Macroeconomic Equilibrium and Spending Multipliers

Short-Run Equilibrium in the AD–AS Model

Short-run equilibrium is the point where the economy’s planned purchases match firms’ planned production at the existing price level. In the aggregate demand–aggregate supply (AD–AS) model, this occurs where aggregate demand intersects short-run aggregate supply:

The intersection determines both real GDP, which measures inflation-adjusted output, and the price level, which measures the average prices of goods and services. Because wages and some other input prices are relatively sticky in the short run, a change in aggregate demand can affect both output and prices.

Aggregate demand is composed of consumption, investment, government purchases, and net exports:

A decline in consumption, investment, government purchases, or net exports shifts aggregate demand leftward. The usual short-run effects are lower real GDP, a lower price level or weaker upward pressure on prices, and higher cyclical unemployment. An increase in any of these spending components generally shifts aggregate demand rightward and raises both real GDP and the price level in the short run.

Key takeaway

Short-run equilibrium explains where actual output and the price level are determined when planned purchases and firms’ production plans are consistent.

Potential GDP and Output Gaps

Potential GDP is the economy’s sustainable full-employment output, not a level at which every person has a job. The difference between actual equilibrium real GDP and potential GDP is the output gap:

As a percentage of potential GDP, the gap is:

A recessionary gap occurs when actual output is below potential output, or $Y<Y_P$. It is associated with high cyclical unemployment, unused factories and other resources, weak consumption and investment, and downward pressure on inflation. On an AD–AS graph, short-run equilibrium lies to the left of long-run aggregate supply.

An inflationary gap occurs when actual output is above potential output, or $Y>Y_P$. It is associated with very low cyclical unemployment, strong competition for labor and other resources, rising wages and production costs, and upward pressure on prices. On an AD–AS graph, short-run equilibrium lies to the right of long-run aggregate supply.

An output gap should not be confused with the price level. A recessionary gap means that output is below sustainable capacity; it does not necessarily mean that the average price level is falling.

Key takeaway

Output gaps compare actual output with productive capacity, while the price level describes the average prices of goods and services.

Planned Expenditure and Equilibrium Output

The expenditure-output model, also called the Keynesian cross, focuses on planned aggregate expenditure and actual output. The vertical axis measures planned aggregate expenditure, and the horizontal axis measures real GDP. The 45-degree line shows every point at which expenditure equals output:

Equilibrium occurs where the aggregate expenditure line intersects the 45-degree line. If planned expenditure is greater than current output, firms experience unplanned decreases in inventories and increase production. If planned expenditure is less than current output, inventories rise unexpectedly and firms reduce production.

A general aggregate expenditure function is:

In a basic closed economy without government or foreign trade, this simplifies to:

Consumption can be represented as:

Here, $C_0$ is autonomous consumption, $MPC$ is the marginal propensity to consume, and $Y-T$ is disposable income. The marginal propensity to consume is:

The marginal propensity to save is:

Since an additional dollar of disposable income must either be consumed or saved:

Key takeaway

The expenditure-output model finds equilibrium where planned spending equals actual output and explains how inventory changes push firms toward that point.

The Spending Multiplier Process

The spending multiplier explains why a change in autonomous spending can produce a larger total change in equilibrium real GDP. The process works through repeated rounds: one person’s spending becomes another person’s income, and the recipient spends part of that additional income. Each round becomes smaller because some income is saved.

In a simple economy with no taxes and no international trade:

The resulting change in equilibrium real GDP is:

For example, if $MPC=0.75$ and investment increases by $\$20$ billion, then:

The first round creates $\$20$ billion of income. Households spend $75\%$, or $\$15$ billion, in the next round. Recipients of that spending then spend $75\%$ of $\$15$ billion, or $\$11.25$ billion. Further rounds continue, becoming progressively smaller, and their total approaches $\$80$ billion.

The multiplier is smaller when saving, taxes, or imports remove more income from the domestic spending stream. A more complete expression can be written as:

where $t$ is the marginal tax rate and $MPI$ is the marginal propensity to import. The exact expression can vary with the definitions used in a problem, but the central principle remains: larger leakages produce a smaller multiplier.

Key takeaway

The multiplier magnifies an initial spending change, but the size of the magnification depends on how much additional income households spend domestically.

Fiscal Multipliers and Closing an Output Gap

Fiscal policy changes affect output through different multipliers. In the simplest model, the government spending multiplier is:

Therefore, a change in government purchases produces:

The tax multiplier is:

The tax multiplier is smaller in absolute value than the government spending multiplier because a tax cut increases disposable income, but households generally save part of the increase rather than spend all of it. The negative sign means that a tax increase reduces equilibrium real GDP.

If government purchases and taxes increase by the same amount, the balanced-budget multiplier is 1 in the simplest model:

For a recessionary gap, suppose potential GDP is $\$1{,}000$ billion and current equilibrium GDP is $\$900$ billion. The gap is $\$100$ billion. If the multiplier is $4$, the required initial spending increase, assuming no price-level effect, is:

In the expenditure-output model, this increase could close the calculated gap. In the AD–AS model, however, the resulting demand increase would likely raise the price level as well, so the actual increase in real GDP could be less than $\$100$ billion.

Key takeaway

Multiplier calculations provide a useful estimate, but they must be adjusted conceptually when higher demand also raises prices.

From Spending Changes to Long-Run Adjustment

The expenditure-output model holds the price level fixed, while the AD–AS model shows how spending changes affect both output and prices. When autonomous spending increases, the aggregate expenditure line shifts upward, equilibrium real GDP rises through the multiplier process, and aggregate demand shifts rightward. In the short run, the new equilibrium generally has higher real GDP and a higher price level.

When autonomous spending decreases, the aggregate expenditure line shifts downward, equilibrium real GDP falls, aggregate demand shifts leftward, and the economy generally experiences lower real GDP and a lower price level or weaker inflationary pressure.

The slope of short-run aggregate supply determines how the effects are divided between output and prices. If short-run aggregate supply is relatively flat, a demand increase produces a larger increase in real GDP and a smaller increase in the price level. If short-run aggregate supply is relatively steep, the output response is smaller and the price-level response is larger.

Over time, wages, expectations, and other input prices adjust. After a recessionary gap, weak demand and high unemployment can put downward pressure on wages and input costs, shifting short-run aggregate supply rightward toward potential GDP. After an inflationary gap, strong demand and labor shortages can raise wages and input costs, shifting short-run aggregate supply leftward toward potential GDP while increasing the price level.

Thus, a demand expansion can raise real GDP in the short run, but sustained demand increases eventually create greater upward pressure on prices. In the long run, productive capacity and potential GDP are more important determinants of real output than the price level alone.

Final takeaway

Use the expenditure-output model to calculate the spending-driven change in equilibrium output, then use the AD–AS model to evaluate how that change is divided between real GDP and the price level.