Acceleration principle
Acceleration principle is an economic theory that explains the relationship between changes in demand for consumer goods and the resulting changes in investment in capital goods [1]. The principle states that when consumer demand increases firms must invest in additional productive capacity to meet this higher demand. Because the required investment in capital equipment is typically much larger than the initial change in consumer demand the effect is said to be accelerated. This relationship plays an important role in explaining business cycle fluctuations and the volatility of investment spending.
Historical development
The concept of acceleration in economics has roots in the early twentieth century. Thomas Nixon Carver first discussed the relationship between consumer demand and capital goods in 1903 [2]. French economist Albert Aftalion developed similar ideas in 1909 in his work on production cycles. C.F. Bickerdike made further contributions in 1914 examining the relationship between demand and investment.
The term acceleration principle itself was introduced by American economist John Maurice Clark in his 1917 article "Business Acceleration and the Law of Demand: A Technical Factor in Economic Cycles" published in the Journal of Political Economy [3]. Clark demonstrated that net investment in producer goods is proportional to the rate of change in demand for finished products rather than its absolute level. This was a significant insight that helped explain why investment spending tends to be more volatile than consumption.
In the 1930s Clark further developed the theory in his book Strategic Factors in Business Cycles published in 1935. He introduced the idea that the accelerator coefficient is not fixed but varies according to economic conditions such as technological change and capacity utilization [4]. American economist Alvin Hansen extended these ideas in the 1940s and emphasized the role of the accelerator effect in generating economic fluctuations.
Theoretical foundation
The acceleration principle is based on the observation that the demand for capital goods is a derived demand [5]. Firms do not want machinery and equipment for their own sake but because these assets are needed to produce consumer goods. When consumer demand rises businesses need more productive capacity which requires investment in new capital equipment. The amount of this investment depends on the capital-output ratio which measures how much capital is needed to produce a given level of output.
The capital-output ratio
The capital-output ratio denoted as v represents the relationship between the stock of capital and the level of output. If a firm needs $3 of capital equipment to produce $1 of output per year then v equals 3. This ratio is assumed to be relatively stable in the short run although it may change over time due to technological progress or changes in the composition of production.
The basic accelerator formula
The simple accelerator model can be expressed mathematically as:
I = v × ΔY
Where I represents net investment, v is the accelerator coefficient (capital-output ratio) and ΔY is the change in output or income. This formula shows that investment depends not on the level of output but on its rate of change [6].
For example if the capital-output ratio is 3 and output increases by $100 then firms will need to invest $300 in new capital equipment. If output increases by only $50 in the following period investment will fall to $150 even though output is still growing.
How the accelerator works
Consider a company that produces furniture and currently has equipment capable of producing 1000 units per year [7]. If demand rises by 10% to 1100 units the firm needs additional equipment to produce the extra 100 units. Assuming a capital-output ratio of 4 the firm must invest $400 in new equipment to produce $100 worth of additional output.
| Year | Output | Change in Output | Required Capital | Net Investment |
|---|---|---|---|---|
| 1 | $1,000 | — | $4,000 | $0 |
| 2 | $1,100 | +$100 | $4,400 | $400 |
| 3 | $1,250 | +$150 | $5,000 | $600 |
| 4 | $1,350 | +$100 | $5,400 | $400 |
| 5 | $1,350 | $0 | $5,400 | $0 |
This example illustrates several important features of the accelerator. In year 3 output growth accelerates and investment rises sharply. In year 4 output continues to grow but at a slower rate so investment falls. In year 5 output remains constant and net investment drops to zero even though the economy is at a high level of activity.
The reverse accelerator effect
The acceleration principle works in both directions [8]. When economic growth slows down or output declines investment falls sharply. If consumer demand decreases firms find themselves with excess capacity and have no need to invest in new equipment. They may even allow existing capital to depreciate without replacement resulting in negative net investment.
This reverse effect helps explain why recessions can become severe. A decline in consumer spending leads to reduced investment which further reduces overall demand through the multiplier effect. The combination of the accelerator and multiplier effects can create a downward spiral that amplifies the initial decline.
The multiplier-accelerator model
American economist Paul Samuelson combined the acceleration principle with the Keynesian multiplier in his influential 1939 paper to create the multiplier-accelerator model [9]. This model demonstrates how the interaction between consumption and investment can generate cyclical fluctuations in economic activity.
In the multiplier-accelerator framework an initial increase in autonomous spending raises income through the multiplier effect. Higher income leads to increased consumption which through the accelerator induces additional investment. This investment further raises income creating a feedback loop. Depending on the values of the multiplier and accelerator the model can produce different patterns including damped cycles, explosive cycles or sustained oscillations.
