Unit 2: Fluctuations Models
Unit 2.1: Overview of Macroeconomic Models
In this section, we will go through a very broad overview of the two most important classes of macroeconomic models. We will then proceed to cover short-run (fluctuations) models in detail, covering long-run (growth) models later in the course.
Production Inputs
At its core, there are two kinds of inputs that contribute to production.
• Labor inputs can be changed in the short-run. • Capital inputs can be changed only in the long-run.
Thus, the key determinant of short-run output is employment. Capital is fixed in the short-run. While growth in capital is the essential element of long-run growth models, short-run models regard capital to be fixed.
Long-Run Models
Long-run models or growth models focus on investment and accumulation of capital. Some models extend the idea of investments to new ideas and technology. An important feature is that these models typically assume full employment of labor and focus on capital accumulation only.
Long-run growth models are typically framed as optimization models. They rely on a micro-level assumption that firms are out to maximize profits and that individuals make decisions to maximize their own well-being. Furthermore, because free market outcomes are efficient, the equilibrium outcome in growth models is efficient by definition. Of course, a key assumption of growth models is that markets are able to reach equilibrium.
Classical-type models have become increasingly sophisticated and nowadays focus on optimal growth and growth mechanisms, but a common feature is that output in these models is solely determined by the economy’s level of inputs, and these inputs are assumed to be fully employed. To state it differently, output in growth models is completely supply driven.
The real weakness of classical growth models is that they provide no explanation for business cycles and no explanation for the involuntary unemployment that accompanies them. Economic fluctuations are a fact of life in capitalist economies, and have been so ever since the dawn of free markets. It is in trying to explain business cycle fluctuations that economists started to deviate from the classical tradition.
Short-Run Models
Classical models predict full employment of resources, but deviations from full employment are obvious and are a fixture of market economies. Some economists in the 19th century and earlier had an idea that business cycle fluctuations might be better explained by demand-side fluctuations than by supply-side factors, whereas classical economics basically ignored the demand side of the economy. Early credit goes to Thomas Malthus, Simonde de Sismondi and Karl Marx for economic models that incorporated the possibility of imbalances between demand and supply as a driver of business cycles.
Following inspiration from these early contributors, John Maynard Keynes was really the first economist to develop a coherent theory of macroeconomic fluctuations and a way to explain why resources might not be fully employed. Keynes had two big insights.
First, while classical models assume that labor markets reach equilibrium and full employment, Keynes observed that the economy practically features a high degree of wage rigidity, sometimes called sticky wages. That is, the labor market may not necessarily reach equilibrium all the time, which could lead to surpluses of workers who want jobs but are unable to find them. Three main sources of sticky wages in the short-term are:
1. Long-term contracts 2. Efficiency wages1 3. Minimum wage laws
Practically, according to Keynes, the wage will be stuck above the equilibrium level, and thus the economy might not operate at full employment. Note that price increases in this model can help boost employment by reducing the real wage (since it is usually nominal wages that are sticky).
1 We say that employers pay efficiency wages when they pay above-market wages in order to boost retention and
Second, while classical models assume that markets always create equilibrium between demand and supply, Keynes observed that there may practically be imbalances and that aggregate demand might not be sufficient to purchase aggregate supply. Again, while classical models are completely supply-driven and assert that supply automatically generates demand, Keynes postulated that the economy might not generate enough demand to purchase all of the output that could be supplied. In this case, contrary to classical models, it might be demand rather than supply that effectively determines the economy’s GDP. One underlying source of imbalances between demand and supply can be price rigidities that prevent markets from reaching equilibrium. Later in the course, we will spend some time on the fundamentals of wage and price rigidities.
The question of which type of model is more appropriate is a deep and long-standing question that is nowhere near resolved. If there is anything close to consensus on the matter, it seems to be that demand-driven fluctuations models are more appropriate for the short-run, but that classical growth models provide a stronger set of tools for understanding the long-run.
Endogenous and Exogenous Variables
Models of how the economy functions typically include a large number of variables. But, practically, a model cannot explain how every relevant variable is determined.
An endogenous variable is determined within the model. For example, in a supply and demand model, the price is an endogenous variable. The model explains where the equilibrium price comes from. By contrast, an exogenous variable is determine by some force outside of the model. For example, while the weather might be an important factor in the market for apples, the supply and demand model does not explain where the weather comes from. It’s important, but it is not explained by the model. The weather is determined exogenously.
Models with a large number of endogenous variables are richer, because they can explain more and they allow more interdependence between various factors in the economy, but models are increasingly intractable to work with as the number of endogenous variables rises. We will work with three different fluctuations models in this unit, each one richer in the sense that it determines more endogenous variables. However, all three are fundamentally fluctuations models in the sense that GDP can fluctuate and need not be always at full-employment level.
1. Keynesian model – GDP is the only endogenous variable.
2. IS/LM model – Both GDP and the interest rate are endogenous. The IS/LM model allows us to add money and a financial sector to the Keynesian model.
Unit 2.2: The Keynesian Model
When the Great Depression hit in the 1930’s, Keynes’ fundamental insight was that the problem was, in fact, a shortfall in demand. Keynes hypothesized that employment and output were low because of insufficient spending on goods and services. The Keynesian model was the first model to formalize an equilibrium relationship between spending and output. More generally, it is the first macroeconomic model where demand features centrally.
The Keynesian model has only one endogenous variable. Our aim is to study the determinants of GDP, which we will abbreviate 𝑌𝑌. Remember that GDP is a measure both of a nation’s output and of a nation’s income. Production and income are dual sides of the same thing.
Consumption Spending
The biggest component of spending on goods and services in an economy is consumer spending. In turn, the most important determinant of consumer spending is income. If you want to know how much money someone is going to spend, the most important thing to know is his income.
The consumption function is a formula that relates consumer spending to income. We let 𝐶𝐶 stand for consumption spending and 𝑌𝑌 stand for income. The consumption function is:
𝐶𝐶 = 𝑎𝑎 + 𝑏𝑏𝑌𝑌
In this equation 𝑎𝑎 is called autonomous spending. This is the part of consumer spending that takes place irrespective of income. Even if income is 𝑌𝑌 = 0, consumer spending on basic necessities will still be 𝑎𝑎, financed by borrowing or by dipping into savings.
The marginal propensity to consume (MPC) is 𝑏𝑏 and we assume that 0 < 𝑏𝑏 < 1. The MPC is the amount by which spending rises for each additional $1 of income. For example, if 𝑏𝑏 = 0.9 then each additional $1 of income that the consumer earns is associated with an increase in spending of $0.90. If a person earned an additional $1000, then his consumption spending would rise by $900, with the other $100 saved. This makes sense – when people get additional money, they don’t spend it all. Some is spent but some is saved.2
We can illustrate the consumption function on a diagram.
2 The marginal propensity to save (MPS) is the amount by which savings rises for each $1 increase in income. By
Autonomous spending 𝑎𝑎 is the intercept – this is the level of consumer spending when income is zero. Beyond this, consumer spending rises as income rises, but not at a 1-for-1 rate. Each $1 increase in income is associated with an increase of 𝑏𝑏 in consumption spending. Mathematically, the MPC 𝑏𝑏 is the slope of the consumption function.
𝑏𝑏 =∆ consumption spending∆ income
Other Components of Spending
While consumer spending is the largest piece of spending in the economy, there are of course other components of spending on goods and services.
For the Keynesian model, we assume that investment spending, government spending and net exports are exogenous. They are important determinants of total spending, but they are determined outside of our model. In other words, we will treat investment spending, government spending and net exports as fixed.
Aggregate Expenditures
Aggregate expenditure (AE) is the total level of spending on all final goods and services produced in the economy. We know that this spending comes from four components – from consumption spending, investment spending, government spending and net exports. Thus, we can write:3
𝐴𝐴𝐴𝐴 = 𝐶𝐶 + 𝐼𝐼 + 𝐺𝐺 + 𝑁𝑁𝑁𝑁
Drawing a diagram of the aggregate expenditures function is simple. Since we know what consumer spending looks like, and the other components are fixed, we simply add 𝐼𝐼 + 𝐺𝐺 + 𝑁𝑁𝑁𝑁 to consumer spending in order to obtain total aggregate expenditures.
