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ECON1110LectureNotes5.doc

ECON 1110 Lecture Notes 5

ECON 1110 Intermediate Macroeconomics

James R. Maloy

Spring 2020

Lecture Notes for Topic 5: Keynesian Macroeconomics (I)

Readings: Froyen Ch. 5 (8th Ed. Ch. 6)

I. The Foundations of the Keynesian Revolution

The Great Depression of the 1930s and the enormous long-term persistency of high unemployment and low output could not be explained by the classical model. In the classical framework, recessions were possible but were expected to be of relatively short duration and would correct themselves. A depression that lasted for years with no sign of recovery was unfathomable. According to the classical model, output was entirely determined by supply factors, and no change in aggregate demand, and no government policy, could be effectively used to alleviate the problems. Indeed, many of the policies undertaken at the time, such as tax and tariff increases, were exactly opposite of those we typically expect to see from government policy in a recession. For example, governments at the time faced falling tax revenues due to the high level of unemployment. To close the resulting budget deficit, governments raised taxes. Under the classical analysis, such tax increases should not affect the economy, but in reality caused great harm. Indeed, it is generally agreed that governmental mistakes greatly lengthened the Depression. However, we shall see in this course that there is considerable disagreement on precisely what was wrong about these policies and what (if anything) should have been done instead.

The fundamental problem was that the assumptions of the classical model were not realistic in describing the state of the US economy in that period. Two main approaches emerged. One, espoused by some such as Mises, centered on interferences with market mechanisms that prevented efficient, market-clearing outcomes. These arguments varied but typically centered on market imperfections and interventionist policies in the 1920s that created an economic bubble, which collapsed in the 1930s, which were in turn made worse by more interventionist policies. These ideas argued that markets work properly but the conditions for them to do so were impeded during this entire time period, such as by rampant expansionary monetary policy in the 1920s or Hoover's policies on preventing wage cuts in the misguided belief that high wages cause prosperity.

An alternative approach centered on free markets being fundamentally inefficient. Some were fundamental criticisms of the system, such as Marxism or economic fascism (corporatism), the latter of which was proposed by Mussolini as a "third way" between the extremes of capitalism and communism, and was a major influence on Hoover and FDR's market intervention policies. Many of these types of communist and corporatist policies involve micro-level intervention, e.g. controlling production, wages, etc. (often via government-managed cartels) in individual firms or industries.

Keynes too looked at markets and viewed them as fundamentally inefficient, but developed a radical new way of looking at the problem. Rather than focusing on micro-management of individual industries, he proposed macro-management that focused on macro aggregates without consideration for what was actually being done at the micro level. This is simultaneously a strong point and weak point of his model. He correctly noted a fundamental flaw of micro-intervention that has led to extreme inefficiency and eventual collapse of all such attempts: lack of information. Central planning of micro-level production decisions requires an amount of information and co-ordination that simply does not exist. For example, if you order your automobile industry to produce a certain amount of cars, you must ensure that all industries that produce components such as steel or tires also produce the correct amount. One of the key strengths of private markets is that efficiency does not require much information: all that you need to know are your own costs and revenues. If there is a shortage of tires, the price will rise and supply will follow!

Heavily influenced by mercantilism , he argued that aggregate demand, not aggregate supply, was the factor that determined output. He asserted that the Depression was the result of aggregate demand being too low; the economy had become stuck in a sub-optimal equilibrium with low demand causing low production, which in turn causes low levels of employment, which of course leads to low demand. At a micro level this behavior was optimal: if you own a firm and no one is buying your product, the optimal strategy is to lay off workers and cut back production. However, at a macro level this leads to poor economic outcomes, contradicting the classical view that micro optimality leads to macro optimality. He argued for a positive role for government to intervene in markets: to ensure that aggregate demand was sufficient to achieve full employment levels of production. Essentially, this is macro-planning: the job of the government is to ensure that total demand is at a sufficient level, but let the private sector decide which products are actually produced. This reduces the inefficiencies of micro-planning; Keynes recognised that the private sector, not the government policymaker, was best placed to make individual production decisions. However, this strength is also a weakness: his model therefore does not distinguish between $1tn on infrastructure such as roads and rail and $1tn on worthless gadgets at Walmart. Indeed, Keynes wrote that in the extreme, a government could create the necessary aggregate demand by burying a big pile of money and then letting the private sector decide how to dig it back out again. In reality, the long-run effects are very much dependent on what is bought-and how it is paid for, e.g. borrowing the money and then burying it, which leaves future generations with a bill for the $1tn that was buried. Keynes ignored these long-run effects; his model was a short-run model and only was concerned about the jobs created today by burying money, not the long-run effects of such a blatant misallocation of scarce resources. This is a key problem: Keynesians argue that these policies are socially optimal but do not properly account for long-run costs and benefits in their analysis.

