promote Growth

We can now use the Solow model and its empirical application to make some
analyses of the policy decisions that governments face.

Evaluating the Rate of Saving
We take the example of the U.S. and ask the question: is the U.S. above, below, or
approximately at the golden rule level of capital? We obtained three facts about the
U.S. economy:

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1. k is about 250% of GDP: k = 2.5y
2. Capital depreciation is about 10% of GDP: δk = 0.1y
3. Capital income is about 30% of GDP: MPK * k = 0.3y (we make this conclusion

from the classical theoretical prediction that the factors earn the share of
income equal to their marginal product derived in chapter 3)

Using these facts we derive that δ = 0.4, and MPK = 0.12, this means that net
marginal product of capital (MPK –δ) is 8%. This is much bigger than the U.S.
economy’s average growth rate (n+g = 3%). This indicates that the U.S. is well below
its golden rule level of capital. In fact all countries in practice are below their golden
rule level of capital, which indicates that in practice, increasing the savings rate is a
good thing.

Changing the Rate of saving
The government can increase the rate of saving directly by increasing public saving,
by either decreasing G or increasing T. The government can also affect saving by
affecting the level of private saving through tax incentives. One possibility is to shift
from income taxes to consumption taxes, but there are disagreements over how
effective this would be

Allocating the Economy’s Investment
In the Solow model, capital is simplified as being only of one type but in reality there
are many types of capital. This means that capital must be allocated. Some economists
say that the capital allocation process should be left to financial markets. Others say
that the government should invest in infrastructure, a form of public capital, and in
education, a form of human capital. It is also suggested by some economists that
governments should actively encourage particular forms of capital if there are
externalities associated with certain types of investments (for a theory of externalities
look for a microeconomics textbook).

Establishing the Right Institutions
Not all countries have the same institutions guiding the allocation of scarce resources.
Different institutions might have very different effects on production efficiency. An
example of an institution is a legal tradition. Different countries often have very
different levels of development of legal institutions. The development of government
is also an important difference in institution. Some governments do not work
effectively for the development of the domestic economy, or are corrupt. The
development of these institutions is an important necessary element of economic
growth.

Encouraging Technological Progress
The Solow model takes technological progress as exogenous, so does not explain it.

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The drivers of technological progress are not fully understood, but one important
aspect of it is intellectual property rights. If a company can obtain a patent on a piece
of technology, so that other companies are not allowed to use that technology
without permission, this gives a incentive for firms to invest in research and
development.

9.4. Beyond the Solow Model: Endogenous Growth Theory

Endogenous growth theories try to explain technological progress.

The Solow model developed in the previous sub-chapters and chapter 8 does not
explain technological progress, but instead takes it as given (an exogenous variable.
This subchapter introduces four examples of an endogenous growth theory, a theory
where technological progress is explained (i.e. where technology is an endogenous
variable).

The Basic Model
This basic model makes one key assumption different from the Solow model, namely
that there are constant rather than diminishing returns to capital, using the following
production function:

Y = AK

Where A is a constant measuring the output produced per unit of capital. In this
model, unlike in the Solow model, K does not just include physical capital, but also
knowledge. Using a similar capital accumulation equation as in the Solow model:

ΔK = sY – δK

We can calculate the growth rate of output

ΔY/Y = sA – δ

This shows that as long as the saving rate is high enough, there will be constant
economic growth. Because K also includes knowledge, it models technological
progress as part of investment.

A Two-Sector Model
This more expanded model is a kind of combination between the Solow model and
the Basic model. It consists of two sectors: Universities that invest in technological
progress, and manufacturing firms, firms that produce output. The addition of
universities is what distinguishes it from the Solow model. The model consists of the
following three equations:

 Y = F(K, 1-u)EL) (Production in manufacturing firms
 ΔE = g(u)E (University investment in technology)

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 ΔK = sY – δK (Capital accumulation)

Where u is the percentage of workers employed in universities. Just like in the Solow
model, the production function has constant returns to scale. If we include knowledge
E to be a part of capital, then it also has constant returns to capital. For any given
value of u, this model works just like the Solow growth model. As a result, there are
two decision variables in the model, the saving rate, and the percentage of workers
employed in research.

The Microeconomics of Research and Development
These two models do not go into the microeconomic foundations of decision makings
with respect to research. Three key facts show the relevance of this:

1. Much research is done by firms and is driven by profit motive.
2. Research is profitable because it gives rise to temporary monopolies, due to

intellectual property rights and first mover advantages.
3. When one firm innovates, this opens the door to new innovation

The study of the microeconomics of R&D is focused on the positive and negative
externalities generated by private research. In practice, positive externalities
dominate, which is an argument for research subsidies.

The Process of Creative Destruction
The economist Schumpeter came up with the theory of creative destruction, the
process by which entrepreneurs innovate and create new products or new ways of
developing an old product, thereby destroying the markets for old products or
production methods. The theory says that economic progress is always associated
with the destruction of old industries. I.e. there are always losers to economic
progress.

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10. Introduction to Economic Fluctuations

In the short run, the economy fluctuates instead of staying fixed at its natural level.
These fluctuations can be understood within the model of aggregate supply and
demand.

Part IV: Business cycle theory: The economy in the short run contains chapter 10 to
14. The classical theory introduced in part II chapters 3 to 7, addresses the long run of
an economy. However, in the short run many of the relations of the classical theory
break down. Monetary neutrality does not hold and production is not fixed, but
affected by short run fluctuations such as of the money supply and demand for goods
and services. Also, the unemployment rate is not equal to the natural rate of
unemployment but fluctuates in the short run. Part IV introduces the basic Keynesian
theory, an adaptation of the classical theory that is developed to describe short run
fluctuations, or alternatively, the Business Cycle.

10.1. The Facts about the Business Cycle

We start with the basic facts about the business cycle.

GDP and its Components
Taking the U.S. as an example, we can see that GDP growth is not at all steady. A
period in which there is negative real GDP growth is called a recession, and if this is
severe, it is called a depression. The exact line between a recession and a depression
is vague. Moreover, if we look at the components of GDP, we see that investment is
much more volatile than consumption. This is an important fact that needs to be taken
into account in theories of the business cycle.

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Unemployment and Okun’s law.
Okun’s Law states that there is a negative relationship between unemployment and

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GDP. This means that if there is a recession, unemployment rises. This can be
understood theoretically by the idea that workers produce goods and services and
therefore if they become unemployed economic output should also decline. There is
very strong statistical evidence (A correlation of -0.89) that Okun’s law is the case, as
seen in the following graph:

The approximate numerical relation that is taken from empirical research is that the
there is a linear relation between the unemployment rate and GDP with a factor of 2:
Percent change in real GDP = 3% - 2 * Change in unemployment rate

Leading Economic Indicators
Many economists are busy trying to predict short run fluctuations. There are two
reasons why government economists need to do this:

1. The economic environment affects the government e.g. through tax revenue
2. The government wants to stabilize the economy through fiscal and monetary

policy.

To predict short run fluctuations, economists use leading indicators, variables that
tend to fluctuate in advance of the whole economy. A list of ten leading indicators is
used by the Conference Board, a private research group:

 Average workweek of production workers in manufacturing
 Average initial weekly claims for unemployment insurance
 New orders for consumer goods and materials, adjusted for inflation
 New orders for nondefense capital goods
 Index of supplier deliveries
 New building permits issued
 Index of stock prices
 Money supply (M2) adjusted for inflation
 Interest rate spread: the yield spread between 10-year Treasury notes and 3-

month Treasury bills
 Index of consumer expectations

This list is far from complete, but contains some of the important leading indicators
10.2. Time Horizons in Macroeconomics

The short and long run is an often used distinction with a specific meaning.