Equilibrium – The Keynesian Cross
The basic idea is that the level of spending on goods and services in an economy depends on the level of income earned in the economy. In other words, spending (AE) is a function of the economy’s income / output (GDP). The diagram below summarizes the Keynesian aggregate expenditures function.
3 This might look suspiciously like the GDP identity. The difference is that this definition of AE does not include
The intuition is simple. As an economy’s output / income rises, spending rises as well.
To see how to find equilibrium GDP graphically, we construct the 45-degree line, which represents all the points where output and spending are equal. It is constructed by drawing a 45 degree ray emanating from the origin. Again, this is just a geometrical construction to map out all the points where GDP and spending are equal.
We find the equilibrium in the Keynesian model graphically by combining the aggregate expenditures function together with the 45-degree line to obtain what economists call the
To understand how equilibrium is reached, let us consider economies with the two levels of GDP that are labeled on the diagram.
• At GDP1 the corresponding level of spending on goods and services is AE1
→ Spending is greater than output (AE1 > GDP1)
→ Firms are forced to reduce their inventories
→ Inventories decline
→ Firms take falling inventories as a signal to raise output
GDP1 cannot be the equilibrium level of GDP in this economy because spending is greater than output. Consumers cannot permanently buy more goods and services than what firms produce. Firms will increase their output higher than GDP1.4
• At GDP2 the corresponding level of spending on goods and services is AE2
→ Spending is less than output (AE2 < GDP2)
→ Firms are forced to add to their inventories
→ Inventories rise
→ Firms take rising inventories as a signal to reduce output
GDP2 cannot be the equilibrium level of GDP in this economy either, because spending is less than output. Firms will not permanently produce more output than what the economy purchases. Firms will reduce their output to something lower than GDP2.
4 This adjustment process ties back to price rigidities. We are assuming that firms facing excess demand will respond
The only equilibrium in this model occurs where spending and output are equal. Spending cannot permanently remain higher than output – firms will run out of inventories raise their output. And spending cannot permanently remain lower than output – firms will be adding excess inventories and reduce their output.
Keynesian equilibrium occurs where output and spending are equal. Graphically, this is the point where the aggregate expenditures line crosses the 45-degree line.
To reiterate the point, macroeconomic equilibrium in the Keyensian model occurs when spending and output are equal.
Numerical Example of the Keynesian Model
Suppose that expenditures in an economy are made up of the following components:
• 𝐶𝐶 = 200 + 0.75𝑌𝑌 • 𝐼𝐼 = 100
• 𝐺𝐺 = 50 • 𝑁𝑁𝑁𝑁 = 25
Aggregate expenditures are the sum of all components of spending:
𝐴𝐴𝐴𝐴 = 𝐶𝐶 + 𝐼𝐼 + 𝐺𝐺 + 𝑁𝑁𝑁𝑁
Now we have a model. Keynesian equilibrium occurs where GDP 𝑌𝑌 and spending 𝐴𝐴𝐴𝐴 are equal.
𝑌𝑌 = 𝐴𝐴𝐴𝐴
𝑌𝑌 = 𝐶𝐶 + 𝐼𝐼 + 𝐺𝐺 + 𝑁𝑁𝑁𝑁
To solve for equilibrium, we substitute our models for each of the components of expenditures.
𝑌𝑌 = 𝐶𝐶 + 𝐼𝐼 + 𝐺𝐺 + 𝑁𝑁𝑁𝑁
𝑌𝑌 = (200 + 0.75𝑌𝑌) + 100 + 50 + 25 𝑌𝑌 − 0.75𝑌𝑌 = 200 + 100 + 50 + 25
0.25𝑌𝑌 = 375 𝑌𝑌∗= 1500
The equilibrium level of GDP in this economy is 𝑌𝑌∗ = 1500. This is the level of output / income that creates a Keynesian equilibrium between output and spending.
General Solution
Let’s solve the Keynesian model in general. The components of aggregate expenditure are:
• 𝐶𝐶 = 𝑎𝑎 + 𝑏𝑏𝑌𝑌
• 𝐼𝐼 is fixed exogenously • 𝐺𝐺 is fixed exogenously • 𝑁𝑁𝑁𝑁 is fixed exogenously
Keynesian equilibrium occurs where output and spending are equal:
𝑌𝑌 = 𝐴𝐴𝐴𝐴
𝑌𝑌 = 𝐶𝐶 + 𝐼𝐼 + 𝐺𝐺 + 𝑁𝑁𝑁𝑁
𝑌𝑌 = (𝑎𝑎 + 𝑏𝑏𝑌𝑌) + 𝐼𝐼 + 𝐺𝐺 + 𝑁𝑁𝑁𝑁 𝑌𝑌 − 𝑏𝑏𝑌𝑌 = 𝑎𝑎 + 𝐼𝐼 + 𝐺𝐺 + 𝑁𝑁𝑁𝑁
𝑌𝑌(1 − 𝑏𝑏) = 𝑎𝑎 + 𝐼𝐼 + 𝐺𝐺 + 𝑁𝑁𝑁𝑁 𝑌𝑌∗ = � 1
1 − 𝑏𝑏�(𝑎𝑎 + 𝐼𝐼 + 𝐺𝐺 + 𝑁𝑁𝑁𝑁)
Multipliers
Generally, the spending multiplier is the change in equilibrium GDP that results from an additional $1 of spending. Often, the question is motivated from a policy perspective, so we think about how much an additional $1 of government spending will raise equilibrium GDP; but any kind of spending will work. The basic result is that an additional $1 of spending raises equilibrium GDP by more than $1 in the Keynesian model. We will describe the multiplier effect verbally, graphically and mathematically.
Intuitively, the idea is as follows. Consider an economy where the MPC is 0.9, and suppose that the government pays a carpenter $1000 to build a playground. This new playground immediately increases GDP by $1000. Since 𝑀𝑀𝑀𝑀𝐶𝐶 = 0.9, the carpenter turns around and spends $900 of this money (saving the other $100), adding another $900 to GDP. This $900 provides income to someone, who spends $810 (90% of the additional $900 of income). This adds $810 to GDP and provides $810 of income to someone, who will go on to spend $729 and add $729 to GDP, etc…
Overall, the total increase in GDP is much more than the initial $1000. This is the multiplier effect. If West Chester University shuts down, the cost to the town’s economy will be much greater than the direct loss of expenditures from university students – the multiplier effect will compound it.
To calculate the multiplier effect quantitatively, recall from the previous section that the equilibrium GDP in the Keynesian model is:
𝑌𝑌∗ = � 1
1 − 𝑏𝑏�(𝑎𝑎 + 𝐼𝐼 + 𝐺𝐺 + 𝑁𝑁𝑁𝑁)
Thus, the increase in equilibrium GDP 𝑌𝑌∗ when the government increases its spending by 1 is:
𝜕𝜕𝑌𝑌∗
𝜕𝜕𝐺𝐺 = 1 1 − 𝑏𝑏
For the numerical example of finding Keynesian equilibrium that we solved in an earlier section,
the MPC was 𝑏𝑏 = 0.75, meaning that the multiplier is 1
1−0.75= 4.
We can confirm this answer by going back to our numerical example. Let’s find the equilibrium GDP in this model again, but after raising government spending from 𝐺𝐺 = 50 to 𝐺𝐺 = 51.
𝑌𝑌 = 𝐴𝐴𝐴𝐴
𝑌𝑌 = 𝐶𝐶 + 𝐼𝐼 + 𝐺𝐺 + 𝑁𝑁𝑁𝑁
𝑌𝑌 = (200 + 0.75𝑌𝑌) + 100 + 51 + 25 𝑌𝑌 − 0.75𝑌𝑌 = 200 + 100 + 51 + 25
0.25𝑌𝑌 = 376 𝑌𝑌∗= 1504
This illustrates the multiplier effect. The original equilibrium GDP is 𝑌𝑌∗= 1500. But a $1 increase in government spending raises equilibrium GDP from 𝑌𝑌∗= 1500 to 𝑌𝑌∗ = 1504. Because the multiplier is 4, each additional $1 of government spending raises GDP by $4. A $100 increase in government spending would raise GDP by $400 in this economy. Conversely, to raise GDP by $1 million, only a $250,000 expenditure is required.