Keynes' model was fundamentally a disequilibrium model designed to explain how the economy operates when it is not in the full-employment classical equilibrium. He did not really argue that the classical model was "wrong"--he argued that it was a special case of the economy operating the way we'd like it to behave, i.e. the ideal state, akin to the physics assumption of being in a vacuum. However, he argued that this special case was not realistic as the real world was not characterized by perfect information and fully flexible wages and prices. This is expressed in the title of his General Theory: how the economy operates in general, such as during the disequilibrium that classical economists largely ignored as a transitory, self-correcting event, or times when the economy is in an equilibrium, but it is a sub-optimal one. He and his followers produced a model that made aggregate demand the major determinant of output, and argued that aggregate demand was not stable and required government intervention to stabilise it.

It is interesting to note Keynes' rationale for his new model. As one observer of economic thought put it: "The liberal capitalism of the modern age, which Smith had heralded, whose victory Ricardo had proclaimed, and which Marx sought to destroy, was transformed by Keynes and given a new life." During the apparent collapse of capitalism during the 1930's and greater adherence to communist and fascist ideology (although there is some debate about what Keynes actually thought of fascist economics), Keynes decided that his task was to save capitalism--although some opponents of Keynes argue that his system actually destroys it . Keynes was most closely associated with the old UK liberal party, which was mostly centrist, and was not a proponent of socialism/communism/fascism.

The model considered here is VERY incomplete and is not remotely realistic. In the next topic, we will add the effects of money and interest rates. In later topics, we will also look at the role of aggregate supply. For now, we assume that there is no money or interest, prices are constant and the quantity of output demanded will be supplied at that price (e.g. a horizontal AS curve at that price level). In the Keynesian model demand determines output, not supply.

II. Conditions for Equilibrium in the Simple Keynesian Model

The simple Keynesian model hypothesised that equilibrium required aggregate supply (output, Y) to be equal to aggregate demand (E).

Y = E

Assuming that the economy is closed with no imports or exports, aggregate demand (E) consists of three components: consumption (C), investment (I), and government purchases (G). So in equilibrium we have:

Y = C + I + G

Recalling some of the simplification to national income accounts discussed in the first week of lectures, we know that we can define Y as both national income and national product. Defining Y as national product implies that:

Y C + Ir + G

where Ir is realised, or actual, investment. The difference between realised and planned investment (I) lies in the inventory component of investment. A firm will plan to have a certain quantity of goods in inventory at the end of the year, but unexpectedly high or low sales may leave them with more or less inventory than the management had planned.

So in equilibrium, it must be that:

C + I + G = Y C + Ir + G

Or that there are no unplanned changes in inventories:

I = Ir

Now defining Y as national income implies that:

Y ≡ C + S + T

since national income is divided among consumption, savings, and taxes.

Therefore, in equilibrium:

C + I + G = Y C + S + T

Simplifying gives another way to state equilibrium for the model:

I + G = S + T

So the three ways of stating equilibrium are:

Y = E = C + I + G (aggregate demand equals aggregate supply)

I + G = S + T (government spending and investment must be paid for by savings and taxes)

I = Ir (no unexpected changes in inventory)

Note that in this model it is aggregate demand (C + I + G) driving aggregate supply—the reverse of the Classical model and Say’s Law. Unlike the classical theory, aggregate demand in Keynes’ model is neither neutral nor stable. Keynes therefore had to throw out the entire classical model—the vertical AS curve which leads to AD shocks affecting only prices, as well as classical demand theory—the loanable funds framework and the quantity theory of money. Keynes’ attack centered on the role of interest rates in creating the self-balancing and stable classical aggregate demand curve as well as the stability of velocity in the quantity theory. Much of this will be covered in later topics—right now, we will start by analyzing the factors that drive consumption, investment and government spending as a starting place to understanding Keynesian AD theory.

