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# The Aggregate Expenditure Model

The aggregate expenditure model provides an important framework to understand how economic activity is generated.

The model starts by aggregating the components of the economy that generate expenditure, including planned spending by households (consumer spending, C), by firms (investment spending, I) by the government (government spending, G) and net export spending (X-M).

The model also assumes that the price level is constant.

The simplest way to see what happens is to consider the 45 degree diagram which contains the key elements of the aggregate expenditure model. The ‘X’ axis considers the level of real national output (Y=GDP) and the ‘Y’ axis aggregates the various expenditure components. The 45 degree line represents equilibrium points where spending and output equate.

We can consider a hypothetical schedule showing aggregate spending and output. Equilibrium in the short run occurs at the point at which planned expenditure coincides with an economy’s real output - which in the example, is at \$60 (00bn).

Graphically, we can see how aggregate expenditure is composed.

## Consumption

The simple consumption function suggests that some consumption in an economy is ‘autonomous’ (‘a’) and not related to the level of real income. Other consumption is ‘induced’ by additional increases in income, and is a proportion of new income (bY), where ‘b’ is the marginal propensity to consume (ΔC/ΔY). Hence:
C = a+bY
Therefore, if Y is 50, a = 10, and bY = 0.5, C will be 35 (which we can confirm in the schedule).

## Adding investment and government spending

The aggregate expenditure model assumes that investment and government spending are also autonomous - in other words they are not determined by current income, but rather by income in a previous time period. This means, graphically they are parallel to the consumption line (and would be horizontal if shown separately.) When we add net trade we can find equilibrium, which will be where aggregate expenditure equals the economy’s ability to produce output, which is at \$60 (00bn) in the graph. ## Deflationary gaps

A deflationary gap can be shown using the aggregate expenditure model. A deflationary gap arises when the level of planned expenditure is insufficient to purchase all the output that could be produced over a period of time. This would be associated with demand deficient unemployment. Closing a deflationary gap would require a stimulus to the economy to increase aggregate spending - this could be achieved through expansionary fiscal or monetary policy, or a combination of both.

According to Keynes, such an expansion would best be undertaken by an increase in government spending. This is because stimulating investment spending or export spending would be difficult to achieve because they are spending decisions taken by economic agents over which policy makers have less control. In addition, government spending on public and merit goods can achieve a long lasting benefit to an economy (both in terms of growth and development).

## Inflationary gaps

An inflationary gap can also be shown using the aggregate expenditure model. An inflationary gap arises when the level of planned expenditure is above that which is required to purchase all the output that could be produced over a period of time. This would be associated with demand pull inflation. Closing an inflationary gap would require constraints on the economy to reduce aggregate spending - this could be achieved through contractionary fiscal or monetary policy, or a combination of both. According to Keynesian analysis, fiscal policy is likely to have a more predictable effect (especially if the monetary system is faced with a liquidity trap) and, given that spending is difficult (or less desirable) to constrain, raising taxes would be the preferred fiscal measure.

## Illustrating the multiplier effect

The aggregate expenditure model is also a convenient was to show the multiplier effect of a change in an injection of spending into the economy.
Here we can see that the increase in investment expenditure (ΔI) of \$10 (bn) leads to an increase in real output (ΔY) of \$20 (bn), suggesting a multiplier value of +2.0. ## Mathematical solution

We can solve the aggregate expenditure model mathematically. If we call real income Y, and total spending E, (with E0 equalling autonomous spending only) and the marginal propensity to spend as ß, then the model produces two equations:

Y = E, and
E = E0 + ßY

If we substitute for E in the first equation, we can find equilibrium output.

## Example for a closed economy

If autonomous consumption (Ca) is 80, ß is 0.5Y, I is 40, and G is 80, then:

We can find E0 (autonomous spending), which is:

(80 + 40 + 80) = 200

The co-efficient for Y is:

(0.5Y)

Hence:
Y = 200 + 0.5Y

Subtract 0.5Y from both sides, to get:

0.5Y = 200,
therefore Y = 400.

## For an open economy

If we add for an open economy, with X = 60, and M = 0.1Y, then equilibrium in an open economy is:

E0 (autonomous spending) = (80 + 40 + 80 + 60) = 260

The coefficients for Y:

(0.5Y + (- 0.1Y))

Hence:

Y = 260 + 0.4Y

Subtract 0.4Y from both sides, to get:

Y-0.4Y = 260, or

0.6Y = 260,

therefore Y = 260/0.6

Y = 433.34.