Keynesian Model with Taxes
We can modify the Keynesian model slightly to incorporate taxes. Let’s suppose that consumers in this economy pay taxes equal to 𝑇𝑇. In this case, consumption depends not on total income 𝑌𝑌 but only on after-tax, disposable income 𝑌𝑌 − 𝑇𝑇. The components of aggregate expenditures are:
Equilibrium GDP in the Keynesian model occurs where output and spending are equal:
𝑌𝑌 = 𝐴𝐴𝐴𝐴
𝑌𝑌 = 𝐶𝐶 + 𝐼𝐼 + 𝐺𝐺 + 𝑁𝑁𝑁𝑁
𝑌𝑌 = �𝑎𝑎 + 𝑏𝑏(𝑌𝑌 − 𝑇𝑇)� + 𝐼𝐼 + 𝐺𝐺 + 𝑁𝑁𝑁𝑁 𝑌𝑌 = 𝑎𝑎 + 𝑏𝑏𝑌𝑌 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼 + 𝐺𝐺 + 𝑁𝑁𝑁𝑁 𝑌𝑌 − 𝑏𝑏𝑌𝑌 = 𝑎𝑎 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼 + 𝐺𝐺 + 𝑁𝑁𝑁𝑁 𝑌𝑌(1 − 𝑏𝑏) = 𝑎𝑎 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼 + 𝐺𝐺 + 𝑁𝑁𝑁𝑁
𝑌𝑌∗ = � 1
1 − 𝑏𝑏�(𝑎𝑎 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼 + 𝐺𝐺 + 𝑁𝑁𝑁𝑁)
The tax multiplier is the change in equilibrium GDP that results from a $1 increase in taxes. Note that the tax multiplier is negative. A $1 increase in taxes reduces consumption spending and therefore reduces GDP. For our model, the tax multiplier is:
𝜕𝜕𝑌𝑌∗
𝜕𝜕𝑇𝑇 = − 𝑏𝑏 1 − 𝑏𝑏
Recall from the previous section that the government spending multiplier is:
𝜕𝜕𝑌𝑌∗
𝜕𝜕𝐺𝐺 = 1 1 − 𝑏𝑏
It is interesting to note that the tax multiplier is smaller in absolute value than the government spending multiplier. For example, if the MPC is 𝑏𝑏 = 0.75, then the government spending multiplier is:
𝜕𝜕𝑌𝑌∗
𝜕𝜕𝐺𝐺 = 1
1 − 0.75 = 4
The tax multiplier is:
𝜕𝜕𝑌𝑌∗
𝜕𝜕𝑇𝑇 = −
0.75
1 − 0.75 = −3
The answer is simple – When the government spends $1, the whole $1 goes into the economy. When taxes are cut by $1, the recipient spends only some part of the tax cut, with the rest of the money saved. Thus, in the Keynesian model, government spending gives you more “bang for your buck” than an equivalent reduction in taxes.
Keynesian Model with Endogenous Imports
As a final example of working with Keynesian models, we will consider a model where spending on net exports falls as income rises. This is a reasonable assumption because people buy more imports as they get richer. Our model is now:
• 𝐶𝐶 = 𝑎𝑎 + 𝑏𝑏𝑌𝑌
• 𝐼𝐼 is fixed exogenously • 𝐺𝐺 is fixed exogenously • 𝑁𝑁𝑁𝑁 = 𝑄𝑄 − 𝜙𝜙𝑌𝑌
In this model, 𝜙𝜙 is called the marginal propensity to import. It represents the increase in imports (decline in net exports) resulting from each $1 of new income.
We solve the model using the same approach that we did before. Keynesian equilibrium occurs where output and spending are equal:
𝑌𝑌 = 𝐴𝐴𝐴𝐴
𝑌𝑌 = 𝐶𝐶 + 𝐼𝐼 + 𝐺𝐺 + 𝑁𝑁𝑁𝑁
We now substitute our models for each component of spending and solve for equilibrium GDP.
𝑌𝑌 = (𝑎𝑎 + 𝑏𝑏𝑌𝑌) + 𝐼𝐼 + 𝐺𝐺 + (𝑄𝑄 − 𝜙𝜙𝑌𝑌) 𝑌𝑌 − 𝑏𝑏𝑌𝑌 + 𝜙𝜙𝑌𝑌 = 𝑎𝑎 + 𝐼𝐼 + 𝐺𝐺 + 𝑄𝑄
𝑌𝑌(1 − 𝑏𝑏 + 𝜙𝜙) = 𝑎𝑎 + 𝐼𝐼 + 𝐺𝐺 + 𝑄𝑄 𝑌𝑌∗ = � 1
1 − 𝑏𝑏 + 𝜙𝜙�(𝑎𝑎 + 𝐼𝐼 + 𝐺𝐺 + 𝑄𝑄)
For this model, the government spending multiplier is:
𝜕𝜕𝑌𝑌∗
𝜕𝜕𝐺𝐺 = 1 1 − 𝑏𝑏 + 𝜙𝜙
Recall the government spending multiplier in the standard model is 1
Why is the spending multiplier smaller in our new model with endogenous imports? In this model, when spending and incomes rise, some of this additional income gets sucked into increased imports rather than going back to domestic spending. For this reason, the total increase in GDP is smaller than if there were no import spending to consider.
Analytically, the important point to take away from this example is that the Keynesian model actually can be made quite rich, but ultimately it is always solved in the same way. The components of aggregate expenditure might be complicated functions of GDP, but the basic essence of a Keyneisan model is that equilibrium occurs where output (GDP) and spending (AE) are equal.
Policy and Controversy
The Keynesian model is the motivation for fiscal policy. When the government increases spending, or lowers personal taxes, the result is an increase in aggregate expenditures on goods and services and, consequently, an increase in equilibrium GDP. In fact, there is a multiplier effect – according to the Keynesian model, increases in government spending ultimately raise GDP by an amount larger than the amount of the spending increase.
Expansionary fiscal policy is raising government spending or reducing taxes in an effort to increase equilibrium GDP. Contractionary fiscal policy is reducing government spending or raising taxes in an effort to reduce equilibrium GDP.
To return back to where we started in the beginning of the section, the historical context for the Keynesian model was the Great Depression. Keynes had a straightforward solution. He said that the problem was an insufficient level of spending – in other words, not enough demand. The solution, according to Keynes was to increase spending. Government spending would generate more sales, more production, and higher incomes. People would spend most of this money, leading to even more increases in economic activity, etc…
The logic is appealing, but it remains controversial. Notice that, in this entire model, there is nothing about supply – How is all of this output actually produced? The AD/AS model will attempt to incorporate the labor market and employment, but what about investments in capital and growth in technology? The Keynesian model is completely silent on these issues.
Unit 2.3: IS/LM Model
The IS/LM model was developed on the back of a napkin – true story.
One weakness of the Keynesian model is that it says nothing about the financial / money sector of the economy. A British economist who was a critic of Keynes was sitting at lunch one day and raised an interesting criticism. In the Keynesian model, when GDP rises, the demand for money rises, which pushes the interest rate up. But a higher interest rate reduces investment spending, which in turn reduces GDP (with a multiplier). This reduction in GDP lowers the demand for money and reduces the interest rate. The critic claimed that there was essentially an “indeterminacy” in the Keynesian model if we include interest rates in our analysis. GDP affects the interest rate, but the interest rate in turn affects GDP.