III. The Components of Aggregate Demand

Again, assume a closed economy with no imports or exports.

Consumption:

Unlike classical loanable funds theory which argued that interest rates drove savings and consumption, Keynes argued that consumer expenditures was a stable function of disposable income, where disposable income (YD) is the difference between national income and taxes (YT). Keynes proposed the following consumption function:

C = a + b YD a > 0, 0 < b < 1

Or:

C = a + b(Y T)

The intercept a is autonomous consumption (the amount people would consume if they had no income), and b is the slope of the consumption function, or the marginal propensity to consume (MPC). It gives the percentage of a change in disposable income that will go toward consumption. The MPC can be defined as the derivative of the consumption function with respect to disposable income (dC/dYD).

The Saving Function

Recall that disposable income can be divided into consumption or savings:

YD = Y T = C + S

Or

S = YD C

Substituting for C yields:

S = YD (a + b YD)

S = -a + (1 – b)YD

Why is the intercept of the savings function (-a)? Because remember that if disposable income is zero, consumption is a. So people are therefore dissaving a, and saving is negative at zero income. As disposable income increases, we eventually reach a point where people earn enough to stop borrowing and start saving.

The Keynesian consumption function was a direct result of Keynes' view of the psychology of the consumer from the General Theory:

The fundamental psychological law, upon which we are entitled to depend with great confidence both a priori from our knowledge of human nature and from the detailed facts of experience, is that men are disposed, as a rule and on the average, to increase their consumption as their income increases, but not by as much as the increase in their income.

The Keynesian consumption function therefore does not show a proportional relationship between consumption and income because of the autonomous consumption (a) term. The ratio of consumption to income is given by the average propensity to consume (APC):

image1.wmf

b

Y

a

Y

C

APC

D

D

+

=

=

APC is therefore greater than the MPC and decreases as disposable income increases, just as Keynes' statement above implies. This Keynesian consumption function is also known as the absolute income hypothesis. Consumption reacts to actual current income. Any change in current disposable income will yield a change in consumption.

Empirical tests of the Keynesian function have yielded mixed results. An example of one estimated for the period 1929-41 for the United States is:

image2.wmf

D

Y

75

0

5

26

C

.

.

+

=

Thus for short-run periods, the Keynesian theory appears to be a plausible description of reality.

The idea that APC declines (and corresponding APS, the average propensity to save, rises) as income increases worried early Keynesian economists, who feared that the economy might stagnate as national income grew. As it turns out, studies have shown that, even as national income has grown over the past century, the estimated values of APC for any given decade do not change by very much. It is obvious from these studies that in the long run the relationship between consumption and income is proportional, indicating that the original Keynesian theory is not a good explanation of this long run phenomenon. New models had to be devised to explain why APC is proportional to income in the long run, but not proportional in the short run..

Another empirical failing of the Keynesian model is that quarterly changes in consumption were not explained by changes in income; the idea of Keynes' absolute income hypothesis that consumption changes when current income changes is not well supported by data. Two newer models were developed to correct these failings of the Keynesian theory, the life cycle hypothesis and the permanent income hypothesis (see appendix to these notes).

Investment

Keynes believed that changes in investment were a major source of the instability of aggregate demand and national income. Indeed, evidence has shown that investment is by far the most variable component of aggregate demand. Consumption generally changes only as a result of changes in income (hence Keynes argument that it was a stable function of income), but investment seems to change wildly over time. This observation becomes the key to the Keynesian explanation of business cycles.

Keynes listed two sources of changes in investment. The first, as in the classical model, is the interest rate (MC of investment). Keynes also expected a negative relationship between investment and the interest rate, although he argued that this relationship was weaker than in classical theory. The simple Keynesian model of this topic does not include interest rates, so we’ll ignore this until a later topic when interest rates are introduced. The other source was business expectations (MR of investment). Keynes was heavily influenced here by his work in financial markets, which he viewed as fundamentally inefficient and prone to volatility induced by herd mentality. Buying shares of stocks and building a factory have the same decision-making environment: uncertainty regarding the future. Long term investments have to be decided on with very little knowledge of future events. An individual will not possibly be able to predict the future (psychics aside), so the decision-maker will make decisions based on past experiences or simply see what everyone else was doing and follow their lead. The latter was the primary factor in the instability of investment. Investment decisions would follow a herd mentality, and changes in information or changes in the behaviour of others would have drastic effects on investment decisions. Note that this is a fundamentally different view of human behavior than the classical theory. Rather than rational, optimal individuals, people are part of a collective herd which is prone to irrational, inefficient behavior. Keynes’ model therefore used early versions of social psychology. If the crowd believes that the future is awesome, expected returns on both financial and real assets will be inflated; both financial markets and business investment will thus increase drastically in a bubble. In a panic, the opposite occurs.