The previous chapters have explained to some extent the difference between short
run, long run, and very long run, but it has not been addressed rigorously, which is

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done in this subchapter.

How the Short Run and Long Run Differ
The predominant view among economists is that there is one main difference
between the short run and the long run, and that is that monetary neutrality works in
the long run, but breaks down in the short run (meaning that money is not neutral in
the short run). The fundamental reason why this is the case, according to this
predominant view, is that prices are flexible in the long run, but sticky in the short run.
This means that it takes time for prices to adjust to equilibrate supply and demand.
For example, in the long run, according to the quantity theory of money, increasing
the money supply will cause an equal increase in the price level. But in the short run,
the price level is not immediately affected. The result is that in the short run, real
variables, such as real GDP, the real interest rate, and unemployment, are affected,
until the price level catches up.

The Model of Aggregate Supply and Aggregate Demand
In the classical model, output is determined by the supply of goods and services,
which is determined by the production function. However, due to short run price
stickiness, in the short run model, aggregate demand also influences output. The next
subchapters develop the basis of this model, which is then fully developed in detail
throughout the next three chapters.

10.3. Aggregate Demand

Aggregate Demand (AD) is the relationship between the aggregate price level, and
the quantity of goods and services demanded.

The Quantity Equation as Aggregate Demand.
We build here a simple theory of Aggregate demand based on the Quantity theory of
Money. This is a simplified version and it will be refined in the subsequent chapters.
The quantity equation is:

MV = PY

This can be rewritten to:

Y = (M/P)*V

Where M/P is real money balances. According to the quantity theory of money,
money velocity stays constant, so that this equation denotes the relationship between
Y and P. If P rises, demand for Y must decline. This gives the following graph for the
AD curve:

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The reason that this curve slopes downward is fully explained in chapter 11, but for
now, a simplified explanation is that it slows downward because if the price level is
high, there is higher demand for real money balances, but since M stays the same and
V stay the same, less of that real money balances are spent, so that expenditures is
lower. This is a highly simplified and not very complete explanation, so if you do not
follow it, don’t worry and wait until chapter 11.
We can clearly see from this equation that a reduction in the money supply shifts the
AD curve to the left, and that an increase in the money supply shifts it to the right.

10.4. Aggregate Supply

Aggregate supply (AS) is the relation between the aggregate price level and the
quantity of goods and services supplied.

In the long run, the LRAS (Long run AS) curve is determined by the production
function, and independent of the price level. This means that a decrease in AD
decreases the price level, but leaves output unchanged:

In the short run, the SRAS (Short run AS) curve is horizontal at the price level, because

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prices do not change. This means that a decrease in AD leaves prices unchanged, but
decreases output.

We see here that in the long run, output is determined by AS, and the price level by
AD, but in the short run output is determined by AD and the price level by AS. In
Chapter 14, this statement will be nuanced to an extent.

From the Short Run to the Long Run.
We now have two models, one for the short run, and one for the long run. We can
combine the two to see the transition between the short run and the long run. See the
next figure for this explanation. For example, if an economy is in long run equilibrium
(Point A), and the money supply is decreased, then in the short run this will leave
prices unchanged (point B) and output decreases, but as prices start to adjust over
time, output starts to increase again, and prices start do decrease, so that in the long
run, we are back to the original level of output.

10.5. Stabilization Policy

Stabilization policy are policies enacted by the government with the intent of
stabilizing the economy at its natural rate.

We now turn to the role of the government in stabilizing short run fluctuations. A
short run fluctuation can be caused by a shock, a change in an exogenous variable
caused by some exogenous event. A demand shock is a shock that shifts the demand
curve, and a supply shock is a shock that shifts the supply curve. Policy actions aimed
at reducing the severity of short run fluctuations are called stabilization policy.

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Demand Shock
Suppose that the velocity of money suddenly increases. This shifts the aggregate
demand curve to the right. The central bank could stabilize this by decreasing the
money supply, thereby shifting the AD curve partially back.

Aggregate Supply Shocks
Say that some exogenous event has a short run adverse effect on supply, such as a
drought that destroys the crops in an agricultural economy. This will cause the
Aggregate supply curve to shift upward, threatening a short run decrease in GDP. The
central bank could compensate this by increasing the money supply, shifting the AD
curve to the right:

10.6. Conclusion

This chapter introduced the concepts of Aggregate Demand and Aggregate Supply,
and their role in short run fluctuations.

Chapters 11 and 12 will develop the fundamentals of the Aggregate Demand curve in
far more detail from Keynesian theory. Chapter 13 will develop the small open
economy version of Keynes’ theory, and chapter 14 develops the Aggregate Supply
curve in more detail.

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11. Aggregate Demand I: Building the IS–
LM Model

The IS-LM model is the most widely accepted interpretation of Keynes' theory.

The economist Keynes formulated a theory in which he outlined that it is aggregate
demand that determines output in the short run, not aggregate supply as in the
classical theory. These two opposing views have later been combines into
the neoclassical synthesis. The predominant model that is currently accepted that
captures Keynes’ theory is called the IS-LM model. It is a model that shows the
determinants of aggregate demand, and therefore replaces the oversimplified AD
curve based on the quantity equation in chapter 10. The IS-LM model consists of
the IS-curve, and the LM-curve. The IS curve is the curve that captures the equilibria
in the goods market, and the LM curve shows the equilibria in the money market. This
will be explained in the following subchapters.

11.1. The Goods Market and the IS Curve

IS-curve stands for Investment-Saving curve. It plots the relation between the
interest rate and the level of income for which the goods market is in equilibrium.

The IS curve is derived from multiple steps which will be explained here.

The Keynesian Cross.
The Keynesian Cross is the first step of deriving the IS-curve. It captures Keynes’
basic idea that it is inadequate spending that is the cause of lower output during
recessions. It is based on the distinction between actual expenditure and planned
expenditure. Actual expenditure is what people actually spend on goods and services,
and it is equal to GDP as explained in chapter 3. Planned expenditure is what people
would like to spend on goods and services, given their income. So actual expenditure
is simply

Y

And planned expenditure is the demand for expenditure given the level of income:
PE = C(Y-T) + I + G

The assumption of the Keynesian cross is that the goods market is in equilibrium
when planned expenditure equals actual expenditure:

Y = PE = C(Y-T) + I + G
Note that in the classical theory, this was always the case, because in the classical
theory, the goods market is assumed to always be in equilibrium. The argument why

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the goods market should move to equilibrium, is that if there is too little expenditure,
the inventories of firms will increase (they sell less than they produce), and they will
try to adapt to this. The Keynesian cross is summarized in this graph:

The multiplier effect
We now consider the effect of an increase in government expenditures. We will see
that according to the Keynesian cross, income will rise with more than the increase in
expenditures. That is, ΔY is bigger than ΔG, and ΔY/ΔG is the government-purchases
multiplier. If the government expenditures are increased by 1$, then income will rise
by ΔY/ΔG dollars. This is because due to the increase in income due to extra
government expenditures, there is also more disposable income, so an increase in
consumption as well. Setting the goods market equation given above to equilibrium,
and deriving the effect of an increase in government expenditures on income gives:
ΔY/ΔG = 1/(1-MPC)
Where MPC is the marginal propensity to consume. Equivalently, the tax multiplier is:

ΔY/ΔT = -MPC/(1-MPC)

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From these multipliers we see that the short run effect of increasing government
expenditures (or decreasing taxes) is to increase income by a larger amount than the
increase. This is consistent with Keynes’ proposal that in times of recessions, the
government should stimulate demand. There are many examples in history after
WWII where governments have done precisely that. For example the Obama
spending package tried to stimulate the economy in 2009.