Another economist at the lunch was John Hicks. He said that we can expand the Keynesian model to incorporate financial markets and the interest rate. The result is not indeterminate. Instead, we need to find an equilibrium where the goods / spending market and the financial markets are
simultaneously in equilibrium. He sketched a graph, and the IS/LM model was born.5 The IS/LM model involves two endogenous variables. While the Keynesian model determines equilibrium GDP only, the IS/LM model determines both GDP and the interest rate.
Before we begin, we need to review a basic relationship from principles.
Interest rates and Investment
An important relationship in macroeconomics is that investment spending falls when the interest rate rises. To understand why this relationship holds, remember that the macroeconomic definition of investment refers to physical investments like new plant machinery and equipment. It does not refer to financial “investments” like buying stocks or bonds.
To understand why investment spending falls when the interest rate rises, consider the two ways that firms can finance investments – by borrowing money or by using its own cash reserves.
If the firm finances investment spending by borrowing money, then the relationship is obvious. When the interest rate is high, the cost of borrowing money is high, and so firms are less likely to undertake investment projects.
5 The name IS/LM is a historical artifact. IS stands for “investment/savings”. LM stands for “liquidity/money”. A
Even if the firm finances investment spending by using its own cash, the relationship is still the same. An increase in the interest rate means that the firm will find it more profitable to buy financial assets, relative to using the cash to invest in new factories and machines. To put it in basic finance terms, a higher interest rate reduces the net present value of investment projects. Lower interest rates mean that the opportunity cost of the firm’s cash is low (not very profitable to put the money in financial assets), so the firm is inclined to use its cash to undertake investment spending. Again, higher interest rates mean less investment.
The IS Curve
The starting point for deriving the IS curve is the Keynesian model from the previous section. Consumption spending is a linear function of after-tax income.
𝐶𝐶 = 𝑎𝑎 + 𝑏𝑏(𝑌𝑌 − 𝑇𝑇)
The key modification is the investment function. We assume that investment is a linear function of the interest rate, which is denoted 𝑟𝑟.
𝐼𝐼 = 𝐼𝐼0− 𝑑𝑑𝑟𝑟
Here, 𝐼𝐼0 is the intercept of the investment function and −𝑑𝑑 is the slope. The slope is negative. Each unit increase in the interest rate 𝑟𝑟reduces investment spending by 𝑑𝑑. In this function, 𝑑𝑑 is basically the sensitivity of investment spending to changes in the interest rate.
Government spending and net exports are exogenous, as with our previous model.
• 𝐺𝐺 is exogenous • 𝑁𝑁𝑁𝑁 is exogenous
Keynesian equilibrium occurs where output and spending are equal:
𝑌𝑌 = 𝐴𝐴𝐴𝐴
𝑌𝑌 = 𝐶𝐶 + 𝐼𝐼 + 𝐺𝐺 + 𝑁𝑁𝑁𝑁
For Keynesian equilibrium, we substitute in our models for each of the spending components:
This equation characterizes the IS relationship, and it has two endogenous variables – GDP 𝑌𝑌 and the interest rate 𝑟𝑟. The IS curve is drawn with the interest rate 𝑟𝑟 on the vertical axis and with GDP
𝑌𝑌 on the horizontal axis, so we should solve this relationship for 𝑟𝑟 in order to write the IS relation in slope-intercept form.
𝑌𝑌 = [𝑎𝑎 + 𝑏𝑏(𝑌𝑌 − 𝑇𝑇)] + [𝐼𝐼0− 𝑑𝑑𝑟𝑟] + 𝐺𝐺 + 𝑁𝑁𝑁𝑁
𝑌𝑌 + 𝑑𝑑𝑟𝑟 = 𝑎𝑎 + 𝑏𝑏𝑌𝑌 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0+ 𝐺𝐺 + 𝑁𝑁𝑁𝑁
𝑑𝑑𝑟𝑟 = 𝑎𝑎 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0 + 𝐺𝐺 + 𝑁𝑁𝑁𝑁 − 𝑌𝑌 + 𝑏𝑏𝑌𝑌
𝑑𝑑𝑟𝑟 = 𝑎𝑎 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0 + 𝐺𝐺 + 𝑁𝑁𝑁𝑁 − (1 − 𝑏𝑏)𝑌𝑌
𝑟𝑟 =𝑎𝑎 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼𝑑𝑑0 + 𝐺𝐺 + 𝑁𝑁𝑁𝑁− �1 − 𝑏𝑏𝑑𝑑 � 𝑌𝑌
This relationship is now in the form of the equation of a line. The intercept is 𝑎𝑎−𝑏𝑏𝑏𝑏+𝐼𝐼0+𝐺𝐺+𝑁𝑁𝑁𝑁 𝑑𝑑 and the slope is − �1−𝑏𝑏
𝑑𝑑 �. The slope is negative, so the IS curve is downward sloping.
If we graph the relationship, we have the IS curve.
The economic intuition that underlies the IS curve is simple. At higher interest rates, there is less investment spending, and so equilibrium GDP is lower.
Shifts of the IS Curve
Recall that the slope-intercept version of the IS curve is:
𝑟𝑟 =𝑎𝑎 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼𝑑𝑑0+ 𝐺𝐺 + 𝑁𝑁𝑁𝑁− �1 − 𝑏𝑏𝑑𝑑 � 𝑌𝑌
Increases in autonomous consumption 𝑎𝑎, autonomous investment 𝐼𝐼0, government spending 𝐺𝐺 and net exports 𝑁𝑁𝑁𝑁 increase the intercept of the IS curve and shift the IS curve right.
An increase in taxes 𝑇𝑇 reduces the value of the intercept and shifts the IS curve left.
The table below shows how changes in exogenous variables affect the IS curve.
Change Shift in IS curve
Increase 𝑎𝑎 Shift IS right
Increase 𝑇𝑇 Shift IS left
Increase 𝐼𝐼0 Shift IS right
Increase 𝐺𝐺 Shift IS right
Increase 𝑁𝑁𝑁𝑁 Shift IS right
Declines in any of these exogenous variables obviously shift the IS curve in the opposite direction. The intuition behind the shifts is that exogenous increases in spending create a higher equilibrium GDP for any value of the interest rate, and thus these increases shift the whole IS schedule to the right.
Changes in the MPC 𝑏𝑏 and in the interest sensitivity of investment 𝑑𝑑 are more complex because they change both the intercept and the slope of the IS curve.
One special case – when 𝑑𝑑 = 0, the IS curve is vertical. This makes intuitive sense. If investment does not depend on the interest rate, then changes in the interest rate do not impact spending and do not impact equilibrium GDP. The IS curve is vertical in this case – changes in interest rate have no impact on GDP.
The LM Curve
The IS curve gives us a whole set of possible equilibria in the output market. If the interest rate is low, equilibrium output in the Keynesian expenditure model is high and if the interest rate is high, then equilibrium output falls. The IS curve cannot uniquely determine the equilibrium because it gives a set of possible equilibria at different interest rates.
Along similar lines, the LM curve gives us a set of possible equilibria in the money market.
There are two sides of the money market. The demand side is essentially a portfolio balance problem. By demand for money, we mean the public’s desire to hold wealth as money (cash balances) instead of holding their wealth in the form of other financial assets. This demand depends on a few important factors:
• Interest rate – As the interest rate rises, demand for cash balances falls since individuals will prefer to keep their wealth in the form of financial assets which pay interest.
• GDP (income) – As GDP increases, demand for cash balances rises since consumers with higher income spend more, and will hold more money in order to finance their purchases.
• Other exogenous factors – There are other things that make people want to hold some money balances – maybe precautionary savings in case of an emergency, for example.
With this in mind, we will express demand for money as follows:
demand for money = 𝑚𝑚0 − ℎ𝑟𝑟 + 𝑘𝑘𝑌𝑌
In words, demand for money is a linear function of the interest rate and income.
• The intercept 𝑚𝑚0 represents exogenous factors that create a demand for money.
• ℎ is the sensitivity of money demand to the interest rate 𝑟𝑟. An increase in the interest rate reduces demand for money. The parameter ℎ measures the sensitivity of the relationship.