We have now established that factors other than current income (Y) influence investment—it is driven by expectations of future income. Therefore, we can take investment as exogenous for now in our calculation of national income. The investment function for now will just be I, and it is independent of the current level of income. However, it is fundamentally volatile and can suddenly change. We will expand our study of investment in the next topic.

Government Spending and Taxes

Like investment, government spending is not considered to be directly influenced by the level of income, but rather by the decision-making of politicians, who may or may not take economic factors in their budget decisions. For now, we will leave government spending as G. To simplify things, we will assume that the government just sets taxes as a fixed lump-sum amount (T), and taxes do not vary with income. Therefore, the only component of national income which is itself dependent on national income (Y) in the simple Keynesian model is consumption.

IV. Determining Equilibrium Income (or Output)

Recall that equilibrium is where aggregate demand and aggregate supply are equal:

Y = C + I + G

Y is the endogenous variable we are trying to calculate. I and G, as well as T, are determined exogenously, as well as the autonomous part of consumption, a. The other component of consumption is income-induced expenditure which is dependent on the level of income. Recalling that we defined consumption as:

C = a + b(Y T)

substituting yields:

Y = a + bY bT + I + G

Solving for equilibrium Y:

Y bY = a bT + I + G

Y(1 b) = a bT + I + G

Y = [1/(1 – b)] [(a bT + I + G)]

We therefore have solved for equilibrium output in this economy. The first term, 1/(1-b), is called the autonomous expenditures multiplier. Note that b is the MPC, and that 1-b is the marginal propensity to save (MPS). Multipliers will be discussed in more detail below. The second term is called autonomous expenditures; that is, the expenditures that do not depend on the level of income. We have already discussed a, I, and G. The other component, bT, shows the (negative) effect of taxes on income.

Changes in Equilibrium Income: The Multiplier

A feature of the Keynesian system is that changes in autonomous components of national income generate even larger changes in equilibrium income. Note that this is very different from the classical model—rather than self-correction, demand is wildly volatile. This is known as the multiplier process. Basically, a change in one component of national income yields an initial increase in income. The person who receives this income saves a portion (MPS) and spends the rest (MPC). This portion that is spent becomes the income of another, and the process continues.

Multipliers in the Keynesian model are calculated by taking partial derivatives of the equation for equilibrium income:

Y = [1/(1 – b)] [(a bT + I + G)]

For example, the investment multiplier is ∂Y/∂I = 1/(1 – b), which is 1/MPS. If MPC (b) is 0.8, then MPS is 0.2. Therefore, the value of the multiplier is 1/(0.2) = 5. A $1 increase in investment increases income by $5. Since Y = C + I + G, and Y has increased by $5, the right-hand side of the equation must also increase by $5 to maintain equilibrium. We already know that $1 of this $5 increase in income is because of the change in investment. How do we account for the other $4? The other $4 represents an increase in consumption—remember that if b, the MPC, is 0.8, it means that 80% of any change in income will go towards consumption. Therefore, when income increased by $5, consumption increased by $4. The other 20% of the increased income $1) was saved—and channelled to investment, hence the original $1 increase in investment! Now our equation is in balance and equilibrium is attained. This result must be true because of the one of the other conditions for equilibrium:

I + G = S + T

Since nothing has happened to G or T, the increase in investment must be matched by an increase in savings. Therefore, this $1 increase in investment has increased income by $5, consumption by $4, and savings by $1.

Similar multipliers can be found for other components of national income. The government spending multiplier, ∂Y/∂G, is also 1/(1 – b). The tax multiplier, ∂Y/∂T, is -b/(1 – b). Note that the simplicity of this model makes the multipliers very similar--this is not realistic. Also, this model greatly overstates the magnitude of the multiplier. The multipliers in the more complete IS/LM model in the next topic will be smaller.

