**income‐expenditure**model to argue that the economy's equilibrium level of output or real GDP may not corresPond to the natural level of real GDP. In the income‐expenditure model, the equilibrium level of real GDP is the level of real GDP that is consistent with the current level of aggregate expenditure. If the current level of aggregate expenditure is not sufficient to purchase all of the real GDP supplied, output will be cut back until the level of real GDP is equal to the level of aggregate expenditure. Hence, if the current level of aggregate expenditure is not sufficient to purchase the

*natural*level of real GDP, then the equilibrium level of real GDP will lie somewhere

*below*the natural level.

In this situation, the classical theorists believe that prices and wages will fall, reducing producer costs and increasing the supply of real GDP until it is again equal to the natural level of real GDP.

**Sticky prices.** Keynesians, however, believe that prices and wages are not so flexible. They believe that prices and wages are **sticky**, especially downward. The stickiness of prices and wages in the downward direction prevents the economy's resources from being fully employed and thereby prevents the economy from returning to the natural level of real GDP. Thus, the Keynesian theory is a rejection of Say's Law and the notion that the economy is self‐regulating.

**Keynes's income‐expenditure model.** Recall that real GDP can be decomposed into four component parts: aggregate expenditures on consumption, investment, government, and net exports. The **income‐expenditure model** considers the relationship between these expenditures and current real national income. Aggregate expenditures on investment, *I*, government, *G*, and net exports, *NX*, are typically regarded as *autonomous* or *independent* of current income. The exception is aggregate expenditures on consumption. Keynes argues that aggregate consumption expenditures are determined primarily by current real national income. He suggests that aggregate consumption expenditures can be summarized by the equation

where *C* denotes autonomous consumption expenditure and *Y* is the level of current real income, which is equivalent to the value of current real GDP. The **marginal propensity to consume** ( *mpc*), which multiplies *Y*, is the *fraction* of a change in real income that is currently consumed. In most economies, the *mpc* is quite high, ranging anywhere from .60 to .95. Note that as the level of *Y* increases, so too does the level of aggregate consumption.

Total **aggregate expenditure**, *AE*, can be written as the equation

where *A* denotes total **autonomous expenditure**, or the sum *C + I + G* + *NX*. Different levels of autonomous expenditure, *A*, and real national income, *Y*, correspond to different levels of aggregate expenditure, *AE.*

Equilibrium real GDP in the income‐expenditure model is found by setting current real national income, *Y*, equal to current aggregate expenditure, *AE.* Algebraically, the equilibrium condition that *Y = AE* implies that

In words, the equilibrium level of real GDP, *Y**, is equal to the level of autonomous expenditure, *A*, multiplied by *m*, the **Keynesian multiplier.** Because the *mpc* is the *fraction* of a change in real national income that is consumed, it always takes on values between 0 and 1. Consequently, the Keynesian multiplier, *m*, is always greater than 1, implying that equilibrium real GDP, *Y**, is always a *multiple* of autonomous aggregate expenditure, *A*, which explains why *m* is referred to as the Keynesian multiplier.

The determination of equilibrium real national income or GDP using the income‐expenditure approach can be depicted graphically, as in Figure . This figure shows three different **aggregate expenditure curves**, labeled *AE* _{1}, *AE* _{2}, and *A* _{3}, which correspond to three different levels of autonomous expenditure, *A* _{1}, *A* _{2}, and *A* _{3}. The upward slope of these *AE* curves is due to the positive value of the *mpc.* As real national income *Y* rises, so does the level of aggregate expenditure. The Keynesian condition for the determination of equilibrium real GDP is that *Y = AE.* This equilibrium condition is denoted in Figure by the diagonal, 45° line, labeled *Y = AE.*

To find the level of equilibrium real national income or GDP, you simply find the intersection of the *AE* curve with the 45° line. The levels of real GDP that correspond to these intersection points are the *equilibrium* levels of real GDP, denoted in Figure as *Y* _{1}, *Y* _{2}, and *Y* _{3}. Note that each *AE* curve corresponds to a different equilibrium level for *Y.* Note also that each *Y* is a *multiple* of the level of autonomous aggregate expenditure, *A*, as was found in the algebraic determination of the level of equilibrium real GDP.

**Graphical illustration of the Keynesian theory.** The Keynesian theory of the determination of equilibrium output and prices makes use of both the income‐expenditure model and the aggregate demand‐aggregate supply model, as shown in Figure .

Suppose that the economy is initially at the natural level of real GDP that corresponds to *Y* _{1} in Figure . Associated with this level of real GDP is an aggregate expenditure curve, *AE* _{1}. Now, suppose that autonomous expenditure declines, from *A* _{1} to *A* _{3}, causing the *AE* curve to shift downward from *AE* _{1} to *AE* _{3}. This decline in autonomous expenditure is also represented by a reduction in aggregate demand from *AD* _{1} to *AD* _{2}. At the same price level, *P* _{1}, equilibrium real GDP has fallen from *Y* _{1} to *Y* _{3}. However, the intersection of the *SAS* and *AD* _{2} curves is at the lower price level, *P* _{2}, implying that the price level falls. The fall in the price level means that the aggregate expenditure curve will not fall all the way to *AE* _{3} but will instead fall only to *AE* _{2}. Therefore, the new level of equilibrium real GDP is at *Y* _{2}, which lies below the natural level, *Y* _{1}.

Keynes argues that prices will not fall further below *P* _{2} because workers and other resources will resist any reduction in their wages, and this resistance will prevent suppliers from increasing their supplies. Hence, the *SAS* curve will not shift to the right as in the classical theory and the economy will remain at *Y* _{2}, where some of the economy's workers and resources are *unemployed.* Because these unemployed workers and resources earn no income, they cannot purchase goods and services. Consequently, the aggregate expenditure curve remains stuck at *AE* _{2}, preventing the economy from achieving the natural level of real GDP. Figure therefore illustrates the Keynesians' rejection of Say's Law, price level flexibility, and the notion of a self‐regulating economy.