The Interest Rate, Investment, and the IS Curve.
The second element of deriving the IS curve is investment. Investment is negatively
related to the interest rate and also part of planned expenditures, so this means that
an increase in the interest rate will shift the planned expenditures function downward,
thereby decreasing income. The IS-curve is the curve that summarizes this
relationship between the interest rate and income, through the effect of an
increase/decrease in investment through the multiplier effect on income. This
derivation is summarized here:

How Fiscal policy shifts the IS curve
Fiscal policy shifts the planned expenditure function upwards or downwards, and
therefore it also shifts the IS curve (as does any other external planned expenditure
shock that is not the interest rate itself):

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11.2. The Money Market and the LM Curve

The LM-curve stands for Liquidity money curve. It plots the relation between the
interest rate and the level of income for which the money market is in equilibrium.

The LM curve is based on Keynes’ Theory of Liquidity Preference, which is the first
step of its derivation. This theory states that people prefer to hold money because it
is liquid, that the demand for holding money is based on liquidity preference and that
the interest rate adjusts to equilibrate the demand and supply of real money balances
(explained in chapter 5). The supply of real money balances is determined simply by
the money supply and the price level:

(M/P)s = M/P
Money demand is given by the function of Liquidity preference, which decreases in
the interest rate, because the higher the interest rate, the higher the opportunity cost
of holding money (versus investing in bonds):

(M/P)d = L(r, Y)
We can plot this relation, and see the effect of a decrease in the money supply (which
would be equivalent to an increase in prices):

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Income, Money Demand, and the LM Curve
The second step of its derivation is the relationship between income and liquidity
preference. Liquidity preference is a function of r and of Y. its relation to Y is that if Y
becomes higher, people will need more money in order to cover the larger amount of
transactions they are doing. This means that an increase in income shifts the money
demand function to the right, and this relation is summarized in the LM curve, the
relation between r and Y for which the money market is in equilibrium:

The effect of for example an decrease in the money supply is as follows: it decreases
the supply of real money balances, and therefor increases the interest rate for which
the money market is in equilibrium. Therefore, for the same level of income, a higher
interest rate is needed for money market equilibrium. Therefore the LM curve shifts
upward:

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11.3. Conclusion: The Short-Run Equilibrium

The IS-LM model is the basic model of aggregate demand.

We can now combine the LM curve and the IS curve to find the short run equilibrium
interest rate and level of income. To summarize, the IS-LM model consists of two
equilibrium equations:

 IS: Y = C(Y-T) + I(r) + G (Goods market equilibrium)
 LM: M/P = L(r,Y) (Money market equilibrium)

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12. Aggregate Demand II: Applying the
IS–LM Model

Chapter 11 developed the IS-LM model. In this chapter we first use the IS-LM model
to explain economic fluctuations, then we derived the Aggregate demand function
from the IS-LM model, and finally we use it to study the great depression of the
1930’s.

12.1. Explaining Fluctuations With the IS–LM Model

Fluctuations in the economy can be explained by shocks in the IS-LM model.

According to the IS-LM model, the equilibrium level of income and the interest rate is
determined by the intersection of the IS and LM curves.

The Effects of Fiscal Policy
As explained using the Keynesian cross in chapter 11, fiscal policy has a multiplier
effect, as an increase in government purchases increases planned expenditure by
more than that increase, because it also increases consumption. This means that an
increase in G shifts the IS curve to the right by G multiplied by the multiplier.
However, this analysis was incomplete, because it neglected the effect of this
expansion on the money market. The expansion increases the demand for money,
thereby increasing the interest rate. This interest rate in turn decreases investment, so
that the extent to which output is increased due to a government stimulus is
somewhat diminished due to its crowding out effect on investment. A similar argument
can be made for a tax cut (however the effect of the tax cut is smaller, because it only
indirectly increases planned expenditure through consumption, contrary to
government purchases which also has the direct effect). This is summarized here:

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The Effects of Monetary Policy
The effect of monetary policy on the level of income happens through the so
called monetary transmission mechanism: An increase in the money supply lowers
the interest rate through the money market. This lower interest rate increases
investment. In the ISLM model, this is summarized by a downward shift of the LM
curve.

The Interaction between Monetary and Fiscal Policy
Monetary and fiscal policy both have effects on the interest rate and income. If the
government or the central bank want to alter course, then it is sometimes desirable
for the other party to coordinate so that income is stabilized.

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Shocks in the IS-LM model
The LM curve and IS curve can also shift due to exogenous shocks, and this is what is
often used to explain recessions. For example, if investors suddenly lose confidence in
the economy, the investment function shifts to the left, and the IS curve shifts to the
left, causing a recession (their prophecy was self-fulfilling). In this case, the
government or central bank can try to compensate this.

12.2. IS–LM as a Theory of Aggregate Demand

The IS-LM model is the most widely accepted interpretation of Keynes' theory of
aggregate demand.

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Recall that the AD curve is the relationship between income and the price level. The
price level has a direct effect on the money market, because a higher price level
means a lower supply of real money balances. So inflation is equivalent to decreasing
the supply of real money balances (in the short run). A lower supply of real money
balances shifts the LM curve upward. In other words, increasing the price level shifts
the LM curve upward, increases the interest rate and thereby (through investment)
decreases income. This mechanism is summarized in the AD curve, and it is the reason
that the aggregate demand curve is downward sloping (this is a more complete
explanation than the one given in chapter 10 using the quantity equation). From this
mechanism, we know that any fiscal policy that shifts the IS curve to the right, and
any monetary policy that shifts the LM curve to the right, also shifts the AD curve to
the right. The derivation of the AD curve is summarized here:

The IS-LM model in the Short Run and Long Run
We can now formally explain the difference between the assumptions of the classical
theory and the short run theory within the framework of the IS-LM model. Basically,
both the long run and short run can be captured within the IS-LM model, and they
both have the basic equations:

 IS: Y = C(Y-T) + I(r) + G (Goods market equilibrium)
 LM: M/P = L(r,Y) (Money market equilibrium)

However the difference between the long and short run is in the final equation
necessary to complete the model. In the Keynesian (short run) model, the third
equation is

P =P
Because prices are fixed in the short run. In the classical theory, the level of income is

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fixed at the production function, and prices are flexible:
Y=Y

12.3. The Great Depression

We can now empirically apply the IS-LM model to the Great Depression to see how
it might explain this downward point on the business cycle.

There are two main hypotheses on what the causes of the great depression were.

The Spending Hypothesis: Shocks to the IS Curve
According to this hypothesis, shocks to demand for goods and services were
responsible. Allegedly, the stock market crash of 1929 caused a large downward shift
in consumer spending (because people suddenly became less wealthy), and that the
residential investment boom of the 1920’s suddenly stopped, both causing the IS
curve to shift to the left. Because policymakers at the time were concerned with
balancing the budget rather than stabilizing the business cycle, they further decreased
government expenditure, causing a further shift of the IS curve to the left.