Fiscal Stabilisation Policy

We have established that fiscal policy—changes in taxes and government spending—can indeed influence aggregate demand and output in the Keynesian economy. Keynes argued that the government not only could influence output, but that it would be necessary to use policy to smooth out the fluctuations in aggregate demand that are caused by volatile investment. If the output is too high or too low, the government can use policy to bring the economy back to where it should be.

Appendix: Life Cycle and Permanent Income Hypotheses of Consumption

I. The Life Cycle Hypothesis of Consumption

The idea behind that life cycle theory is that consumption does not just depend on current income as it did in the Keynesian theory, but rather on expected earnings over one's entire lifetime. People do not want to live in a mansion one year and a cardboard box the next; rather the person does what is commonly known as consumption smoothing and tries to maintain a relatively constant consumption level throughout his lifetime. The person therefore saves during periods of high income and dis-saves or borrows during periods of low income. A simple graph can capture the essence of the life cycle hypothesis. Assume the person lives for T years. When the person is young, and still a student, income is very low. Although it may not feel like it at times, the average student lives above his means; rather than starving and having no clothes during their education, you buy your necessities and spend far in excess of your income. This is done by dis-saving. If you had some wealth given to you earlier in life, you spend it; or you take out a loan, or you resort to begging from your parents and other family members, but you are willing to do so to maintain an adequately high level of consumption. After graduation, you enter the workforce, eventually make enough to consume less than your income, and pay back your loans and save for retirement. After retirement, your income falls and you now dis-save again, by spending the wealth you accumulated while working. There is some disagreement on whether consumption will stay constant or gradually increase over the lifetime, but either way it is obvious that consumption is being smoothed.

The life cycle hypothesis can also be expressed more completely by using some simple mathematics. Assume again that the person lives for T years, and for simplicity assume that he wants to consume the same amount each period. Therefore, during each period t, he consumes 1/T of his expected lifetime resources. Further assume that the person wants to leave no bequest for his heirs; he wants to spend the total amount of his current wealth and future earnings. Also assume that there is no interest paid on assets; this greatly simplifies the equations.

Therefore, consumption in each period t,

image3.wmf

[

]

(

)

T

1

t

,

Î

, is given by:

image4.wmf

(

)

[

]

t

e

1

1

t

t

A

Y

1

N

Y

T

1

C

+

-

+

=

where

image5.wmf

1

t

Y

is the individuals labour income in the current period, N is the remaining number of years before retirement (i.e. if the person plans to work for 10 more years then N = 10),
image6.wmf

e

1

Y

is the average annual labour income expected over the future (N – 1) years of employment, and A is the value of presently held assets. Basically, the first term in brackets is how much he is currently earning, the second term is how much in total he plans to earn in the future, and the third term is the amount of assets saved, i.e. wealth, from previous periods.

Consumption depends not just on current income, as it did in the Keynesian model, but also on expected future income and current wealth. The life cycle hypothesis, however, argues that consumption is generally unresponsive to a change in current income that does not affect future income. For example, the effect of a temporary change in income can be calculated by taking the derivative of the consumption function above with respect to the change in current income:

image7.wmf

T

1

Y

C

1

t

t

=

If the increase in current income is expected to be permanent, the total change in current consumption is significantly higher:

image8.wmf

T

N

T

1

N

T

1

Y

C

Y

C

e

1

t

1

t

t

=

-

+

=

+

Therefore, unless the individual is extremely close to retirement (N is small), the effect of a permanent change in income on consumption today is much greater. Therefore, we can conclude that current consumption is not very responsive to temporary changes in income but is much more responsive to permanent changes in income. This should make sense. If you are 30 years old and wish to smooth consumption, you will not go out and blow a one-time $100,000 windfall all today; you will want to save it and divide it up over future periods. Current consumption will not change by very much. If you expect to get the same $100,000 bonus for the rest of your working life, then you will spend a much greater proportion of today's $100,000 right away; after all, you will get another similar amount every year so there is no need to save it to smooth consumption. Empirical studies have given some support to these ideas, indicating that a person spends a much larger portion of a permanent change in income right away than of a one-time increase in wealth. The textbook discusses some of these studies.

