Unit 3: Spending and Output
3.1: The short-run Keynesian model
In beginning to explore how macroeconomic variables are determined and how policy can affect macroeconomic variables, we start with the proposition that spending and output are related to each other. The nature of this relationship is the subject of this unit.
The first economist to formalize this relationship was John Maynard Keynes. Historically, the problem during the Great Depression was low output and poor economic growth. Keynes proposed a very straightforward solution – increase spending. With more people spending money, businesses will increase their output, leading to more jobs, more spending and more growth. Was Keynes right? Let’s examine his model.
Determinants of Consumption Spending
As we saw earlier, consumption is the most important component of spending in an economy. Because of this, it is important to understand what determines consumer spending. The most basic determinant of how much a consumer spends is his income. While the interest rate, wealth, and expectations about future income can also impact consumption spending, there is a very close relationship between what a consumer spends and the income he earns.
The consumption function is a formula that relates consumption spending to income. Letting 𝐶 stand for the level of consumption and letting 𝑌 stand for income, the Keynesian consumption function is as follows. The point is that consumption spending rises when income rises.
𝐶 = 𝑎 + 𝑏𝑌
In this formula, 𝑎 is called autonomous spending. This is spending that consumers undertake irrespective of their income. Even if a person’s income is 𝑌 = 0, he still spends 𝑎 on basic necessities, either by borrowing money or by using up savings.
that the consumer earns causes his spending to rise by $0.80. So an additional $1000 of income would yield an additional $800 of spending.
We can draw a diagram that illustrates this relationship.
From the diagram, we can see that autonomous spending 𝑎 is the intercept of the consumption function. This is the level of consumption spending when income is 0. The marginal propensity to consume 𝑏 is the slope of the consumption function. It is the increase in consumption spending corresponding to each $1 increase in income. By definition of slope:
𝑏 = 𝑀𝑃𝐶 =Δ consumption spending Δ income
For an example of using the formula, if a consumer gets an additional $10,000 of income and spends an additional $9000 of this income, then his MPC is 0.9.
The important point about the consumption function is that each additional dollar of income generates less than a dollar of additional spending, because not all of the income is spent. Some of it is saved. The marginal propensity to save (MPS) is the amount by which savings rises for each $1 increase in income. The basic relationship between the MPC and the MPS is:
𝑀𝑃𝐶 + 𝑀𝑃𝑆 = 1
Aggregate Expenditures
The level of aggregate expenditure in an economy is the total level of expenditure on final goods and services in the economy. This spending is either undertaken by households, businesses, the government or by foreigners. Aggregate expenditure represents all forms of spending on goods produced in an economy. The formula for aggregate expenditures is:1
𝐴𝐸 = 𝐶 + 𝐼 + 𝐺 + 𝑋 − 𝑀
How is aggregate expenditure determined? From the previous section, we know that consumption spending is determined primarily by income. We then assume that the other components of aggregate expenditure are constant. In other words, we assume that investment, government spending and net exports do not depend on income. Indeed, there are other factors that are more important than income in determining the level of I, G, X and M.
Let’s draw a graph of how aggregate expenditures depends on income. We simply take our graph of consumption spending, and then we add 𝐼 + 𝐺 + 𝑋 − 𝑀 to it. These are all constant, so the graph of AE (total spending) is parallel to consumption spending – just shifted up to add in the other components.
The diagram below illustrates the the aggregate expenditure function.
1 This might look suspiciously like the GDP identity. The difference is subtle, and in fact the two are equivalent except
Equilibrium – The Keynesian Cross
In the aggregate expenditures diagram above, we can replace “income” with “GDP”. As we discussed in the previous section, a country’s GDP measures both its output and its income. On a national scale, a country’s output is equal to its income. Using this relabeling, let us again draw the aggregate expenditure function.
The intuition behind this function is very simple. As output in the economy rises, more income is created, and so expenditures in the economy rise as well.
By combining the aggregate expenditure function and the 45-degree line, we obtain the Keynesian cross diagram.
To understand how this model works and how equilibrium is reached, let us consider the two levels of output that are labeled on the diagram.