Turning to the other side of the market, the supply of money at any point in time is fixed by the central bank. If we let 𝑀𝑀 denote the nominal supply of money (the number of dollars in circulation) and we let 𝑀𝑀 denote the price level, then the supply of money expressed in real terms is:
supply of money =𝑀𝑀𝑀𝑀
The expression for real value makes intuitive sense. For example, if the price level doubles from
𝑀𝑀 = 1 to 𝑀𝑀 = 2, then the real value of the money supply is cut in half.
Equilibrium in the money market occurs where supply and demand for money are equal. Substituting in our formulations for each piece, equilibrium is defined as:
supply of money = demand for money 𝑀𝑀
𝑀𝑀 = 𝑚𝑚0− ℎ𝑟𝑟 + 𝑘𝑘𝑌𝑌
As before, we want to graph this relationship with the interest rate 𝑟𝑟 on the vertical axis and with GDP 𝑌𝑌 on the horizontal axis. We write the equilibrium condition in slope-intercept form by solving for 𝑟𝑟.
𝑀𝑀
𝑀𝑀 = 𝑚𝑚0− ℎ𝑟𝑟 + 𝑘𝑘𝑌𝑌 ℎ𝑟𝑟 = 𝑚𝑚0−𝑀𝑀𝑀𝑀 + 𝑘𝑘𝑌𝑌
𝑟𝑟 = �𝑚𝑚ℎ −0 ℎ𝑀𝑀� + �𝑀𝑀 𝑘𝑘ℎ� 𝑌𝑌
This expression characterizes the LM relationship – equilibrium in the money market. Expressed
in slope-intercept form, the intercept of the LM curve is �𝑚𝑚0 ℎ −
𝑀𝑀
ℎ𝑃𝑃� and the slope is � 𝑘𝑘
ℎ�. The slope of the LM curve is positive – It is upward sloping.
The economic intuition is a bit less obvious than the intuition for the downward slope of the IS curve. The basic idea is this – When GDP rises, demand for money rises because people are richer.
But the supply of money is fixed at 𝑀𝑀
𝑃𝑃. Thus, the only way to create equilibrium in the market is for interest rate to rise – because that reduces the demand for money enough to restore equilibrium. Basically, the way to think about the LM curve is that it’s a set of equilibrium points in the money market. When income is very high, we also need a high interest rate in order to generate an equilibrium between demand for money and the fixed supply of money.
Shifts of the LM Curve
Recall that the slope-intercept form of the LM curve is:
𝑟𝑟 = �𝑚𝑚ℎ −0 ℎ𝑀𝑀� + �𝑀𝑀 𝑘𝑘ℎ� 𝑌𝑌
Changes in exogenous demand for money 𝑚𝑚0, the money supply 𝑀𝑀 and the price level 𝑀𝑀 change the intercept of the LM curve.
• An increase in 𝑚𝑚0 increases the value of the intercept and shifts the LM curve left • An increase in 𝑀𝑀 lowers the value of the intercept and shifts the LM curve right • An increase in 𝑀𝑀 increases the value of the intercept and shifts the LM curve left
Summarizing on a table:
Change Shift in LM curve
Increase 𝑚𝑚0 Shift LM left
Increase 𝑀𝑀 Shift LM right
Changes in the interest-sensitivity of money demand ℎ and changes in the income-sensitivity of money demand 𝑘𝑘 change the slope of the LM curve, which is 𝑘𝑘
ℎ.
There are two special cases. When 𝑘𝑘 = 0, meaning that demand for money does not depend on income, the LM curve is horizontal (slope of zero). When ℎ = 0, meaning that demand for money does not depend on the interest rate, the LM curve is vertical (infinite slope).
IS/LM Equilibrium
The IS/LM model explains the determination of two endogenous variables – GDP 𝑌𝑌 and the interest rate 𝑟𝑟.
The IS curve gives a set of possible equilibrium points for the output/spending side of the economy. When the interest rate is low, investment spending is high and so equilibrium GDP is higher. These various equilibrium points are summarized on the IS curve.
The IS/LM equilibrium occurs at the intersection of the IS and LM curves – at the interest rate and GDP where both the goods market and the money market are in equilibrium. In other words, IS/LM equilibrium is a joint equilibrium of the goods market and the financial market. The only GDP / interest rate pair where this occurs is where the IS and LM curves cross.
In the graph above, the equilibrium GDP and interest rate 𝑌𝑌∗ and 𝑟𝑟∗ is the only combination of GDP and the interest rate that is consistent both with equilibrium in the output market (all the points on the IS curve) and with equilibrium in the money market (all the points on the LM curve). The equilibrium that satisfies both conditions is unique, which was Hicks’ key insight.
For example, if the equilibrium interest rate were lower than 𝑟𝑟∗, both sectors of the economy could not simultaneously be in equilibrium. The equilibrium GDP would be higher in the output market, since lower interest rates stimulate investment. But the equilibrium level of GDP required to equilibrate the money market would be lower. Thus, the two markets cannot be jointly in equilibrium with each other at interest rates other than 𝑟𝑟∗.
Fiscal Policy in the IS/LM Model
The IS/LM model is a shorthand way to summarize a lot of information on a single diagram. The model has become very useful for policy analysis.
Equilibrium GDP rises and the equilibrium interest rate rises. The utility of the IS/LM model is that we can analyze this change in both markets simultaneously without switching back and forth between the Keynesian cross and a money-market analysis. The IS/LM model is a simplifying device where we can determine joint equilibrium in a single step.
Incidentally, this diagram illustrates the well-known crowding out phenomenon. When government spending rises, the interest rate rises, which in turn reduces investment spending. We say in this case that government spending “crowds out” some private investment spending.
Monetary Policy in the IS/LM Model
Suppose that the Fed increases the money supply (expansionary monetary policy). Based on our chart from earlier in the section, an increase in the money supply 𝑀𝑀 shifts the LM curve to the right, from LM to LM', which we illustrate on the diagram below.
Simultaneous Shifts of IS and LM
Suppose that the government conducts both expansionary fiscal policy and expansionary monetary policy simultaneously. The increase in government spending 𝐺𝐺 shifts the IS curve to the right, while the increase in money supply 𝑀𝑀 shifts the LM curve to the right.
These shifts are illustrated on the diagram below.
Comparing the two equilibrium points, we can see that the equilibrium GDP rises. But the change in the equilibrium interest rate is indeterminate – it could rise, fall or stay the same depending on whether the IS curve or the LM curve shifts by a larger amount. This is generally true. When both curves shift simultaneously, you can determine what happens to only one of the two endogenous variables.
Changes in the Price Level
Suppose that the price level rises. Using the chart from earlier in the section, an increase in 𝑀𝑀 shifts the LM curve to the left, as shown below.
Solving the IS/LM Model Algebraically
Graphical analysis is a powerful tool, but sometimes there is value in being more precise and providing analytical answers. In this section, we will solve for the equilibrium GDP in the IS/LM model. Recall that the IS curve is characterized by the Keynesian equilibrium condition.
𝑌𝑌 = 𝐴𝐴𝐴𝐴
𝑌𝑌 = 𝐶𝐶 + 𝐼𝐼 + 𝐺𝐺 + 𝑁𝑁𝑁𝑁
Substituting in our model for each component, we then rearrange slightly.
𝑌𝑌 = [𝑎𝑎 + 𝑏𝑏(𝑌𝑌 − 𝑇𝑇)] + [𝐼𝐼0− 𝑑𝑑𝑟𝑟] + 𝐺𝐺 + 𝑁𝑁𝑁𝑁
𝑌𝑌 = 𝑎𝑎 + 𝑏𝑏𝑌𝑌 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0+ 𝐺𝐺 + 𝑁𝑁𝑁𝑁 − 𝑑𝑑𝑟𝑟
This equation characterizes the locus of equilibrium points given by the IS relationship.
The LM curve is characterized by equating the supply of money with the demand for money. We solve this relationship for 𝑟𝑟.