Note that relaxing our initial assumptions will make the equation given above more difficult. Therefore, it is useful to express the general form of the above consumption function as:

image9.wmf

t

3

e

1

2

1

t

1

t

A

b

Y

b

Y

b

C

+

+

=

Again, consumption depends not just on current income, but on future income as well as the level of wealth. The strongest change on current consumption comes from a change in expected future labour income.

It should now be evident that this model provides an explanation why empirical studies have found little relationship between quarterly changes in income and consumption. If the change in income is considered temporary, then it should not have much impact on consumption.

II. The Permanent Income Hypothesis of Consumption

The permanent income hypothesis is an alternative theory of consumption (although in many ways it is very similar to the life-cycle hypothesis) developed by Milton Friedman. Like the life-cycle hypothesis, Friedman proposes that consumption depends on the long-run average of income, but the permanent income hypothesis offers a different explanation. Friedman postulates that consumption is some proportion (κ) of permanent income (Yp):

C = κ Yp

Permanent income is defined as expected average long-run income from labour and asset holdings. However, income in any given period is not necessarily going to be at the long-run average; there is a random component called transitory income (Yt) that will be positive in a "good" year and negative in a "bad" year. Actual income is given by:

Y = Yp + Yt

Basically, transitory income is the deviation of current income from the expected long-run average. The key to the permanent income hypothesis is that consumption depends only on permanent income, not transitory income, as shown in the above consumption function.

Friedman theorised that people used backwards looking (or adaptive) expectations to determine permanent income, and that this expectation was revised after each period:

image10.wmf

(

)

,

p

1

t

t

p

1

t

p

t

Y

Y

j

Y

Y

-

-

-

+

=

0 < j < 1

Basically, people expect some proportion j of the difference between actual income and last period's expectation of permanent income to represent a change in permanent income. For example, if this deviation in income this year (the deviation between actual income and expected permanent income) is $20,000 and j = 0.2, then the consumer believes that 20% of this change in income is a change in permanent income and will increase his expectation of permanent income by $4,000. The remaining 80% is considered transitory income. Since consumption only depends on permanent income, consumption will increase by

image11.wmf

(

)

(

)

000

4

Y

p

,

k

k

=

D

, not by κ(20,000). Consumption is therefore smoothed, as it was in the life-cycle hypothesis. Like the life-cycle hypothesis, the permanent income hypothesis shows that in the long-run, consumption is some proportion (κ) of actual income (since in the long run, expectations are correct and expected permanent income is equal to actual income). In the short run, consumption is not proportional to income, since during periods when transitory income is high, people will save more and thus APC will be lower during periods of high income. The opposite will happen during periods of low income. This result is consistent with the empirical studies that first shed doubt on the viability of the original Keynesian consumption function for long-run analysis. The model also explains why there is little connection between actual quarterly changes in income and consumption levels. Transitory changes in actual income will not affect consumption, in contrast to Keynes' theory.

� Note that, despite the completely historically inaccurate and frankly baffling urban myth that Hoover was laissez-faire and believed in the classical model, Hoover was actually a staunch interventionist and many of his policies and FDR's policies were similar.)

� Recall that mercantilism argued for government policy to direct a nation's consumption towards a desirable macro outcome. Keynes' monetary theory also re-introduced a link between money and wealth, which will be covered in Topic 6.

� A key issue, which was (and still is) largely ignored as US economists quickly adopted Keynes' ideas, was that Keynes' model was developed to explain the UK economy of the 1920s-30s. The UK situation was in many respects very different from the US and other nations. Some have argued that using Keynes' ideas as a general theory of all economies at all time periods is fundamentally flawed. Note that this is a different argument than the more common one that Keynes' model is simply wrong altogether.

� Spiegel, H. W. The Growth of Economic Thought, 3rd ed. (Durham: Duke University Press, 1999), 607.

� This logical absurdity of saving something by destroying it is best expressed by the quote from a US officer regarding the destruction, with many civilian casualties, of the city of Ben Tre during the Vietnam war: "It became necessary to destroy the town to save it [from the communist Viet Cong]".

� Note that this argument indicates that the counter-balancing we saw in the classical model that kept AD stable no longer occurs!

� Again, this reduces or eliminates the counter-balancing we saw in the classical demand theory--AD is therefore not fundamentally stable in the Keynesian model!

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