3.6 Introducing the multiplier model (2024)

The previous section showed that the level of economic output fluctuates over time; in this section, we introduce a model that helps explain these fluctuations.

Economic activity involves interactions between people who are connected across many different markets. When someone receives income, they may save some of it, but the part they spend will be spent on goods and services produced by other people. From the circular flow model, their spending represents demand for the goods and services of firms, who pay people to produce and sell those items. The firm’s owners and its employees receive income and, in turn, spend some of it, generating demand for goods and services produced by other firms. Since economic actors are connected in this way, the direct effect of a demand shock—a change in spending decisions—is amplified through the economy via further indirect spending, employment, and production effects, and measured by changes in GDP.

multiplier process

A mechanism through which the direct effect of an increase (or decrease) in aggregate spending is amplified through indirect effects that further increase (or decrease) aggregate output. See also: fiscal multiplier, multiplier model.

You can imagine that during business cycle upswings, more people are employed. A second household member may get a job or more hours of work. The household will be able to buy more goods and services—a new dishwasher or more restaurant meals, for example. Demand for goods increases and firms increase their employment further to produce more goods and services: output increases. The total wage and profit income of the providers of these goods and services will rise, and so on. A similar, but reverse, process would happen during a downswing when lay-offs and cuts in hours of work occur. This is the multiplier process.

supply side, supply-side

The economy is in supply-side equilibrium when the markets involved in the production of output are in equilibrium. In the WS–PS model, it is the labour market equilibrium; that is, where the price-setting real wage equals the wage-setting real wage. See also: demand side.

multiplier model

A model of aggregate demand that includes the multiplier process. See also: fiscal multiplier, multiplier process.

demand side, demand-side

The demand side of the economy refers to the expenditure on the goods and services it produces, which consists of consumption, investment, government purchases, and purchases by foreigners. In a microeconomic model of the market for a particular good, it refers to the decisions of the buyers of the good. See also: supply side.

We studied a supply-side model in Units 1 and 2. The multiplier model is a demand-side model, which demonstrates how spending decisions generate demand for goods and services and, as a result, determine the levels of employment and output. In Unit 4, we integrate supply-side and demand-side models to explain how shocks are transmitted, thereby generating business cycles characterized by fluctuations in output, employment, and inflation.

By saying ‘we assume’ in the context of a model, we are drawing attention to conditions in the model that are important for the conclusions that can be drawn. Read Section 2.8 in the microeconomics volume for more information about economic models.

In the multiplier model, we assume that firms respond to changes in demand by adjusting their output, rather than their prices.

capacity utilization

A firm, industry, or entire economy is at full capacity utilization if it is producing as much as the stock of its capital goods and current knowledge will allow. If is is producing less, it is ‘below full capacity utilization’ or ‘at a low capacity utilization rate’.

This means that a second assumption is also important for our model: firms will be willing to supply any amount of the goods demanded by those making purchases in the economy. If there is an increase in demand, firms increase their production to meet this extra demand and do not change their price. If demand falls, they will cut production. We are therefore assuming that firms are not operating at full capacity utilization.

Simplifying the model

Section 3.3 showed that when we measure GDP as expenditure, the components are consumption, fixed investment, changes in inventories, government spending, and net exports (\(\text{GDP} \equiv C + I + II + G + X − M\)). To concentrate on the mechanisms in the model, we begin with a restricted case that excludes the government and foreign trade.

Therefore, the GDP identity at this stage simply reduces to:

\[Y \equiv C + I + II\]

where we use the symbol, \(Y\), to denote aggregate output (income) in our model, but in this restricted world this would be identical to GDP, so we again use the identity sign \(‘≡’\).

Aggregate demand

aggregate demand

The total of the components of planned spending in the economy: AD = C + I + G + X – M. It is the total amount of demand for (or planned expenditure on) goods and services produced in the economy. See also: consumption, investment, government spending, exports, imports.

In general, aggregate demand (AD) is the total demand that comes from households, firms, the government, and other countries for the goods and services the country produces. In our restricted model, which has no government spending or trade with other economies, it is the total amount that households and firms wish to spend on output—that is, their planned expenditure.

The role that unplanned changes in inventories play in the model is explained below.

To clarify the difference between planned and unplanned expenditure, we assume that all changes in inventories, \(II\), are unplanned. This implies that \(II\) is not part of aggregate demand.