The Money Hypothesis: A Shock to the LM Curve
This hypothesis says that it was a fall in the money supply that caused the depression.
They blame the Federal Reserve for letting the money supply drop by 25% through
1929 to 1933. Allegedly, however the channel through which this happened was not
through the decrease in the supply of real money balances, because there was a
period of deflation as well. Through what is called the Pigou effect, the effect that
deflation causes real money balances to rise thereby increasing people’s wealth and
their spending, some economists would expect the economy to restabilize. However
there are two proposed theories for why the deflation would depress income rather
than stabilize it.

 Debt-deflation theory. According to this theory, a decrease in the price level
raises the amount of debt (as analysed in chapter 5). This decreases people’s
wealth, thereby depressing their spending.

 The effect of expected deflation on investment. If people expect a high level of
deflation, this means that the ex-ante real interest rate increases. This is not
the nominal interest rate (which is the interest rate studied in the IS-LM
model), so this causes the IS curve to shift downward, and this would be the
explanation of the economic downturn.

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12.4. Conclusion
This chapter addressed the IS-LM model, the dominant short run model for a closed
economy. The next chapter formulates the small open economy version of this
model, the Mundell-Fleming model, by introducing trade and capital flows.

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13. The Open Economy Revisited: The
Mundell–Fleming Model and the
Exchange-Rate Regime

The Mundell-Fleming model is the open economy version of the IS-LM model.

Chapters 11 and 12 introduced the IS-LM model, the closed economy model of the
short run. This chapter introduces the Mundell-Fleming model, the adaptation of the
IS-LM model for a small open economy. It makes the same assumption as the classical
small open economy model introduced in chapter 6: that the domestic economy is a
small open economy with perfect capital mobility.

13.1. The Mundell–Fleming Model

The Mundell Fleming model replaces the IS and LM curves with the IS* and LM*
curves.

The Mundell-Fleming Model takes the same basic form as the IS-LM model: However,
the IS curve is renamed the IS* curve and the LM curve is renamed the LM* curve.
There are two basic differences with the IS-LM model.

 The interest rate is fixed at the world interest rate, just like in the classical
model of a small open economy: r = r*

 The Planned expenditure function includes a term for net exports: NX(e). Note
that we write Net exports as a function of the nominal instead of the real
exchange rate. This is because we assume prices to be fixed in the short run.

The IS* and LM* curves
In the Mundell-Fleming model, we no longer plot the IS* and LM* curves as a relation
between the interest rate and income, because the interest rate is always fixed at the
world interest rate. Instead, we plot them as a function of the nominal exchange rate.
So it is now the exchange rate that equilibrates the goods market, and the new goods
market equilibrium condition becomes
Y = C(Y-T) + I(r*) + G + NX(e)

The money market equilibrium is still dependent only on income and the interest rate,
and not on the exchange rate, so the LM equilibrium condition remains unchanged,
except that the interest rate is fixed:

(M/P)d = L(r*,Y)

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Therefore, the LM* curve is a straight line in the new graph, because it does not
depend on the nominal exchange rate:

All the effects analysed in chapters 11 and 12 with the IS-LM model can easily be
applied to the Mundell-Fleming model, except that it is net exports that equilibrates
the goods market, the interest rate stays fixed, and the LM curve is vertical. However
there are a number of new issues that can be analysed specifically for an open
economy, which will be done in the next subchapters

13.2. The Small Open Economy Under Floating Exchange Rates

Floating exchange rates are one of the two main exchange rate regimes.

There are roughly two exchange rate regimes: floating exchange rates, addressed in
this subchapter and fixed exchange rates, addressed in the next subchapter. Under
floating exchange rates, the central bank allows the exchange rate to be freely
determined by market forces, and does not intervene to keep it stable. This will mean
that the exchange rate adjusts to keep the goods market and money market in
equilibrium. We can analyse the effects of fiscal policy, monetary policy and trade
policy under floating exchange rates:

 Fiscal policy is ineffective under floating exchange rates. Shifting the IS* curve
to the right will only increase the exchange rate, thereby making the domestic
currency more expensive, and depressing net exports. Since the LM curve is
vertical (There is only one value of the level of income for which it is in
equilibrium, given the fixed values of M and r*), the decrease in net exports
must be exactly as big as the increase in government spending.

 Monetary policy is effective under floating exchange rates. An increase in the
money supply shifts the LM* curve to the right, thereby lowering the exchange
rate and increasing the level of income.

 Trade policy is ineffective under floating exchange rates. Trade policy, for
example policy that tries to restrict imports with the goal of increasing net
exports, will shift the IS* curve. However this shift will not increase income, but
instead change the exchange rate, which decreases NX again. The net result is
lower import and lower export, so that net exports remain the same

13.3. The Small Open Economy Under Fixed Exchange Rates

Fixed exchange rates are one of the two main exchange rate regimes.

Under fixed exchange rates, the central bank keeps the exchange rate fixed at a
certain level by changing the money supply accordingly. It does this by announcing an

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exchange rate and agreeing to always exchange currencies at that rate. By the law of
one price, the market exchange rate will then also shift to that value. The result of this
is that it cannot increase the money supply at will, because if it does, then the demand
for the domestic currency will drop, threatening a lower value of the currency. This
will force it to buy domestic currency, thereby lowering the money supply again.

Note: a fixed exchange regime fixes the nominal exchange rate. In the short run this is
equivalent to fixing the real exchange rate, but this is not so in the long run when
prices are flexible.
We can now evaluate the effectiveness of fiscal, monetary and Trade policy under
fixed exchange rates:

 Fiscal policy is effective under fixed exchange rates. Raising government
expenditure will shift the IS* curve to the right. This induces an increase in the
exchange rate, but to keep the exchange rate fixed, the central bank increases
the money supply which shifts the LM curve to the right, so that the exchange
rate is back at its original level. The result is an increase in Y.

 Monetary policy is ineffective under fixed exchange rates. As explained
earlier, if the Central bank decides to increase the money supply, this will
induce a decrease in the exchange rate, which will force the CB to decrease the
money supply again, leaving the money supply and Y unchanged.
o However, another type of monetary policy is effective, namely a change
in the value of the fixed exchange rate. If the central bank increases the
value of the fixed exchange rate, it is called a revaluation, and if it
decreases it, it is called a devaluation.

 Trade Policy is effective under fixed exchange rates. The reason that trade
policy was ineffective under floating exchange rates is because it altered the
exchange rate such as to undo the effects of the trade policy. However under
fixed exchange rates, the trade policy induces a change in the money supply (a
shift in the LM* curve), which prevents such a change in the exchange rate.

13.4. Interest Rate Differentials

There can be differences in interest rates among countries due to differences in
country risk and expectations of exchange rate changes.

We have assumed throughout chapter 6 and chapter 13 that a small open economy
with perfect capital mobility has an interest rate equal to the world interest rate r*.
However, in reality there are interest rate differentials, for two primary reasons:

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 Country risk. Some countries’ investment are more risky than others, which
makes investors demand a higher interest rate before they want to invest.

 Expected changes in the exchange rate. If investors expect a currency to
appreciate (increase in value), then they will invest more heavily, causing the
interest rate in that country to decline.