𝑀𝑀
𝑀𝑀 = 𝑚𝑚0− ℎ𝑟𝑟 + 𝑘𝑘𝑌𝑌 𝑟𝑟 = �𝑚𝑚ℎ −0 ℎ𝑀𝑀� + �𝑀𝑀 𝑘𝑘ℎ� 𝑌𝑌
The IS/LM equilibrium GDP occurs where both the IS and the LM relationships are satisfied. The easiest way to solve the system is to plug this expression for 𝑟𝑟 into the IS curve from above:
𝑌𝑌 = 𝑎𝑎 + 𝑏𝑏𝑌𝑌 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0+ 𝐺𝐺 + 𝑁𝑁𝑁𝑁 − 𝑑𝑑𝑟𝑟
𝑌𝑌 = 𝑎𝑎 + 𝑏𝑏𝑌𝑌 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0+ 𝐺𝐺 + 𝑁𝑁𝑁𝑁 − 𝑑𝑑 ��𝑚𝑚ℎ −0 ℎ𝑀𝑀� + �𝑀𝑀 𝑘𝑘ℎ� 𝑌𝑌�
We can now expand, and solve the expression for the IS/LM equilibrium level of GDP.
𝑌𝑌 = 𝑎𝑎 + 𝑏𝑏𝑌𝑌 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0+ 𝐺𝐺 + 𝑁𝑁𝑁𝑁 − �𝑑𝑑ℎ� 𝑚𝑚0+ �𝑑𝑑ℎ�𝑀𝑀𝑀𝑀 − �𝑑𝑑𝑘𝑘ℎ � 𝑌𝑌
𝑌𝑌 − 𝑏𝑏𝑌𝑌 + �𝑑𝑑𝑘𝑘ℎ � 𝑌𝑌 = 𝑎𝑎 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0+ 𝐺𝐺 + 𝑁𝑁𝑁𝑁 − �𝑑𝑑ℎ� 𝑚𝑚0+ �𝑑𝑑ℎ�𝑀𝑀𝑀𝑀
𝑌𝑌 �1 − 𝑏𝑏 +𝑑𝑑𝑘𝑘ℎ � = 𝑎𝑎 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0+ 𝐺𝐺 + 𝑁𝑁𝑁𝑁 − �𝑑𝑑ℎ� 𝑚𝑚0+ �𝑑𝑑ℎ�𝑀𝑀𝑀𝑀
𝑌𝑌∗ = � 1
1 − 𝑏𝑏 + 𝑑𝑑𝑘𝑘ℎ � �𝑎𝑎 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0+ 𝐺𝐺 + 𝑁𝑁𝑁𝑁 − � 𝑑𝑑
ℎ� 𝑚𝑚0+ � 𝑑𝑑 ℎ�
Multipliers in the IS/LM model
The expression above characterizes equilibrium GDP in the IS/LM model analytically, and enables us to study rigorously how changes in economic conditions impact GDP.
The government spending multiplier is the increase in GDP that results from a $1 increase in government spending. Using the expression for equilibrium GDP given above, we can compute the IS/LM spending multiplier by taking the derivative:
𝜕𝜕𝑌𝑌∗
𝜕𝜕𝐺𝐺 =
1 1 − 𝑏𝑏 + 𝑑𝑑𝑘𝑘ℎ
Remember that, in the Keynesian model, the government spending multiplier is:
𝜕𝜕𝑌𝑌∗
𝜕𝜕𝐺𝐺 = 1 1 − 𝑏𝑏
Because 𝑑𝑑𝑘𝑘
ℎ > 0, it follows that the IS/LM spending multiplier is smaller than the simple Keynesian spending multiplier.
Why? In the Keyensian model, when the government raises spending, aggregate expenditures rise and so equilibrium GDP rises with a multiplier. And that’s the end of the story. But the IS/LM model incorporates the money market and interest rates. In this case, higher government spending leads to higher equilibrium interest rates, which chokes off some investment and offsets part of the increase in GDP. By taking into account the impact of government spending on interest rates and investment spending, the IS/LM model produces a lower spending multiplier than the simple Keynesian model does.6
The money multiplier is the increase in GDP that results from each 1-unit increase in the real
money supply 𝑀𝑀
𝑃𝑃. Using the expression for equilibrium GDP to compute the money multiplier:
𝜕𝜕𝑌𝑌∗
𝜕𝜕 𝑀𝑀𝑀𝑀 = � 𝑑𝑑 ℎ� �
1 1 − 𝑏𝑏 + 𝑑𝑑𝑘𝑘ℎ �
The IS/LM model can be made richer with more complex models of various components of aggregate expenditures. But the essential feature of an IS/LM model is that the endogenous variables are GDP and the interest rate, and these richer models are solved in the same way.
6 As a sidenote, it tends to be the case that extensions to the simple Keynesian model mostly reduce the value of the
Unit 2.4: AD/AS Model
Neither the Keynesian nor the IS/LM model incorporates the production side of the economy. These are demand-side models about purchases of goods and services. In this section, we introduce the aggregate demand / aggregate supply (AD/AS) model, which integrates production and supply into our model of macroeconomic fluctuations. In doing so, we will add a third endogenous variable, which relates the demand and supply sides of the macroeconomy – the price level. The AD/AS model has three endogenous variables – GDP, the interest rate and the price level.
The Aggregate Demand Curve
The aggregate demand curve describes the relationship between price and output in the IS/LM model, which is basically the “demand” side of the economy – how much output the economy wants to purchase, as determined by goods/services markets and by financial markets.
In the IS/LM model, when the price level increases, the LM curve shifts to the left, and as a result the equilibrium level of GDP falls.
The aggregate demand curve is just a set of equilibrium points from the IS/LM model at different price levels. Higher price levels lead to lower equilibrium GDP from the perspective of the demand side of the economy.
Once we allow the price level to vary endogenously, there is now a whole set of possible equilibria in the IS/LM model – any point on the AD curve is consistent with demand-side equilibrium. Thus, we need to add a supply relationship in order to find a macroeconomic equilibrium.
Determination of Aggregate Supply – The Labor Market
The aggregate demand relationship basically describes the level of output that an economy
demands, from the expenditure / purchases side. Turning to the supply side, the level of output that an economy can produce depends on two kinds of inputs.
• Labor inputs, which can change in the short-run
• Capital inputs, like factories and machines, which can change only in the long-run
Thus, the key determinant of short-run supply is labor. Capital accumulation is the subject of long-run growth models, which are fundamentally different. Since our focus here is on short-long-run fluctuations, we take the level of capital inputs as given and focus on employment of labor.
The market for workers is like any other market, with a supply and demand.
• Labor supply is the number of workers who are willing to work for a particular wage. The labor supply curve is upward sloping. Higher wages make more people willing to work and make workers willing to work more hours.
The labor market and its equilibrium are illustrated below.
We make one important point immediately. Labor supply and demand depend on the real wage, which is different from the nominal money wage. The nominal wage is 𝑤𝑤 and the price level is 𝑀𝑀. Given these, the real wage is 𝑤𝑤
𝑃𝑃. For example, if the nominal wage stays the same, but the price level doubles, then the real wage is cut in half.
The supply and demand for labor depend on the real wage, not on the nominal wage. That is, economic decisions are made based on the actual, purchasing-power value of the wage paid, not on the nominal number of dollars. The equilibrium in this model is for 𝐿𝐿∗ workers to be employed at an equilibrium real wage 𝑤𝑤
𝑃𝑃 ∗
.
Changes in the wage rate cause a movement along the labor supply and demand curves; they do not shift the curves. Of course, changes in the exogenous factors impacting the labor market can shift labor supply or demand.
The labor supply curve describes the number of workers who want to work at a given real wage. If there is immigration, labor supply rises (shifts right). Policy changes that alter willingness to work, such as restructuring welfare programs, unemployment compensation or the tax structure, would also impact labor supply. As a final example, cultural factors such as acceptance of women in the workplace can impact labor supply.
The Aggregate Supply Curve with Flexible Wages
Suppose that the labor market is in equilibrium, with 𝐿𝐿∗ workers employed at a real wage 𝑤𝑤 𝑃𝑃 ∗
, as
illustrated in the diagram below.