At GDP1 (with corresponding level of expenditure AE1), spending at AE1 exceeds the level of output at GDP1. When purchases of goods and services exceed firm output, firms are forced to draw down their inventories, and so inventories decline. This drop in inventories will be a signal to firms that they should raise their output. If expenditures exceed output, then firms will raise their output.
At GDP2 (with corresponding level of expenditure AE2), output at GDP2 exceeds the level of spending at AE2. When firm output exceeds purchases of goods and services, firms add the excess to their inventories, and so inventories rise. This increase in inventories will be a signal to firms that they should cut their output. If expenditures are less than output, then firms will reduce their output.
At GDP1, spending is greater than output, so firms will increase their output to satisfy demand for purchases. At GDP2, spending is less than output, so firms will cut back on their output since purchases are lower than output. In both cases, GDP approaches the point where output and spending are equal, which is exactly where the AE function crosses the 45-degree line.
purchases unless they raise their output? And there cannot be an equilibrium where output is higher than spending – why would firms continue to produce more output than what is being purchased?
3.2: Fiscal policy and multipliers
The Multiplier Effect
Central to Keynesian analysis of how spending and output are related is the concept of a multiplier. Let’s start with a simple example. Suppose the MPC in an economy is 0.9. The government decides to spend $1000 to build a new playground. This immediately increases GDP by $1000. However, the playground builder who received $1000 from the government will take this additional income and spend $900 of it purchasing goods and services (since the MPC is 0.9). This raises GDP by another $900. This spending in turn gives the store-owner where the builder spends his money an additional $900 of income. The store owner spends $810 of this additional income (again since the MPC is 0.9), which provides $810 in income for someone else, and raises GDP by an additional $810. Whoever receives this $810 spends $729, etc…
Ultimately, the total increase in GDP that results from this initial $1000 expenditure is:
Δ𝐺𝐷𝑃 = $1000 + $900 + $810 + $729 + ⋯
The key point is that GDP increases by much more than the initial $1000 expenditure. Although the initial increase in GDP from the playground construction is $1000, the total change in GDP is much larger because it must account for all the additional purchases and output that result from this initial increase.
This phenomenon is known as the multiplier effect. An additional $1 of spending generates more than $1 of additional GDP. In the simple Keynesian model, the formula for the multiplier is:
𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟 = 1 1 − 𝑀𝑃𝐶
The relationship between the initial change in GDP and the total effect on GDP is:
Δ𝐺𝐷𝑃 = 𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟 × Δ initial spending
To calculate an exact answer for the problem we started with, recall that the MPC in this economy was 0.9. To calculate the multiplier:
𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟 = 1
Therefore, the change in GDP that results from the initial $1000 increase in spending is:
Δ𝐺𝐷𝑃 = 10 × $1000 = $10,000
Thus, we see that a $1000 increase in spending actually generates a $10,000 increase in GDP for this example. This is the multiplier effect.
We can illustrate the multiplier effect on a Keynesian cross diagram. Suppose that there is an increase in spending, which raises aggregate expenditures from AE to AE’, as shown on the diagram below. The increase in equilibrium GDP is much larger than the initial change in spending. This is the multiplier effect. Small changes in spending lead to larger changes in GDP.
There are two extensions to the concept of a multiplier. First, the multiplier works both for increases and for decreases in spending. If the multiplier is 10 and the government reduces
spending by $5 million, then in fact the GDP will fall by $50 million after accounting for all of the other reductions in spending and output that follow from this initial cut.
Fiscal Policy
According to the Keynesian model, increases in spending will increase GDP, with a multiplier. And decreases in spending will lower GDP, again with a multiplier. This suggests that government can manage GDP in the economy by changing government spending. For example, in a recession when GDP is too low, the government can increase spending to stimulate the economy. If it wants to lower GDP, the government can lower spending.
Government policy that seeks to manage GDP by directly impacting the level of spending in the economy is known as fiscal policy. There are two tools of fiscal policy.
1. Changes in government expenditures 2. Changes in taxes
Basically, one way for the government to change the level of spending in the economy is to increase or decrease its own spending. Another way for the government to manage the level of spending in an economy is to change the level of taxes charged to households, which in turn impacts their spending.