Differentials in the Mundell-Fleming Model
We can include these differences in interest rates in the Mundell-Fleming Model by
including a risk premium θ:

r = r* + θ
The higher the risk premium θ, the higher the interest rate will be. A strange
prediction is made when we fill this in into the Mundell-Fleming model:

 Y = C(Y-T) + I(r* + θ) + G + NX(e)
 (M/P)d = L(r* + θ,Y)

An increase in the risk premium now shifts the LM curve to the right, thereby
increasing income. However, in reality an increase in the risk premium of a country
tends to decrease income. There are two reasons why in reality this happens which
are not taken account of in the Mundell-Fleming model:

 The depreciation of the currency may increase the price of imported goods,
thereby increasing the price level.

 The risk premium will also affect the liquidity demand of domestic agents,
shifting the LM curve back

The Mexican crisis of 1994-1995 and the Southeast Asian crises of 1997-1998 are
clear examples of crises that started because of an increase in the risk premium.
13.5. Should Exchange Rates Be Floating or Fixed?

A country must choose between floating or fixed exchange rates, and every country
faces the dilemma of the impossible trinity.

Now that we have developed the Mundell-Fleming model, we can use it to address an
important question in international macroeconomics: should a country have a fixed
exchange rate regime or a floating exchange rate regime?

Advantages of floating exchange regimes and disadvantages of fixed exchange
regimes are:

 Keeping the currency floating allows the central bank to use monetary policy
for different purposes, such as stabilizing the level of output.

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 In a fixed exchange regime, you have to always trade the currency, but if you
run out of foreign currency, your economy is vulnerable to speculative attack.

Advantages of fixed exchange regimes and disadvantages of floating exchange
regimes are:

 A fixed exchange rate removes exchange-rate uncertainty, which helps
international trade

 A fixed exchange regime disciplines a monetary authority so that it does not
perform excessive inflationary policies

Besides fixing the exchange rate, the euro zone has gone one step further and created
a common currency, which is effectively a permanent fixed exchange rate between
the European countries. There are costs and benefits associated with this move:

Costs

 National central banks lose their monetary authority.
 Labour is not very mobile in Europe, which increases the costs of not having an

own monetary policy.
 There is no European fiscal authority that can engage in stabilization policies.

Benefits

 No exchange rate risk
 No costs associated with exchanging currencies
 Political unification

The Impossible Trinity
The analyses of fixed and floating exchange regimes, and the policy effectiveness
allows us to conclude an important international macroeconomic result, namely that it
is impossible for an open economy to have all three of the following macroeconomic
policies:

 Free Capital Flows
 Independent monetary Policy
 Fixed Exchange Rate

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Every country must choose two of the three of these, and this is called the impossible
trinity.
13.6. From the Short Run to the Long Run: The Mundell–Fleming Model With a
Changing Price Level

The Mundell-Fleming model can be used to show how we move from the short to
long run.

Just like we did in chapter 12 for the IS-LM model, we can look at what happens with
the Mundell-Fleming model as it moves to the long run. To do this we write the Net
export function as a function of the real exchange rate again, as in chapter 6: NX =
NX(ε). Having done this, the Mundell-Fleming model explains the aggregate demand
curve for an open economy, as is shown in the following graph:

13.7. A Concluding Reminder

The Mundell-Fleming model developed in this chapter is a model for a small open
economy, just like the classical model developed in chapter 6. However, countries
like the United States do not behave completely like a small open economy, because
their policies affect the world interest rate. Such economies should be seen as lying
somewhere between a closed economy and a small open economy.

The Mundell-Fleming model developed in this chapter is a model for a small open
economy, just like the classical model developed in chapter 6. However, countries like
the United States do not behave completely like a small open economy, because their
policies affect the world interest rate. Such economies should be seen as lying
somewhere between a closed economy and a small open economy.

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14. Aggregate Supply and the Short- Run
Trade-off between Inflation and
Unemployment

Chapters 11 to 13 have expanded on chapter 10 by deriving the Aggregate Demand
curve from the IS-LM and Mundell-Fleming models. This chapter expands on chapter
10 by delving deeper into the Aggregate Supply curve.

14.1. The Basic Theory of Aggregate Supply

There are two basic theories of aggregate supply but they come to similar
conclusions.

In this subchapter, we explain two prominent theories that explain the shape of the
Aggregate Supply curve. The Keynesian Aggregate Supply curve was horizontal,
assuming that prices do not alter supply of goods and services at all in the short run.
In this chapter, this assumption is nuanced to an extent, so that the aggregate supply
curve becomes upward sloping, which is in between the classical model and the
Keynesian model. Both theories explained in this subchapter result in the aggregate
supply equation of the following form, but in a different way:

Y = Y + α(P – EP), α > 0

Where EP is expected inflation, and Y = F(K,L) .

Sticky-Price Model
The sticky-price model is the most widely accepted explanation for the upward-
sloping nature of the SRAS curve, and entails that because prices are sticky. The
model begins by assuming that firms have a desired price

p = P + a(Y- Y)
There are firms with sticky prices and firms with flexible prices. Firms with flexible
prices simply set the desired price, but firms with sticky prices set their prices to what
they expect:

p = EP
s is the fraction of firms with sticky prices and 1-s the fraction with flexible prices, so
the price level is:

P = sEP + (1-s)(P+a(Y-Y)

We rearrange this to:

Y = Y + (s/((1-s)a))(P-EP)

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The Imperfect Information Model
A different theory for the upward slope of the aggregate supply curve is
the imperfect-information model. In this model, the aggregate supply curve is upward
sloping because of temporary misperceptions about prices. If producers expect the
price level in the future to be high, then the future value of their profit will be
relatively lower. This means they will work less hard, or invest less, so that supply is
lower. In other words, when actual prices exceed expected prices suppliers have a
higher output than they would if they’d always have perfect information on prices, so
that the aggregate supply curve becomes:

Y = Y + α(P – EP)

Implications
The two theories of aggregate supply differ in the explanations they give for the
behaviour of aggregate supply, but the form of the AS curve that they generate is the
same, namely a function of the natural rate of output (determined by the production
function), the price level, and the expected price level. We can now complete the
partial analysis of the IS-LM and Mundell-Fleming model (which was only an
aggregate demand analysis and assumed that aggregate supply was completely
determined by the price level). When an unexpected shift to the right of the aggregate
demand curve occurs, this has the immediate effect of causing an economic boom,
because suppliers have not adjusted their prices to the new level of demand yet. The
new price level and income is determined by the intersection between the demand
curve and the short run aggregate supply curve. However, as prices begin to adjust,
the short run aggregate demand curve shifts to the left, because the expected price
level moves towards the actual price level. The intersection between the new short
run AS curve and the AD curve lies on the Long run AS curve again, this time with a
higher price level:

It is important to see that this model captures both short run monetary non-neutrality
and long run monetary neutrality.

14.2. Inflation, Unemployment, and the Phillips Curve

The Phillips curve gives the relation between inflation and unemployment in the
short run.

Two of the goals of macroeconomic policy are keeping inflation low and keeping
unemployment low. These goals, however, conflict in the short run according to the
theory of the Philips curve, the curve that is derived from the AS curve and gives the

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relation between inflation and unemployment. It is derived by combining the AS curve
and Okun’s law (see chapter 10). Okun’s law can be written as follows:

(1/α)(Y-Y) = -β(u-un)
If we substitute this in the aggregate supply equation and add a variable v for a supply
shock, we get the equation for the Philips curve:

π = Eπ - β(u-un) + v
According to this equation, trying to decrease inflation in the short run will increase
unemployment.