Now, suppose that there is a change in the price level. As long as the nominal wage 𝑤𝑤 is free to change, then the market will remain in equilibrium with 𝐿𝐿∗ workers employed. For example, suppose that the equilibrium nominal wage is 𝑤𝑤 = 10 when the price level is 𝑀𝑀 = 1. Then the price level increases to 𝑀𝑀 = 2. As long as the nominal wage is free to rise to 𝑤𝑤 = 20, then the labor market remains in equilibrium at the same real wage as before. The critical assumption here, of course, is that nominal wages are flexible.
To restate the argument one more time – the number of workers employed is the key determinant of supply in the short-run. As long as wages are flexible, the price level has no impact on the number of workers who are working – the labor market remains in equilibrium at full employment with 𝐿𝐿∗ workers working, regardless of the price level. Since the labor market is at full employment at any price level, the level of output supplied is the same no matter the price level.
The aggregate supply (AS) relationship gives output supplied at various price levels. We have just seen that, as long as nominal wages are flexible, aggregate supply is the same at any price level. In other words, the aggregate supply curve with flexible wages is vertical.
This formulation is often referred to as the “classical” aggregate supply curve, which refers back to the fundamental assumption in classical models that wages and prices are flexible.
The Aggregate Supply Curve with Wage Rigidity
The argument above is the classical, full-employment model. In this model, the labor market is always in equilibrium and so output does not depend on the price level. The aggregate supply curve is vertical. Of course, when AS is vertical, aggregate demand has no effect on output. But this argument relies critically on flexible wages. The nominal wage has to adjust when the price level changes in order to keep the real wage and the labor market at equilibrium.
Keynes found this model of aggregate supply to be unsatisfactory. In particular, he strongly disputed the proposition that nominal wages are flexible. According to Keynes, nominal wage rigidity occurs when dollar wages cannot easily adjust to market conditions. Keynes claimed that, as a practical matter, the economy is characterized by nominal wage rigidity that comes from three important sources.
• Contracts – Many workers are employed with long-term contracts that specify nominal wages, making it difficult for wages to adjust to market conditions.
• Efficiency wages – Many employers pay a nominal wage higher than the equilibrium wage and are reluctant to cut it because of a prevailing view that worker retention and morale will suffer.
• Minimum wages – Wages are not free to adjust if the adjustment would drive the nominal wage lower than the legal minimum wage.
Now, as a practical matter, wage rigidity tends to be an issue in the downward direction. That is, there is usually no impediment to wages that rise with market conditions, but there are a number of impediments to falling wages. Let’s now consider the impact of price changes in labor markets, but assuming that the nominal wage is rigid in a downward direction.
Suppose that the labor market is in equilibrium with 𝐿𝐿∗ = 1000 workers employed at a nominal wage of 𝑤𝑤 = 10 when the price level is 𝑀𝑀 = 1. The equilibrium is illustrated below.
But suppose that the price level drops to 𝑀𝑀 = 0.5. Now we have a problem. In order for the labor market to remain in equilibrium at the same real wage as before, the nominal wage would have to drop to 𝑤𝑤 = 5. But, we have assumed that the nominal wage cannot fall below 𝑤𝑤 = 10 because of wage rigidities. Thus, the real wage rises to 𝑤𝑤
𝑃𝑃 = 10
0.5 = 20. This reduces the number of workers that firms want to hire (quantity of labor demanded).
This rigidity induces unemployment. 1500 workers want to work at this new real wage (quantity of labor supplied), but firms only hire 500 workers (quantity of labor demanded) since the real wage is too high. Only 500 workers will be employed at this lower price level.7
If the price level drops further to 𝑀𝑀 = 0.25, then the problem gets even worse. With the nominal wage rigid at 𝑤𝑤 = 10, the real value of the wage rises further to 𝑤𝑤
𝑃𝑃 = 10
0.25= 40, which reduces even more the number of workers that firms want to hire. The more the price level drops, the more the real value of the wage rises, and the more firms reduce the number of workers they hire.
7 Generally, this illustrates the “short-side principle”. When quantity supplied and quantity demanded in a market
Summarizing, as the price level drops below 𝑀𝑀 = 1, fewer and fewer workers are employed as the price level continues to drop. As a result, the supply of output falls.
The aggregate supply curve is kinked. Increases in price level beyond the price level that creates an equilibrium real wage in the labor market do not have any impact on output – the nominal wage rises in response to price increases, and the labor market remains in equilibrium.
But, when the price level falls below 𝑀𝑀 = 1 (the price level that generates equilibrium with the going nominal wage in our model), the nominal wage cannot adjust downward. Falling prices push up the real value of the rigid nominal wage, and so firms reduce their hiring and output falls.
In summary, Keynes suggested that the aggregate supply curve is in fact upward sloping (becoming vertical once equilibrium in the labor market is reached). He disputed that the labor market is always at full-employment equilibrium, his main objection being wage rigidities.8 In fact, Keynes argued that, for all practical purposes, the economy in the short-run is almost always stuck at a wage above the equilibrium level, which puts the economy on the upward-sloping part of the aggregate supply curve. Thus, in the Keynesian world, increases in the price level actually
do increase supply of output because they lower the real wage and stimulate more hiring.
There is one very important implication. In the classical, flexible-wage formulation the aggregate supply curve is vertical, and so changes in aggregate demand have no impact on equilibrium GDP. Output is entirely supply-driven. But in the Keynesian formulation, with nominal wage rigidity, the aggregate supply curve is upward sloping. In this case, increasing the level of aggregate demand can increase equilibrium GDP. This was the underlying foundation for Keynes’ argument that demand-side stimulus like government spending can raise GDP.
8 Over time, economists have developed a number of other rationales for an upward-sloping aggregate supply curve.
Analyzing Macroeconomic Shocks in the AD/AS Model
We now proceed to use the AD/AS model to analyze shocks to the economy. Now that we have introduced a supply-side component, we can study both demand and supply-side shocks.
The IS/LM model describes the demand side of the economy – the interaction of expenditures (the IS curve) and the financial market (the LM curve). This is where the AD curve is derived from. The labor market describes the supply side of the economy, and labor employment is the key determinant of short-run production. This is where the AS curve is derived from. The AD/AS diagram brings together the demand side and the supply side of the economy. Changes to the IS/LM equilibrium shift the AD curve. Changes in the labor market shift the AS curve.
In combining these diagrams, the IS/LM diagram is conventionally on top and the labor market on the bottom, with the AD/AS diagram in the middle. Here is the “cookbook” procedure for analyzing the impact of macroeconomic shocks using AD/AS analysis.
1. Make the initial shift(s) on the IS/LM diagram or on the labor market diagram. Demand side shocks, such as spending or money market changes, impact the IS/LM equilibrium. These shifts are detailed in the previous section on the IS/LM model. Supply side shocks in the labor market impact the labor market equilibrium.
2. Make the appropriate shift(s) to the AD/AS diagram corresponding to the changes in (1).
• If equilibrium GDP 𝑌𝑌 rises on the IS/LM diagram, AD shifts right. • If equilibrium GDP 𝑌𝑌 falls on the IS/LM diagram, AD shifts left. • If equilibrium employment in the labor market rises, AS shifts right. • If equilibrium employment in the labor market falls, AS shifts left.
3. Shift the LM curve to reflect the price level change in the AD/AS diagram from (2). The magnitude of the shift should be such that the equilibrium level of GDP 𝑌𝑌 is consistent on the AD/AS diagram and on IS/LM diagram.
A few common mistakes to be careful of.
• Never begin your analysis on the AD/AS diagram. The shifts to the AD and AS curves come as a result of the changes on the IS/LM diagram or in the labor market.
• The AS curve shifts only as a result of changes in the labor market. Changes in the IS/LM model never shift the AS curve.
Expansionary Fiscal Policy with Flexible Wages
When wages are flexible, the AS curve is vertical, as we discussed earlier. Suppose that the level of government spending 𝐺𝐺 increases. I will describe verbally each step of how to analyze this change using the AD/AS model. The diagram follows.
