Aggregate Expenditure and Equilibrium Output
(Part E)
by
Charles Lamson
The Multiplier
Now that we know from the last several posts how the equilibrium value of income is determined, we ask: How does the equilibrium level of output change when planned investment changes? If there is a sudden change in planned investment, how will output respond, if it responds at all? As we will see, the change in equilibrium output is greater than the initial change in planned investment. Output changes by a multitude of the change in planned investment. So, this multiple is called the multiplier. The multiplier is defined as the ratio of the change in the equilibrium level of output to a change in some autonomous variable. An autonomous variable is a variable that is assumed not to depend on the state of the economy---that is, a variable is autonomous if it does not change in response to changes in the economy. In this post, we consider planned investment to be autonomous. This simplifies our analysis and provides a foundation for later discussions. With planned investment autonomous, we can ask how much the equilibrium level of output changes when planned investment changes. Remember that we are not trying here to explain why planned investment changes; we are simply asking how much the equilibrium level of output changes when (for whatever reason) planned investment changes. (Beginning in a later post, we will no longer take planned investment as given and it will be explained how planned investment is determined.) Consider a sustained increase in planned investment (I) of $25 billion---that is, suppose I increases from $25 billion to $50 billion and stays at $50 billion if equilibrium existed at I = $25 billion, an increase in planned investment of $25 billion will cause a disequilibrium, with planned aggregate expenditure greater than aggregate output by $25 billion. Firms immediately see unplanned reductions in their inventories, and, as a result, they begin to increase output.  Let us say the increase in planned investment comes from an anticipated increase in travel that leads airlines to purchase more airplanes, car rental companies to increase purchases of automobiles, and bus companies to purchase more buses (all capital goods). The firms experiencing unplanned inventory declines will be automobile manufacturers, bus producers, and aircraft producers---GM, Ford, McDonnell Douglas, Boeing, and so forth. In response to declining inventories of planes, buses, and cars, these firms will increase output. Now suppose these firms raise output by the full $25 billion increase in planned investment. Does this restore equilibrium? No, it does not, because when output goes up, people earn more income and a part of that income will be spent. This increases planned aggregate expenditure even further. In other words, an increase in I also leads indirectly to an increase in consumption spending (C). To produce more airplanes, Boeing has to hire more workers or ask its existing employees to work more hours. It also must buy more engines from General Electric, more tires from Goodyear, and so forth. Owners of these firms will earn more profits, produce more, hire more workers, and pay out more in wages and salaries. This added income does not vanish Into thin air. It is paid to households that spend some of it and save the rest. The added production leads to added income, which leads to added consumption spending. If planned investment (I) goes up by $25 billion initially and is sustained at this higher level, an increase of output of $25 billion will not restore equilibrium, because it generates even more consumption spending (C). People buy more consumer goods. There are unplanned reductions of inventories of basic consumption items---washing machines, food, clothing, and so forth---and this prompts other firms to increase output. The cycle starts all over again.    Why doesn't the multiplier process go on forever? The answer is because only a fraction of the increase in income is consumed in each round. Successive increases in income become smaller and smaller in each round of the multiplier process, due to leakage as saving, until equilibrium is restored.  *Again note that the triple equal sign means this is an identity, or something that is always true. The Multiplier Equation Is there a way to determine the size of the multiplier without using graphic analysis? Yes, there is. Assume that the market is in equilibrium at an income level of Y = 500. Now suppose planned investment (I)---thus planned aggregate expenditure (AE)---increases and remains higher by $25 billion. Planned aggregate expenditure is greater than output, there is an unplanned inventory reduction, and firms respond by increasing output (income) (Y). This leads to a second round of increases, and so on. What will restore equilibrium? Look at Figure 10 (from last post, and reintroduced below) and recall: planned aggregate expenditure (AE ≡ C + I) is not equal to aggregate output (Y) unless S = I; the leakage of saving must exactly match the injection of planned investment spending for the economy to be in equilibrium. Recall also, we assumed that planned investment jumps to a new higher level and stays there: it is a sustained increase of $25 billion in planned investment spending. As income rises, consumption rises and so does saving. Our S = I approach to equilibrium leads us to conclude:  Otherwise, I will continue to be greater than S, and C + I will continue to be greater than Y.   