Adaptive Expectations and Inflation Inertia
In order to make the Philips curve useful for policymakers, we must know what
determines expected inflation. One often used theory for this is the theory of
adaptive expectations. The theory states that economic agents base their expectation
of inflation on inflation levels in the past. The Philips curve now becomes:
π = π-1 - β(u-un) + v
we see here that the rate of unemployment will be equal to its natural rate, if inflation
stays the same. For this reason the natural rate of unemployment is also sometimes
called the non-accelerating inflation rate of unemployment (NAIRU).

Two causes of Rising and Falling Inflation
There are two types of shocks that can cause inflation

 Demand-pull inflation. Inflation caused by high aggregate demand.
 Cost-push inflation. Inflation caused by an adverse supply shock (v in the

Philips curve)

Disinflation and the Sacrifice Ratio
For practical policymakers it is not enough to know that there is a relation between
unemployment and inflation. They also want to know how strong the relation is. This

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is captured by the sacrifice ratio, the percentage of GDP that must be forgone to
reduce inflation by 1 percentage point. Typical estimates range around 5%

Rational Expectations and the Possibility of Painless Disinflation
The previous analysis is based on the theory of adaptive expectations, that expected
inflation is based on inflation in the past. However, some economists advocate
rational expectations. The theory states that inflation expectations are based on
people’s analyses of the determinants of inflation, including government policy. A
conclusion of this theory is that if the government can make clear beforehand to
people that they will decrease inflation, then expected inflation will decrease as well,
so that there can be a decrease in inflation, without an increase in unemployment.

Hysteresis and the Challenge to the Natural-Rate Hypothesis
The chapters 10 to 14 have all been based on an assumption called the natural-rate
hypothesis. This is the hypothesis that fluctuations in aggregate demand and supply
only affect the short run levels of unemployment and output, and that in the long run
they will move back to their natural rate, described by the classical model. However,
this hypothesis is not uncontroversial. There is a different hypothesis that there is a
phenomenon called hysteresis, which refers to effects to the natural rate caused by
short run fluctuations. In other words, an economic downturn not only changes
income in the short run, but also in the long run by diminishing the natural rate of
output or increasing the natural rate of unemployment. There are multiple possible
channels for hysteresis:

 A recession can move people in a type of permanent unemployment because
them not having a job for a long time causes them to lose skills, or by giving
them a certain stigma that deters employers from hiring them.

 A recession may cause high unemployment, which turns more workers into
outsiders, so that unions increase wages, which in turn stop those outsiders
from getting a job again. This may set the wage level at a permanently higher
level, and therefore also unemployment.

14.3. Conclusion

We have developed and applied the AS-AD model. However many aspects of these
theories are still controversial, and the debate about them continues.

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15. A Dynamic Model of Aggregate
Demand and Aggregate Supply

The DAD-DAS model is the dynamic version of the AD-AS model. that is, it explains
how the short run equilibrium moves over time to the long run equilibrium.

Part V expands upon the models in part IV, IS-LM and Mundell-Fleming, in specific
ways. This chapter formulates a dynamic version of the AS-AD model. the next
chapter delves deeper into the consumption function, and chapter 17 delves deeper
into the theory of investment.
The AS-AD model of part IV was a Static model. it showed the short run equilibrium
and the long run equilibrium, but it did not show how the short run equilibrium
changed over time. This chapter introduces the DAS-DAD model (D for dynamic), the
dynamic version of the AS-AD model. It shows how the short run equilibrium moves
over time, and thereby models the movement of output and inflation after exogenous
shocks.

15.1. Elements of the Model

The basic elements of the model are similar to the static model (chapters 10 to 14),
but formulated somewhat differently.

In the dynamic model, the variables are defined for each period, rather than just for
their equilibrium. This means that all the variables have a subscript that denotes the
period which that variable denotes. For example, Yt means income in period t. We
first go through all the constituent elements of the model before we solve the model
and determine the DAD and DAS curves.

Output: The Demand for Goods and Services
The demand for goods and services is given by:

Yt = Yt – α(rt – ρ) + εt
Where εt is some demand shock, such as a change in fiscal policy or a change in
consumption demand due to a stock market boom, and where the constant ρ is the
real interest rate for which aggregate demand is equal to natural output. The constant
α is the sensitivity of investment demand and consumption demand to a change in the
real interest rate. This equation is similar to the equation for the IS curve, but the
variables of the income identity are simply written less explicitly.

The Real Interest Rate: The Fisher Equation
The real interest rate that we use in this model is the ex-ante real interest rate. This

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should not be controversial, since it is the ex-ante real interest rate that determines
demand. We derive it from the fisher equation:

rt = it – Etπt+1

Where Etπt+1 is the expectation in period t of the level of inflation in period t +1.

Inflation: The Phillips Curve
The supply curve in this dynamic model is derived from the Phillips curve. This form of
the Phillips curve denotes the relation between inflation, output, and supply shocks:

πt = Et-1πt + φ(Yt – Yt) + vt
Where the constant φ is the extent to which inflation responds to a change in output
away from its natural level, and where vt is any supply shock, such as one caused by a
drought, or by an oil cartel.

Expected Inflation: Adaptive Expectations
In this model, we simply assume adaptive expectations of inflation (see chapter 14):

Etπt+1 = πt

The Nominal Interest Rate: The Monetary-Policy Rule
One of the key differences between this model and the static model is that in this
model, monetary policy is inserted more explicitly in the model itself. In the static
model, a monetary expansion would be formulated as a shift in the AD curve to the
right, but in this model we formulate an explicit monetary policy rule: a target for the
interest rate for which the central bank then allows the money supply to change in
order to achieve that interest rate. This interest rate is then inserted in the DAD
curve, so that monetary policy influences the slope of the DAD curve, but does not
move it. The monetary policy rule is a rule that sets the nominal interest rate as a
response to the level of inflation:

it = πt + ρ + θπ(πt – π*t) + θY(Yt – Yt)
Where θπ is the sensitivity that the central bank gives to staying at the target inflation
π*t, and θY is the sensitivity that the central bank gives to staying at the natural level of
output. Note that the central bank is indirectly targeting the real interest rate by
including the current level of inflation in the first part of the equation. One
assignment of values to θπ, and θY is done by the Taylor Rule, formulated by the
economist John Taylor, who said to assign 0.5 to both.

The following table summarizes the equations in this model:

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15.2. Solving the Model

By solving the model we derive the dynamic aggregate demand and dynamic
aggregate supply curves.

It follows from this model that the values in every time period t depend on the values
of some variables in period t-1. Variables in period t-1 are already determined from
the perspective of period t, they happened in the past), and so within period t, they
are called predetermined variables. We can determine the DAD and DAS curves
using this model, and determine the long run equilibrium and the short run equilibrium
in each period.

The Long-Run Equilibrium
The long run equilibrium is reached when output is at its natural level, the real interest
rate is at the rate which sets aggregate demand at natural output given no demand
shocks, inflation is at the central bank’s target inflation and expected equals inflation,
and when the nominal interest rate is at the natural real interest rate plus the target
level of inflation.

