6.3: Aggregate expenditure and equilibrium output in the short run

National Accounts as in Chapter 4 measure actual expenditure, output and national income and GDP(Y). The Aggregate Expenditure function gives planned expenditure (AE). In a modern industrial economy actual output and income may differ from what was planned, either on the output side or on the purchase and sales side. A simple example of the time sequence of output and sales shows why.

In most cases business install capacity and produce output in anticipation of sales in the near future. This is apparent from the stocks of goods offered in most retail outlets or online. Auto manufacturers, for example like to have an inventory of 30 to 60 days of finished vehicle sales available for retail buyers. Coffee and donut shops have coffee and snacks available to customers when they walk in. Even service industries like cell phone companies try to have staff and product on hand and ready to serve customers on demand. In these and other cases producers incur costs that they expect to recover from later sales. If sales don't match expectations some inventories of products build up or fall short, capacity is not matched to demand and some sales opportunities are lost or costs are not recovered.

As a result, if planned expenditure (AE) and GDP are different then plans in some part of the economy have not been realized and there is an incentive to change output. However, when actual output (GDP) is equal to planned expenditure (AE) expenditure and output plans are successful and, unless underlying conditions change there is no incentive to change output.

Equilibrium output

Output is said to be in short-run equilibrium when the current output of goods and services equals planned aggregate expenditure:

Y=A0+(c–m)Y

(6.2)

Then spending plans are not frustrated by a shortage of goods and services. Nor do business firms make more output than they can sell. In short-run equilibrium, output equals the total of goods and services households, businesses, and residents of other countries want to buy. Real GDP is determined by aggregate expenditure.

Short-run equilibrium output: Aggregate expenditure and current output are equal ().

Figure 6.7 The diagram and equilibrium GDP

The line gives the equilibrium condition. At point E the AE line crosses the line and . This is the equilibrium. At Y₁, AE>Y and unplanned reductions in inventories provide the incentive to increase Y.

line labeled , illustrates the equilibrium condition. At every point on the line, AE measured on the vertical axis equals current output, Y, measured on the horizontal axis. This line has a slope of 1.

Figure 6.7 starts from a positive intercept on the vertical axis to show autonomous aggregate expenditure A₀, and has a slope equal to (c–m) which is less than one. The line has a slope equal to one. At every point on the line, the value of output (and income) measured on the horizontal axis equals the value of expenditure on the vertical axis. With a positive vertical intercept and slope less than 1 the AE line crosses the line at E. Since E is the only point on the AE line also on the line, it is the only point at which output and planned expenditure are equal. It is the equilibrium point.

Income Y₂ is the only income at which aggregate expenditure just buys all current output. For example, assume as shown in the diagram, that output and incomes are only Y₁. Aggregate expenditure at D is not equal to output as measured at B. Planned expenditure is greater than current output. Aggregate spending plans cannot all be fulfilled at this current output level. Consumption and export plans will be realized only if business fails to meet its investment plans as a result of an unplanned fall in inventories of goods.

In Figure 6.7 all outputs less than the equilibrium output Y₂, are too low to satisfy planned aggregate expenditure. The AE line is above the line along which expenditure and output are equal. Conversely, if real GDP is greater than Y₂ aggregate expenditure is not high enough to buy all current output produced. Businesses have unwanted and unplanned increases in inventories of unsold goods.

Table 6.3 extends the numerical example in Table 6.2 to show equilibrium when GDP(Y) is 200 and the unwanted inventory changes at other income levels. When GDP in column (1) is less than AE in column (4) current output does not cover current planned expenditure. Inventories fall and producers can't meet their inventory targets. The unwanted change in inventories in column (5) is negative.

Table 6.3 Equilibrium GDP: .

GDP (Y)	Autonomous	Induced	Aggregate	Unplanned
	Expenditure	Expenditure	Expenditure	Inventory
	(A0=100)	(c–m)Y=0.5Y
(1)	(2)	(3)	(4)	(5)
0	100	0	100	-100
50	100	25	125	-75
100	100	50	150	-50
175	100	87.5	187.5	-12.5
200	100	100	200	0
250	100	125	225	+25
300	100	150	250	+50

You can construct a diagram like Figure 6.7 using the numerical values for GDP and aggregate expenditure in Table 6.3 and a line to show equilibrium Y_e=200. Example Box 6.1 at the end of the chapter illustrates equilibrium for this basic model using simple algebra.

Adjustment towards equilibrium

Unplanned changes in business inventories cause adjustments in output that move the economy to equilibrium output. Suppose in Figure 6.7 the economy begins with an output Y₁, below equilibrium output Y_e. Aggregate expenditure is greater than output Y₁. If firms have inventories from previous production, they can sell more than they have produced by running down inventories for a while. Note that this fall in inventories is unplanned. Planned changes in inventories are already included in planned investment and aggregate expenditure.

Unplanned changes in business inventories: indicators of disequilibrium between planned and actual expenditures – incentives for businesses to adjust levels of employment and output (Y).

If firms cannot meet planned aggregate expenditure by unplanned inventory reductions, they must turn away customers. Either response—unplanned inventory reductions or turning away customers—is a signal to firms that aggregate expenditure is greater than current output, markets are strong, and output and sales can be increased profitably. Hence, at any output below Y_e, aggregate expenditure exceeds output and firms get signals from unwanted inventory reductions to raise output.

Conversely, if output is initially above the equilibrium level, Figure 6.7 shows that output will exceed aggregate expenditure. Producers cannot sell all their current output. Unplanned and unwanted additions to inventories result, and firms respond by cutting output. In the last few years, producers of commodities including iron ore, copper, metallurgical coal, base metals, natural gas, and crude oil have faced declining demand for their products and lower prices and rising inventories. Producers responded by lowering production to try to reduce excess inventory. In general terms, when the economy is producing more than current aggregate expenditure, unwanted inventories build up and output is cut back.

Hence, when output is below the equilibrium level, firms raise output. When output is above the equilibrium level, firms reduce output. At the equilibrium output Y_e, firms sell their current output and there are no unplanned changes to their inventories. Firms have no incentive to change output.

Equilibrium output and employment

In the examples of short-run equilibrium we have discussed, output is at Y_e with output equal to planned expenditure. Firms sell all they produce, and households and firms buy all they plan to buy. But it is important to note that nothing guarantees that equilibrium output Y_e is the level of potential output Y_P. When wages and prices are fixed, the economy can end up at a short-run equilibrium below potential output with no forces present to move output to potential output. Furthermore, we know that, when output is below potential output, employment is less than full and the unemployment rate u is higher than the natural rate u_n. The economy is in recession and by our current assumptions neither price flexibility nor government policy action can affect these conditions.