1. The increase in 𝐺𝐺 shits IS to the right (to IS')
2. Equilibrium 𝑌𝑌 increases on the IS/LM diagram so AD shifts to the right (to AD')
3. The price level 𝑀𝑀 increases on the AD/AS diagram, so LM shifts to the left (to LM'). Notice that equilibrium 𝑌𝑌 does not change in the AD/AS model, so in order to keep 𝑌𝑌 consistent across the two diagrams (indicated by the dashed line), we need to shift the LM curve to the left sufficiently far so as to restore the initial level of 𝑌𝑌.
Ultimately, when we compare the original equilibrium with the new equilibrium:
• GDP (𝑌𝑌) does not change • The interest rate (𝑟𝑟) rises • The price level (𝑀𝑀) rises
Expansionary Fiscal Policy with Wage Rigidity
Suppose instead that the economy is characterized by the Keynesian, upward-sloping supply curve because there is wage rigidity. We assume that the initial equilibrium is on the upward-sloping part of the AS curve. Consider now the effect of an increase in government spending in this model.
1. The increase in 𝐺𝐺 shits IS to the right (to IS')
2. Equilibrium 𝑌𝑌 increases on the IS/LM diagram so AD shifts to the right (to AD')
3. The price level 𝑀𝑀 increases on the AD/AS diagram, so LM shifts to the left (to LM'). The equilibrium level of 𝑌𝑌 increases in the AD/AS diagram, so when we shift LM to the left, we shift it only enough to make the equilibrium level of GDP agree with the equilibrium on the AD/AS diagram.
Contrasting the original equilibrium with the new equilibrium:
• GDP (𝑌𝑌) rises
Now we see the important contrast between the classical, flexible-wage formulation and the Keynesian, rigid-wage formulation. In this case, an increase in government spending leads to a higher equilibrium GDP. Broadly, in classical models demand-side shocks do not change equilibrium GDP. But in the Keynesian case, demand-side shocks can increase GDP.
Let’s try to understand the economics underlying this key difference. In the Keynesian formulation, the nominal wage is “stuck” above the market clearing wage when the initial equilibrium is on the upward-sloping segment of the AS curve. In this case, when AD increases and pushes the price level up, the real value of the “stuck” nominal wage falls. The lower real wage encourages firms to hire more workers. Thus, employment rises and the aggregate supply of output produced by firms rises. This was Keynes’ original story for the mechanism by which demand-side stimulus could result in an increase in the economy’s output. In the classical model, the labor market is always in equilibrium and the nominal wage just adjusts along with the price level, so changes in AD creating changes in the price level have no impact on output.
Even in the Keynesian formulation, if the price level increased so much as to bring the real wage back to the equilibrium level, then we would be on the vertical part of the AS curve and increases in AD would have no further effect on output. But Keynes said that, as a practical matter in the short-run, the economy is practically always on the upward-sloping part of the AS curve where nominal wages are stuck above equilibrium.
Multipliers in the AD/AS Model
The spending multiplier is the increase in GDP that results from a $1 increase in government spending. In the section on IS/LM models, we argued that the IS/LM multiplier is smaller than the simple Keynesian multiplier. The reason is that the interest rate is endogenous in the IS/LM model. When spending rises, it pushes the interest rate up, which reduces investment spending – offsetting the overall GDP increase to some extent.
Along similar lines, the AD/AS multiplier is even lower than the IS/LM multiplier. The price level is endogenous in the AD/AS model. Higher spending raises AD and pushes the price level up. The increase in price level shifts the LM curve left, raises the interest rate, and reduces investment spending even more, which offsets even more of the initial increase to GDP. Thus, the AD/AS spending multiplier is even lower than the IS/LM spending multiplier.
Expansionary Monetary Policy with Flexible Wages
We will now analyze the impact of expansionary monetary policy, an increase in the money supply
𝑀𝑀, using the AD/AS model with flexible wages.
1. An increase in 𝑀𝑀 shifts the LM curve to the right (to LM')
2. Equilibrium 𝑌𝑌 increases on the IS/LM diagram so AD shifts to the right (to AD')
3. The price level increases on the AD/AS diagram, so the LM curve shifts leftward to account for this increase in 𝑀𝑀. Notice that the equilibrium level of GDP 𝑌𝑌 does not change on the AD/AS diagram. Thus, in order to make equilibrium GDP agree on the AD/AS and on the IS/LM diagrams, we need to shift the LM curve leftward all the way back to its original position (to LM''). This ensures that equilibrium GDP 𝑌𝑌 is consistent.
When we compare the new equilibrium with the original equilibrium:
• GDP (𝑌𝑌) does not change
• The interest rate (𝑟𝑟) does not change • The price level (𝑀𝑀) rises
Expansionary Monetary Policy with Wage Rigidity
Let us reconsider the effect of an increase in the money supply 𝑀𝑀 in the AD/AS model where we assume that nominal wages are rigid.
1. An increase in 𝑀𝑀 shifts the LM curve to the right (to LM')
2. Equilibrium 𝑌𝑌 increases on the IS/LM diagram so AD shifts to the right (to AD')
3. The price level increases on the AD/AS diagram, so the LM curve shifts leftward to account for this increase in 𝑀𝑀. However, the equilibrium level of GDP does not fall all the way back to the original level. Thus, when we shift the LM curve left (to LM''), we do not need to shift it all the way back to its original position in order to make equilibrium GDP 𝑌𝑌 agree with equilibrium GDP on the AD/AS diagram.
In this case, when we compare the old equilibrium and the new equilibrium:
• GDP (𝑌𝑌) rises
• The interest rate (𝑟𝑟) falls • The price level (𝑀𝑀) rises
Increase in the Labor Force
Finally, we consider a supply-side change. The examples above demonstrate how to use the AD/AS model to analyze demand-side changes, both shifts to the IS curve and shifts to the LM curve. For this example, we consider the effect of an increase in labor supply. We will use the model with flexible wages.
1. An increase in the labor force shifts the labor supply curve to the right (to Ls') 2. Equilibrium employment 𝐿𝐿 increases in the labor market, so AS shifts right (to AS') 3. The price level falls in the AD/AS diagram, so LM shifts to the right (to LM'). The
magnitude of the shift is sufficient to make the level of GDP 𝑌𝑌 in the IS/LM equilibrium consistent with the level of 𝑌𝑌 in AD/AS equilibrium (shown by the dashed line).
Comparing the original equilibrium with the new equilibrium:
• GDP (𝑌𝑌) rises
This example reinforces an important point from the flexible-wage, classical formulation. Only supply side changes can grow real output in the economy. When the AS curve is vertical, changes in AD never impact equilibrium GDP. The only source of increases in GDP is a rightward shift of the AS curve.
In the rigid-wage, Keynesian formulation, an increase in labor supply would have the same effects outlined here. Supply-side changes always increase GDP and reduce the price level regardless of whether wages are flexible or rigid. The difference between the two models is the impact of demand-side changes. In the Keynesian, rigid-wages model with the AS curve sloping upwards, there is also the possibility that increases in aggregate demand can raise output, which is not possible with a vertical AS curve when wages are flexible.
Predicting Macroeconomic Variables
The AD/AS model is quite rich in its ability to predict the effect of short-run fluctuations in macroeconomic conditions. Even though we are only solving for three endogenous variables (GDP, interest rates and the price level), many other macroeconomic variables are functions of these three.
• The strongest determinant of consumption spending is income. Generally, consumption spending will move in the same direction as GDP.
• A key determinant of investment spending is the interest rate. As we discussed, the relationship is inverse – higher interest rates lead to less investment spending.
• Net exports are tied both to GDP and to the interest rate. Higher GDP typically reduces net exports, because consumers will spend some of this additional income on imports. Higher interest rates typically reduce net exports as well – the rationale for this deals with exchange rate movements, which we will discuss in a later unit.
• The unemployment rate is linked to GDP changes via Okun’s Law. It typically falls when GDP rises (or rises more quickly).