In our restricted model with no government or trade, aggregate demand is simply the sum of consumption, \(C\), and planned fixed investment, \(I\).

\[\text{AD}= C + I\]

So if, as discussed above, we wish to build a demand-side model, in which aggregate demand determines the output firms supply, we just need a model of these two components.

Consumption

Consumption includes the goods and services purchased by households. We assume that their consumption spending has two parts:

autonomous consumption

In a model of consumption demand, autonomous consumption is planned consumption expenditure that does not depend on other variables in the model (such as income, or the interest rate).

• A fixed amount: How much people will spend, independent of their income. This fixed amount, also known as autonomous consumption, is shown as \(c_0\) on the vertical axis of Figure 3.11.
• A variable amount: This depends on current income, and is an upward-sloping red line in Figure 3.11.

consumption function (aggregate)

A relationship that shows how consumption spending in the economy as a whole depends on other variables. For example, in the multiplier model, aggregate consumption depends on current disposable income and autonomous consumption. See also: disposable income, autonomous consumption.

So we can write consumption spending as a function of income, which we call the aggregate consumption function:

\[\begin{align} \text{aggregate consumption} &= \text{autonomous consumption} \\ &+ \text{consumption that depends on income} \\ \\ C &= c_0 + c_1Y \end{align}\]

marginal propensity to consume (MPC)

The change in consumption when disposable income changes by one unit.

The term, \(c_1\), gives the effect of one additional unit of income on consumption, called the marginal propensity to consume (MPC). In Figure 3.11, we show income on the horizontal axis, and aggregate consumption on the vertical axis, both measured in billions of euros. The slope of the consumption line is equal to the marginal propensity to consume. A steeper consumption line means a larger consumption response to a change in income. A flatter line means that consumption does not vary much when incomes change. We assume that the marginal propensity to consume is positive, but less than one. This means that only part of an increase in income is consumed; the rest is saved.

The aggregate consumption function plays an important role in the multiplier model. In our version of the model, we will use the consumption function illustrated in Figure 3.11, in which the marginal propensity to consume, \(c_1\), equals 0.6. This means that each additional euro of income increases consumption by \(0.6 \times \text{€1 = 60} \text { cents}\).

Our assumed value of 0.6 for aggregate consumption may hide large variations in household behaviour. For example, for households with low wealth, data shows that consumption closely tracks income. The marginal propensity to consume for this group might be 0.8 or even higher. But for wealthy households the marginal propensity to consume is likely to be much closer to zero. For now, you can think of the marginal propensity as an average across households in the economy.

The term, \(c_0\), in the aggregate consumption function captures all the other influences on consumption that are not related to current income. Taken literally, it is how much a person with no income would consume, but that is not the best way to think about it. It is just the consumption that is independent of income, and for this reason we call it autonomous consumption.

Consumption behaviour is explored in depth in Sections 3.10 and 3.11, where we shall explore further the determinants of autonomous consumption.

Investment

exogenous

Exogenous means ‘generated outside the model’. In an economic model, a variable is exogenous if its value is set by the modeller, rather than being determined by the workings of the model itself. See also: endogenous.

In the model without government, investment \((I)\) is the spending by firms on new equipment and new commercial buildings, as well as spending on residential structures (the construction of new housing). Unlike consumption, we assume that fixed investment does not depend on the level of output. In later sections, we shall consider the determinants of investment in much more detail, but for now we simply take the value of investment as exogenous: that is, we take its value as given, rather than being affected by other variables within the model.

The aggregate demand function

We can now specify the aggregate demand function—meaning here, how aggregate demand relates to the level of output, \(Y\). In our restricted model, given our assumed consumption function, this becomes:

\[\begin{align} \text{aggregate demand} &= \text{consumption} + \text{investment}\\ \text{AD} &= C + I \\ &= c_0 + c_1Y + I \end{align}\]

autonomous demand

In a model of demand for goods and services, autonomous demand is planned expenditure that does not depend on other variables in the model (such as income, or the interest rate).

To graph the aggregate demand function, we add investment, \(I\), to the consumption line from Figure 3.11. Because investment is independent of the level of output, this simply leads to a parallel upward shift. Later in the unit, we shall consider the determinants of investment, but at this stage we simply need to assume that it is not a function of output. In this respect, investment is similar to autonomous consumption—we refer to \(c_0+I\) as autonomous demand.