It is possible to figure how much Y must increase in response to the additional planned investment before equilibrium will be restored. Y will rise, pulling S up with it until the change in saving is exactly equal to the change in planned investment---that is, until S is again equal to I at its new higher level. Because added saving is a fraction of added income (the MPS), the increase in income required to restore equilibrium must be a multiple all of the increase in planned investment. Recall that the marginal propensity to save (MPS) is the fraction of a change in income that is saved. It is defined as the change in S (△S) over the change in income (△Y): MPS = △S/△Y Because △S must be equal to △/ for equilibrium to be restored, we can substitute △I for △S and solve: MPS = △I/△Y Therefore: △Y = △I x 1/MPS As you can see, the change in equilibrium income (△Y) is equal to the initial change in planned investment (△I) times 1/MPS. The multiplier is 1/MPS: multiplier ≡ 1/MPS Because MPS + MPC ≡ 1 , MPS ≡ 1 - MPC, it follows that the multiplier is equal to: Multiplier ≡ 1/1 - MPC  Recall from last post that in our example, the MPC is .75, so the MPS must equal 1 - .75 or .25. Thus, the multiplier is one divided by .25, or 4. The change in the equilibrium level of Y is 4 x $25 billion, or $100 billion dollars. Also note that the same analysis holds when planned investment falls. If planned investment falls by a certain amount and is sustained at this lower level, output will fall by a multiple of the reduction in I. As the initial shock is felt and firms cut output, they lay people off. The result: income, and subsequently consumption, falls. The Size of the Multiplier in the Real World In considering the size of the multiplier, it is important to realize that the multiplier we derived in this post is based on a very simplified picture of the economy. First, we have assumed that planned investment is autonomous and does not respond to changes in the economy. Second, we have thus far ignored the role of government, financial markets, and the rest of the world in the macroeconomy. For these reasons, it would be a mistake to move on from this post thinking that national income can be increased by $100 billion simply by increasing planned investment spending by $25 billion. In reality, the size of the multiplier is about 1.4. That is, a sustained increase in autonomous spending of $10 billion into the U.S. economy can be expected to raise real GDP over time by about $14 billion (Case & Fair, 2004). This is a far cry from the value of 4.0 that we used in this post.  The Multiplier in Action: Recovering from the Great Depression The Great Depression began in 1930 and lasted nearly a decade. Real output in 1938 was lower than real output in 1929, and the unemployment rate never fell below 14 percent of the labor force between 1930 and 1940. How did the economy get "stuck" at such a low level of income and a high level of unemployment? The model that we analyzed in this post can help us answer this question. If firms do not wish to undertake much investment (I is low) or if consumers decide to increase their saving and cut back on consumption, then planned spending will be low. Firms do not want to produce more because, with many workers unemployed, households do not have the income to buy the extra output that firms might produce. Households, who would purchase more if they had more income, cannot find jobs that would enable them to earn additional income. The economy is caught in a vicious circle. How might such a cycle be broken? One way is for planned aggregate expenditure to increase, increasing aggregate output via the multiplier effect. This increase in AE may occur naturally, or it may be caused by a change in government policy. In the late 1930s, for example, the economy experienced a surge of both residential and nonresidential investment. Between 1935 and 1941, total investment spending (in real terms) increased 64 percent and residential investment more than doubled. There can be no doubt that this increased investment had a multiplier effect. In just five years, employment in the construction industry increased by more than 400,000, employment in manufacturing industries jumped by more than 1 million, and total employment grew by more than 5 million. As more workers were employed, more income was generated, and some of this added income was spent on consumption goods. Inventories declined and firms began to expand output. Between 1935 and 1940, real output (income) increased by more than one-third and the unemployment rate dropped from 28.3 percent to 14.6 percent.  However, 14.6 percent is a very high rate of unemployment; the Depression was not yet over. Between 1940 and 1943 the depression ended, with the unemployment rate dropping to 1.9 percent in 1943. This recovery was triggered by the mobilization for World War II and the significant increase in government purchases of goods and services, which rose from $14 billion in 1940 to $88.6 billion in 1943. In the next several posts, we will explore this government spending multiplier, and you will see how the government can help stimulate the economy by increasing its spending. *CASE & FAIR, 2004, PRINCIPLES OF ECONOMICS, 7TH ED., PP. 445-450* end |
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