The Dynamic Aggregate Supply Curve
To derive the aggregate demand curve, we simply substitute the equation for adaptive
inflation expectations in the Phillips curve to find:

πt = πt-1 + φ(Yt – Yt) + vt

The Dynamic Aggregate Demand Curve
To find the dynamic aggregate demand curve we take the equation for the demand
for goods and services and we substitute the Fisher equation in, and in that equation
we substitute the monetary policy rule and the equation for adaptive expectations.
After simplifying, the DAD curve becomes:
Yt = Yt – (αθπ/(1+ αθY))(πt – π*t) + (1/(1+ αθY))εt
As hinted at before, the DAD curve is similar to the AD curve, but it has two essential
differences:

 It is written as a function of inflation rather than the price level, denoting its
dynamic nature.

 More importantly, it is drawn for a given monetary policy rule, rather than a
given money supply. Monetary policy thus enters the DAD curve through the
weights the central bank puts on keeping inflation stable and keeping output
stable. A shift in the aggregate demand curve as a result of monetary policy can
only happen by changing the target level of inflation.

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The short-run equilibrium is determined simply by the intersection of the DAS and the
DAD curves. This intersection determines both the level of inflation and the level of
output:

15.3. Using the Model

The DAD-DAS model can be used to analyse movements of the short run equilibrium
to the long run equilibrium.

We can use the model to analyse long run growth, supply shocks, and demand shocks,
in order to predict the movement of variables over time.

Long Run Growth
In order to see the effect of long run growth, we only have to increase the natural rate
of output. If you do this, both the DAD and DAS curves shift to the right, so that
inflation stays the same, and output rises. We conclude that this model predicts that
stable long run economic growth with stable inflation is possible

Aggregate Supply Shocks and Aggregate Demand Shocks
An aggregate supply shock is formulated in this model as a change in vt if there is a
negative supply shock of one period, inflation will rise and output will fall. However
this will not immediately recover, as expected inflation will stick at the new level of
inflation. It will take time for the policy of the central bank of higher interest rates to
take inflation back at its original level. This example denotes a period of stagflation, a
situation of low output and high inflation caused by a negative supply shock. The
movements of all the endogenous values in this model are given here:

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A similar analysis can be done for a demand shock. A sequence of 5 periods of a
demand shock is depicted here:

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A shift in Monetary Policy
A change in the target level of inflation can also be analysed in this model. A reduction
in the target level of inflation would simply shift the DAD curve to the left
permanently. This slowly lowers inflation, so that the DAS curve slowly adjusts as
well, until it is at the long run equilibrium again.

15.4. Two Applications: Lessons for Monetary Policy

The two main lessons of the DAD-DAS model are the trade-off between output
variability and inflation variability, and the Taylor principle.

We can use this model to conclude two lessons for monetary policy. The first has to
do with the weight that the central bank puts on balancing output versus balancing
inflation. The second has to do with the effect that inflation can spiral out of control if
the central bank does not apply the right policies. Both have to do with the values
that the central bank assigns to θπ and θY.

The Trade-off Between Output Variability and Inflation Variability.
The values of θπ and θY determine the slope of the DAD curve. This slope determines
the effect that a supply shock has on inflation and output. If the weight on output is
higher, then the effect on output of a supply shock will be balanced, but the effect on

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inflation less so. This trade-off is an unavoidable choice that the central bank must
make. One example that shows this is that the Fed and the ECB (European Central
Bank) have assigned different weights to them. The ECB is primarily focused on
stabilizing inflation, whereas the Fed has a more balanced weight distribution.

The Taylor Principle.
Besides the trade-off between inflation stabilization and output stabilization there is
also something called the Taylor Principle. This principle states that for inflation to be
stable, the central bank must respond to a percentage change in inflation by
increasing the nominal interest rate by higher than a percentage change. This can be
shown by the DAD-DAS model, but it can also be explained intuitively: If inflation
rises, and the nominal interest rate rises by exactly the same amount, then the real
interest rate has remained the same. Because it is the real interest rate that
determines demand, demand will not change as a result of the central bank’s policy.
As a result, inflation will stay at a higher level. In order to stabilize it, the rise in the
nominal interest rate must be higher than the rise in inflation. If the rise in the nominal
interest rate is even lower than the rise in inflation, then inflation will spiral out of
control. According to some economists, this is exactly what happened during the
period of high inflation in the 1970’s.

15.5. Conclusion: Toward DSGE Models

This chapter has developed the dynamic model of aggregate supply and aggregate
demand. It forms the basis of more advanced macroeconomic models, called dynamic
stochastic general equilibrium models (DSGE). These models are based on micro
foundations (studied in microeconomics courses), and relatively complicated, so will
not be studied in this book, but the model developed in this chapter comes closest to
these models compared to the other models studied.

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16. Understanding Consumer Behaviour

In part IV, chapters 10 to 14 about short run AS-AD theories we have assumed a
consumption function C(Y-T), but we have not looked at the specifics of this
function. There have been many disagreements about the nature of this
consumption function, and in this chapter we look at the different theories that have
been developed about the role of consumption in macroeconomics.

16.1. John Maynard Keynes and the Consumption Function

Keynes hypothesised three conjectures about the consumption function.

Since Keynes, the consumption function has been central in the macroeconomic
debate. Keynes made three basic conjectures about consumption:

1. The marginal propensity to consume is between zero and one.
2. The ratio of consumption to income, the average propensity to consume, falls

as income rises.
3. Income is the primary determinant of consumption; the interest rate does not

play an important role.

These three conjectures are the basis of the Keynesian consumption function used in
this book:

C = C + cY, C > 0 , 0 < c < 1
This consumption function captures the three Keynesian conjectures. These
conjectures were tested using household surveys and at first were upheld. However
there were two empirical tests that the theory did not withstand:

 Incomes grew strongly after WWII, but consumption grew at the same rate
 Simon Kuznets constructed data dating back to 1869 that showed that the

share consumption remained relatively stable over time.

In other words, Keynes’ theory held up to short run changes in income, but not to
long run changes. This suggested that there were two consumption functions, one for
the short run and one for the long run. Two theories, one by Modigliani, the other by
Friedman, try to explain this fact. This chapter will explain them both, but first we
must understand the theory of consumer behaviour developed by Irving Fisher, on
which those two theories are based.
16.2. Irving Fisher and Intertemporal Choice

The model of intertemporal choice is the basis for two theories that try to solve
Keynes' consumption puzzle.

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Irving Fisher developed a model to describe how rational individuals make inter-
temporal choices, choices about allocating goods over time. He assumed that
consumers have an inter-temporal budget constraint, a budget that limits what they
can spend during their lifetime. The consumer can choose how much he consumes
today and how much he consumes tomorrow. If he wants to consume more tomorrow
than he earns tomorrow, he will need to save. If he wants to consume more today
than he earns today, he will need to borrow. Both are done for the interest rate. So
we have:

S = Y1 – C
Where Y1 is income in period 1. He can consume in period 2 the amount that he earns
in period 2 plus what he saves plus interest:

C2 = (1+r)S + Y2, which can be written as C2 = (1+r)(Y1 – C) + Y2
We can rewrite this to find the inter-temporal budget constraint:

C1 + C2/(1+r) = Y1 + Y2/(1+r)

You see that the income and consumption done in period 2 is divided by the factor for
the interest rate. This is because a dollar today is worth more than a dollar in the
future, since a dollar today, if invested in a bond, will give 1+ r dollars in the future.
This process is called discounting. This gives the following budget constraint:

Consumer Preferences
Consumer preferences can be represented by indifference curves, curves that show
the set of allocations between the amounts of two goods for which the consumer is
indifferent (If you don’t understand this, see a microeconomics textbook for a full
explanation). The slope along an indifference curve is the marginal rate of
substitution. A rational consumer will chose the allocation of current consumption
and future consumption such that the slope of the inter-temporal budget constraint is
equal to the marginal rate of substitution, as shown here:

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Choosing the optimal consumption given the consumer’s indifference curves is called
optimization. We can formulate a change in income as a shift of the inter-temporal
budget constraint away from the origin. In this case, as you can see from the graph,
both consumption in period 1 and consumption in period 2 increases. A good that is
consumed more when income increases is called a normal good. The key insight
gained from this model is that both goods are normal goods, and
therefore consumption smoothing occurs. This means that an increase in income,
whether it is in period 1 or in period 2, will increase consumption in both periods.