Figure 3.12 shows that the aggregate demand line has an intercept of \(c_0 + I\), and a slope of \(c_1\).

Goods market equilibrium: Y = AD

The second element of the multiplier model is a 45-degree line in the diagram with output, \(Y\), on the horizontal axis and aggregate demand, AD, on the vertical axis. This is a line rising up from the origin at a 45-degree angle. On any graph, the 45-degree line shows all the points where the horizontal distance is equal to the vertical distance.

Therefore, in the multiplier model the 45-degree line shows all the points in the diagram at which aggregate output, \(Y\), (the production of goods and services in the economy) is equal to aggregate demand for goods and services in the economy, AD.

exogenous shock

An exogenous shock (for example a demand shock or a supply shock) is a change in one or more of the exogenous variables in a model—that is, variables that are othewise held constant by the modeller.

When aggregate demand for output is equal to the quantity of output being produced, the economy is in equilibrium. The economy will remain at that level unless something exogenous changes. An exogenous change, or exogenous shock, means a change in something that is determined outside the model—for example, we are going to find the equilibrium when the value of the MPC is set at 0.6, but a change in the MPC would change the equilibrium.

goods market equilibrium

A goods market is in equilibrium when the supply of goods is equal to the demand. In the multiplier model, aggregate demand for goods and services, AD, depends on income, Y, and income is equal to the output that firms supply. Goods market equilibrium is at the value of Y where aggregate demand is equal to output: AD = Y.

So the 45-degree line shows all the points where the economy is in equilibrium. Because in this diagram we are focused on product markets for goods and services rather than the labour market, we call this goods market equilibrium:

\[\begin{align} \text{output} &= \text{aggregate demand for goods produced in the home economy} \\ Y &= \text{AD} \end{align}\]

Figure 3.13 below shows the 45-degree line. At any point on this line, \(Y =\text{AD}\) and the goods market is in equilibrium.

Determining the equilibrium level of output

We know that the 45-degree line shows all the points where the economy would be in goods market equilibrium, with \(Y=\text{AD}\). But we also know that aggregate demand depends on income, \(Y\). By drawing the 45-degree line and the aggregate demand function in the same diagram, we can find the level of output at the point where they cross. At this point the economy will be in equilibrium.

If the equilibrium level of output is low, unemployment in the economy will be high. High equilibrium output would mean low unemployment.

Follow the steps in Figure 3.14 to understand how this works. Pay attention to the role played by the unintended changes in inventories.

Figure 3.14 presents a picture of how the level of output in the economy is determined. Aggregate demand is equal to \(c_0 + c_1Y + I\) (the flatter line), and output is equal to aggregate demand (the 45-degree line), so the economy is in equilibrium at point A where the two lines cross.

Note that in the multiplier model, the MPC is strictly less than one. This means that the AD line is flatter than the 45-degree line. In this case, the equilibrium at the crossing point is stable. If the MPC were greater than one, the equilibrium would be unstable. We explore unstable equilibria in Unit 8.

The figure contains important information about how messages are transmitted in the economy, so that the equilibrium is reached. When aggregate demand is low and inventories of unsold goods are piling up, this sends a message to firms that they should decrease production. On the other hand, if aggregate demand was greater than output, goods would be flying off the shelves and firms’ stocks of unsold inventories would be falling. This would convey the message to firms that they should increase production. But at point A, aggregate demand and output are equal and inventories are not changing—so firms won’t change their output. This is what we mean when we say that point A is an equilibrium.

Goods market equilibrium and the national accounts identity

We now compare the national accounts identity with the goods market equilibrium in the multiplier model. This explains the role of unplanned inventories. Remember from Section 3.3 that in the national accounts, aggregate expenditure is always identically equal to income and output. In our restricted model of an economy with no government and no trade, we saw that this implied that the national accounts identity is:

\[Y \equiv C + I + II\]

The symbol ‘≡’ instead of the equals sign indicates that this is an identity.

The reason the identity holds at all times in the multiplier model—even when \(Y\) is not equal to AD as at points B and C in Figure 3.14—is because \(Y\) includes both planned investment expenditure, \(I\), and any changes in inventories, \(II\). In the multiplier model, it is only at the equilibrium level of output that aggregate demand is equal to output. At this point, therefore, inventory investment is equal to zero.