# The Accelerator Principle

The accelerator principle says that small changes in consumer spending can cause big percentage changes in investment. It played a role in many business-cycle theories and is still used today to explain some of the fluctuation in investment.

In a very simple form the accelerator principle assumes that the ratio of capital to output tends to remain constant. Suppose, for example, that normally it takes \$1000 worth of equipment to manufacture \$1000 worth of shoes each year. Suppose further that each year one tenth of the equipment wears out. If there is no growth or decline, total investment each year will be \$100, all for replacement.

Now suppose that the sales of shoes jumps by 5%, to \$1050 each year. The new desired amount of equipment will also rise by 5%, to \$1050. However, to obtain this new level, investment will have to increase by 50%, to \$150. Thus if firms desire a constant capital-to-output ratio, a small percentage change (either an increase or decrease) in final sales can lead to a big percentage change in investment.

The same logic can work with inventories (though the term "accelerator" usually only refers to the application of this logic to business investment in factories and equipment). Suppose that a business wants to keep an inventory of one month's sales. If annual sales are \$1,200,000, it will want an inventory of \$100,000. In a steady state, with no expansion or contraction of sales, it will order \$100,000 each month to replace the goods it sells and to keep inventories at the desired level.

Now suppose that sales drop 10%, to \$1,080,000 per year. Each month the firm will now sell only \$90,000 worth of goods. If the firm immediately reduces monthly purchases to \$90,000, it leaves inventories at \$100,000. This pattern is shown in the table below. As long as monthly sales just equal monthly purchases, the level of inventories does not change. To reduce inventories, purchases must drop by more than sales. Thus a 10% reduction in final sales will cause more than a 10% reduction in wholesale sales if firms want to keep their inventory-to-sales ratio a constant. The pattern works in reverse as well. A 10% increase in final sales will cause more than a 10% increase in wholesale sales.

 Inventories Adjust to Sales Monthly Sales Monthly Purchases Inventory \$100,000 \$100,000 \$100,000 100,000 100,000 100,000 90,000 90,000 100,000 90,000 90,000 100,000 90,000 80,000 90,000 90,000 90,000 90,000

The attractive aspect of using an accelerator-type of theory to explain investment is that there are sizable swings in inventories that follow business fluctuations. In recessions production drops more than sales as businesses reduce inventories, and during booms production rises by more than sales as businesses increase inventories. In fact there were some U.S. recessions during the years 1946 to 1960 in which much of the reduction in output was due to changes in inventories. The second table shows quarterly GNP and final sales for the years 1953 and 1954. Notice that from the second quarter of 1953 until the second quarter of 1954 GNP drops by \$7 billion. However, final sales continue to rise until the fourth quarter of 1953, and drop only by \$2.6 billion from then until the second quarter of 1954.

 U.S. GNP and Final Sales, 1953-1954 Year and Quarter GNP Final Sales 1953 I \$365.4 \$363.0 II 368.8 365.6 III 367.8 367.1 IV 362.6 367.1 1954 I 362.0 364.6 II 361.8 364.5 III 366.2 368.4 IV 375.0 373.8 Source of Data: National Income and Product Accounts of the United States, 1929-1974, (U.S. Department of Commerce), p ll. (Data are in billions of dollars.)

Final sales differ from GNP because of inventory changes. If final sales exceed GNP, businesses are reducing inventories, and if final sales are less than GNP, businesses are increasing inventories. In the 1953-54 period, businesses switched from inventory accumulation to inventory liquidation, and this change, more than any change in buyer demand, explains the drop in GNP.

Patterns of inventory movement such as those illustrated in this table do not prove that an accelerator-like principle is involved; there are other possible reasons inventories may move in such a pattern. But the accelerator principle, applied both to fixed investment and inventories, is one aspect of business-cycle theory that is still alive today.