How Changes in the Real Interest Rate Affect Consumption
The real interest rate determines the relative cost of period 1 consumption and period
2 consumption, and it determines the discount rate of period 2 income. This means
that a rise in the interest rate will make consumption in period 2 less expensive, and
make income in period 2 less valuable. This means that we can analyse the effect of a
change in the interest rate into two effects:

 Income effect: the change in consumption in either period that arises from
moving to a higher indifference curve. Another way to understand it is that
income increases.

 Substitution effect: the change in consumption in either period that arises from
a change in the relative price of the two consumption periods.

So we conclude from this that depending on the relative sizes of the income and
substitution effects, a change in the interest rate will either depress or stimulate
saving.

Constraints on borrowing
An element that will not be studied in depth here is the notion of borrowing
constraints. The most extreme form of borrowing constraint is a complete
impossibility of borrowing. This effectively means that period 1 consumption cannot

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be higher than period 2 consumption. For these type of consumers that want to
borrow but cannot, consumption is only determined by income.
16.3. Franco Modigliani and the Life-Cycle Hypothesis

the Life-Cycle hypothesis is a possible solution to Keynes' consumption puzzle.

We now turn to one of the two theories of the consumption function. This theory is
called the life-cycle hypothesis, and it means that people would like to have equal
consumption throughout their lives (consumption smoothing). This can be expressed
as follows:

C = (W + RY)/T
Where C is consumption in every period, W is wealth, R is the amount of periods that
the individual works, Y is income in each period, and T is the amount of years that that
person lives. This life-cycle hypothesis can solve the consumption puzzle that Keynes’
theory faced. Wealth does not change very quickly as income changes, so that
consumption does not change as fast as income changes in the short run. However, in
the long run, wealth changes with income, so that changes in income result in equal
changes in consumption. This is captured by the following formula:

C/Y = α(W/Y) + β

There is one empirical problem with the life-cycle hypothesis. The elderly disserve less
than they need to. There are two explanations for this:

 Precautionary saving. They want to save money as a precaution in case they
get older than expected, or in case of unexpected (healthcare) expenses.

 They want to leave wealth to their children.

16.4. Milton Friedman and the Permanent-Income Hypothesis

The Permanent-Income Hypothesis is a possible solution to Keynes' consumption
puzzle.

We now turn to Milton Friedman’s permanent-income hypothesis. This hypothesis
suggests that we can view income as consisting of two components: permanent
income Yp, the part of income that people expect to persist in the future,
and transitory income YT, the income that people expect to be specific to a certain
period, i.e. not to persist.

Y = YP + YT
An example of a change in permanent income is if you get an unexpected job
promotion which you think will persist during your career. An example of a change in
transitory income is a onetime lottery prize. Friedman thought that people want
consumption smoothing, and therefore do not let increases in transitory income affect
their current consumption very much. Rather, they would spread it out over their life

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time. On the other hand a change in permanent income does strongly affect their
consumption. Therefore Friedman made the following consumption function:

C = αYP
He derived from this the Average propensity to consume:

APC = αYP/Y
Therefore, the effect of income on consumption depended on the share of permanent
income in that income. Just like Modigliani’s theory, this can solve Keynes’
consumption puzzle.

16.5. Robert Hall and the Random-Walk Hypothesis

the random-walk hypothesis is an extension of Friedman's permanent income
hypothesis.

This subchapter introduces an extension of Friedman’s hypothesis, by combining it
with the assumption of rational-expectations. The economist Robert Hall showed that
if the permanent income hypothesis is correct and consumers have rational
expectations, then it is impossible to predict changes in consumption. This is called
a random walk. This has an important implication for policy. It means that a policy will
only change consumption if it is unexpected. An expected policy change will not
influence consumption at the moment it is enacted. Instead the changes will take
effect the moment that consumers can predict they will happen.

16.6. David Laibson and the Pull of Instant Gratification

Behavioural economists have criticized the rational-choice based theories of
consumption on a number of grounds.

The study of consumption after Keynes has focused on models of rational decision
making, and not on psychology. Yet there have been some psychological studies that
contradict this assumption of rational choice and rational expectations. This branch of
economics is called behavioural economics. One result is that 76% of Americans say
that they save less than they should. According to rational choice theory this is
impossible, because consumers always choose that which they find best. Another
example is that consumers’ preferences may be time-inconsistent. This means that
they change their choices only because time passes. One example of this is that
people are too impatient in the short run to wait for something, even though they
would like it in the long run (likely causing them to save less than they would ideally
want).
A practical application of this is that policymakers looking to behavioural economics
have thought about how to get people to save more. Studies have shown that if tax
plans have an option to not save while saving is the standard choice, rather than an

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option to save while not saving is the standard choice, people will have a stronger
tendency to save.

16.7. Conclusion

The basic conclusion of this chapter is that Keynes’ consumption function was too
simplistic. He had a consumption function of the form:

Consumption = f(Current Income)
The advances in consumer theory discussed here suggest that the real consumption
function may be closer to the form:

Consumption = f(Current Income, Wealth, Expected Future Income, Interest
rates)

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17. The Theory of Investment

This chapter delves deeper into the determinants of the investment component of
GDP that is so crucial in the models introduced in this book.

Throughout parts II, III, and IV, we have used investments as a part of the models,
without addressing what investment consists of. There are three main categories of
investment:

 Business fixed investment is what people usually think of when they think of
investment: expenditures by firms on equipment and structures that they use
in production

 Residential investment is the building of new houses.
 Inventory investment refers to the goods that businesses produced but that

have not been finished yet or that have not been sold (yet) to customers.

The determinants of these three types of investment differ, so to fully understand
total investment, we must analyse them separately, which we do in this chapter in
that order.
17.1. Business Fixed Investment

The neoclassical model of investment is a model that explains business fixed
investment from the costs and benefits of investing in capital goods.

The predominantly used model of business fixed investment is the neoclassical model
of investment. It is based on an analysis of the costs and benefits for firms of owning
capital goods. The development of this model assumes two types of firms:

 Rental firms. These firms buy capital goods and rent them to production firms.
 Production firms. These firms rent capital goods and use them to produce goods

and services.

This is a theoretical distinction that is not necessary for the theory but simplifies its
development. We will drop the assumption later.
The Rental Price of Capital
We assume that the production function of production firms is a cobb-douglas
production function. As developed in chapter 3, a firm that maximizes its profits
purchases a capital good until the marginal product of capital equals the real rental
price of capital (in equilibrium):

M/P = αA(L/K)1-α

The Cost of Capital

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