British economist John Hicks extended this analysis in 1950 by adding upper and lower bounds to the model [10]. The upper bound or ceiling represents the full employment level of output while the lower bound or floor represents a minimum level of investment related to replacement demand and autonomous investment. These bounds prevent the explosive cycles that the simple model might generate and produce more realistic fluctuations.
Flexible accelerator theory
The simple acceleration principle assumes that firms immediately adjust their capital stock to the desired level. In reality such adjustment takes time due to delivery lags, installation requirements and financial constraints [11]. The flexible accelerator or capital stock adjustment model developed in the 1950s and 1960s addresses this limitation.
Under the flexible accelerator firms adjust their capital stock gradually toward the desired level. Only a fraction of the gap between desired and actual capital is closed in each period. The investment function becomes:
I = λ(K* - K)
Where K* is the desired capital stock, K is the actual capital stock and λ is the speed of adjustment coefficient between 0 and 1. This formulation produces smoother investment patterns that better match observed data.
Limitations and criticisms
The acceleration principle has several recognized limitations [12]:
- Constant capital-output ratio assumption - The theory assumes a fixed relationship between capital and output but this ratio changes over time due to technological progress and shifts in the composition of production
- Full capacity operation - The simple accelerator assumes firms operate at full capacity but in reality most firms maintain some excess capacity to meet unexpected demand
- Financial constraints - The theory ignores the role of profits, credit availability and interest rates in determining investment decisions
- Expectations and uncertainty - Investment decisions depend heavily on expectations about future demand which may not follow simple mechanical rules
- Indivisibility of capital - Capital equipment often comes in discrete units making smooth adjustment difficult
- Asymmetric responses - Firms may respond differently to increases and decreases in demand since it is easier to postpone investment than to rapidly increase it
Applications in economics
Despite its limitations the acceleration principle remains useful for understanding several economic phenomena:
Business cycle analysis
The accelerator helps explain why business cycles occur and why investment is more volatile than consumption [13]. Small changes in consumer demand can trigger large swings in investment spending which amplify economic fluctuations.
Economic forecasting
Economists use variants of the accelerator model to forecast investment spending. By examining trends in output growth analysts can anticipate changes in capital expenditure.
Policy analysis
Understanding the accelerator effect helps policymakers design stabilization policies. Measures that smooth consumption demand can reduce the volatility of investment and moderate business cycle fluctuations.
Advantages of the acceleration principle
- Provides clear explanation for the volatility of investment spending
- Helps explain the relationship between consumption and investment
- Forms the basis for understanding business cycle dynamics
- Can be combined with other theories such as the multiplier for richer analysis
- Emphasizes the derived nature of investment demand
| Acceleration principle — recommended articles |
| Investment — Business cycle — Demand — Economics — Production — Aggregate demand — Profit — Enterprise |
References
- Clark J.M. (1917), Business Acceleration and the Law of Demand: A Technical Factor in Economic Cycles, Journal of Political Economy, Vol. 25, No. 3, pp. 217-235.
- Clark J.M. (1935), Strategic Factors in Business Cycles, National Bureau of Economic Research.
- Samuelson P.A. (1939), Interactions between the Multiplier Analysis and the Principle of Acceleration, Review of Economics and Statistics, Vol. 21, No. 2, pp. 75-78.
- Hicks J.R. (1950), A Contribution to the Theory of the Trade Cycle, Oxford University Press.
- Jorgenson D.W. (1963), Capital Theory and Investment Behavior, American Economic Review, Vol. 53, No. 2, pp. 247-259.
- Koyck L.M. (1954), Distributed Lags and Investment Analysis, North-Holland Publishing.
Footnotes
- Clark J.M. (1917), pp. 217-220
- Clark J.M. (1917), pp. 217-218
- Clark J.M. (1917), pp. 220-225
- Clark J.M. (1935), pp. 85-95
- Clark J.M. (1917), pp. 225-230
- Samuelson P.A. (1939), pp. 75-76
- Clark J.M. (1917), pp. 230-232
- Hicks J.R. (1950), pp. 37-45
- Samuelson P.A. (1939), pp. 76-78
- Hicks J.R. (1950), pp. 95-110
- Jorgenson D.W. (1963), pp. 247-250
- Clark J.M. (1935), pp. 100-115
- Hicks J.R. (1950), pp. 120-135
Author: Sławomir Wawak