Expansionary policy is when the government seeks to raise the level of spending in the economy, which raises GDP with a multiplier effect. Expansionary fiscal policies are to raise government spending or to lower taxes. Both of these increase spending in the economy and increase GDP.
Contractionary policy is when the government seeks to lower the level of spending in the economy, which reduces GDP with a multiplier effect. Contractionary fiscal policies are to lower government spending or to raise taxes. Both of these reduce spending in the economy and reduce GDP.
There are two points about the use of fiscal policy. First, raising government spending has more of an impact on GDP than tax reductions. For a simple example, consider an economy where the MPC is 0.9 and the multiplier is 10. Suppose the government raises spending by $1000. We saw earlier in this section that GDP rises by $10,000 as a result.
Δ𝐺𝐷𝑃 = 10 × $1000 = $10,000
Δ𝐺𝐷𝑃 = 10 × $900 = $9000
Basically, when the government spends money, all of the money gets pumped into the economy. But when the government uses the same money to provide tax cuts, only some of the money gets pumped into the economy because households save part of the money.
The second point is that the impact of government spending on GDP is larger when the MPC is higher. For example, when the MPC is 0.9 then the multiplier is 10. But when the MPC is 0.8 then the multiplier is only 5. This makes sense. If consumers spend more of their money, then spending increases will have a larger impact on the economy because most of these spending increases get returned back into the economy and not saved. One policy implication is that tax reductions have the most impact on the economy when the money goes to people with a high MPC.
Different Perspectives
Keynes developed this model in the Great Depression. He had a very clear answer for how the government could improve the economy – increase government spending. By having the government increase its purchases of goods and services, according to Keynesian economics, it puts more money into people’s hands. They spend the money, creating even more jobs and additional income. This is the Keynesian logic of expansionary fiscal policy.
Classical economists disagree with this entire line of reasoning, and in fact fundamentally disagree with any demand-side model of economic performance. The Keynesian model asserts that the driver of GDP is spending, and that spending increases raise GDP with a multiplier. By contrast, in classical economics, production is the driver of GDP. In those models, the level of output is basically determined by the economy’s productive capacity: technology, worker skills, etc…
One element of this difference is short-run versus long-run orientation. Even Keynesian economists agree that, over the long run, productivity and supply have to grow in order for the economy to grow – not just spending. But Keynesians do believe that, in the short-run, spending matters and that the government can help to stabilize the economy by using fiscal policy. Classical economists believe that demand-side expenditure stimulus does not improve the economy.
3.3: The government in the US economy
Having discussed government spending from a theoretical perspective, the purpose of this section is just to give a brief overview of the government in the US economy.
Terminology
We can sort government spending into three categories.
1. Purchases of goods and services 2. Transfer payments
3. Interest on the debt
Most spending on purchases of goods and services is carried out by state and local governments; think of roads and schools. Most spending on transfers is carried out by the federal government; mostly Social Security, Medicare (health program for the elderly) and Medicaid (health program for the poor).
Note that only (1) counts in GDP directly. This is 𝐺 from the GDP identity. Transfer payments and interest on the debt are not part of the GDP.
(1) + (2) is called government outlays
(1) + (2) + (3) is called government expenditures
Federal Government Expenditures and Revenues
Federal government expenditures in 2014 were $3.50 trillion and federal government revenues were $3.02 trillion. The difference led to a budget deficit of almost $500 billion.
As for expenditures, almost half of the money was spent on transfer payments – Social Security, Medicare and Medicaid. 17% went to defense, and 29% to nondefense spending. Finally, about 6% went to interest on the debt.
The majority of federal government revenues come from individual income taxes (46%) and from payroll taxes (34%).
Growth in Government over Time
The diagram below shows government purchases in real 2012 dollars, since 1950. Note that the diagram shows all levels of government, including state and local government.
As for expenditures by the federal government, the diagram below gives real figures in 2012 dollars. One important thing to note is that almost all of the increase in federal government expenditures has been due to a rapid increase in transfers.
