# Accelerator effect

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The accelerator effect in economics is a positive effect on private fixed investment of the growth of the market economy (measured e.g. by a change in Gross Domestic Product). Rising GDP (an economic boom or prosperity) implies that businesses in general see rising profits, increased sales and cash flow, and greater use of existing capacity. This usually implies that profit expectations and business confidence rise, encouraging businesses to build more factories and other buildings and to install more machinery. (This expenditure is called fixed investment.) This may lead to further growth of the economy through the stimulation of consumer incomes and purchases, i.e., via the multiplier effect.

Economics is the social science that studies the production, distribution, and consumption of goods and services.

Fixed investment in economics is the purchasing of newly produced fixed capital. It is measured as a flow variable – that is, as an amount per unit of time.

In macroeconomics, a multiplier is a factor of proportionality that measures how much an endogenous variable changes in response to a change in some exogenous variable.

## Contents

The accelerator effect also goes the other way: falling GDP (a recession) hurts business profits, sales, cash flow, use of capacity and expectations. This in turn discourages fixed investment, worsening a recession by the multiplier effect.

In economics, a recession is a business cycle contraction when there is a general decline in economic activity. Recessions generally occur when there is a widespread drop in spending. This may be triggered by various events, such as a financial crisis, an external trade shock, an adverse supply shock or the bursting of an economic bubble. In the United States, it is defined as "a significant decline in economic activity spread across the market, lasting more than a few months, normally visible in real GDP, real income, employment, industrial production, and wholesale-retail sales". In the United Kingdom, it is defined as a negative economic growth for two consecutive quarters.

The accelerator effect fits the behavior of an economy best when either the economy is moving away from full employment or when it is already below that level of production. This is because high levels of aggregate demand hit against the limits set by the existing labour force, the existing stock of capital goods, the availability of natural resources, and the technical ability of an economy to convert inputs into products.

Full employment is a situation in which everyone who wants a job can have work hours they need on fair wages. Because people switch jobs, full employment involves a positive stable rate of unemployment. An economy with full employment might still have underemployment where part-time workers cannot find jobs appropriate to their skill level. In macroeconomics, full employment is sometimes defined as the level of employment at which there is no cyclical or deficient-demand unemployment.

In macroeconomics, Aggregate Demand (AD) or Domestic Final Demand (DFD) is the total demand for final goods and services in an economy at a given time. It is often called effective demand, though at other times this term is distinguished. This is the demand for the gross domestic product of a country. It specifies the amounts of goods and services that will be purchased at all possible price levels.

## Multiplier effect vs. acceleration effect

The acceleration effect is the phenomenon that a variable moves toward its desired value faster and faster with respect to time. Usually, the variable is the capital stock. In Keynesian models, fixed capital is not in consideration, so the accelerator coefficient becomes the reciprocal of the multiplier and the capital decision degenerates to investment decision. In more general theory, where the capital decision determines the desired level of capital stock (which includes fixed capital and working capital), and the investment decision determines the change of capital stock in a sequences of periods, the acceleration effect emerges as only the current period gap affects the current investment, so do the previous gaps. The Aftalion-Clark accelerator v has such a form ${\displaystyle I_{t}=\mu v\sum _{i=1}^{\infty }\left(1-\mu \right)^{i}\left(Y_{t-i}-Y_{t-i-1}\right)}$, while the Keynesian multiplier m has such a form ${\displaystyle Y_{t}=mI_{t}={\frac {1}{1-MPC}}I_{t}}$ where MPC is the marginal propensity to consume.The idea of the accelerator has been very well explained by Hayek.

In economics and accounting, fixed capital is any kind of real, physical asset that is used in the production of a product but is not used up in the production. It contrasts with circulating capital such as raw materials, operating expenses and the like. It was first theoretically analyzed in some depth by the economist David Ricardo.

Working capital is a financial metric which represents operating liquidity available to a business, organisation or other entity, including governmental entities. Along with fixed assets such as plant and equipment, working capital is considered a part of operating capital. Gross working capital is equal to current assets. Working capital is calculated as current assets minus current liabilities. If current assets are less than current liabilities, an entity has a working capital deficiency, also called a working capital deficit.

In economics, the marginal propensity to consume (MPC) is a metric that quantifies induced consumption, the concept that the increase in personal consumer spending (consumption) occurs with an increase in disposable income. The proportion of disposable income which individuals spend on consumption is known as propensity to consume. MPC is the proportion of additional income that an individual consumes. For example, if a household earns one extra dollar of disposable income, and the marginal propensity to consume is 0.65, then of that dollar, the household will spend 65 cents and save 35 cents. Obviously, the household cannot spend more than the extra dollar.

## Business cycles vs. acceleration effect

As the acceleration effect dictates that the increase of income accelerates capital accumulation, and the decrease of income accelerates capital depletion (in a simple model), this might cause the system to become unstable or cyclical, and hence many kinds of business cycle models are of this kind (the multiplier-accelerator cycle models).

The multiplier–accelerator model is a macroeconomic model which analyzes the business cycle. This model was developed by Paul Samuelson, who credited Alvin Hansen for the inspiration. This model is based on the Keynesian multiplier, which is a consequence of assuming that consumption intentions depend on the level of economic activity, and the accelerator theory of investment, which assumes that investment intentions depend on the pace of growth in economic activity.

## Accelerator models

The accelerator effect is shown in the simple accelerator model. This model assumes that the stock of capital goods (K) is proportional to the level of production (Y):

Economics, business, accounting, and related fields often distinguish between quantities that are stocks and those that are flows. These differ in their units of measurement. A stock is measured at one specific time, and represents a quantity existing at that point in time, which may have accumulated in the past. A flow variable is measured over an interval of time. Therefore, a flow would be measured per unit of time. Flow is roughly analogous to rate or speed in this sense.

K = k×Y

This implies that if k (the capital-output ratio) is constant, an increase in Y requires an increase in K. That is, net investment, In equals:

In = k×ΔY

Suppose that k = 2 (usually, k is assumed to be in (0,1)). This equation implies that if Y rises by 10, then net investment will equal 10×2 = 20, as suggested by the accelerator effect. If Y then rises by only 5, the equation implies that the level of investment will be 5×2 = 10. This means that the simple accelerator model implies that fixed investment will fall if the growth of production slows. An actual fall in production is not needed to cause investment to fall. However, such a fall in output will result if slowing growth of production causes investment to fall, since that reduces aggregate demand. Thus, the simple accelerator model implies an endogenous explanation of the business-cycle downturn, the transition to a recession.

Modern economists have described the accelerator effect in terms of the more sophisticated flexible accelerator model of investment. Businesses are described as engaging in net investment in fixed capital goods in order to close the gap between the desired stock of capital goods (Kd) and the existing stock of capital goods left over from the past (K−1):

${\displaystyle I_{n}=x(K^{d}-K_{-1})}$

where x is a coefficient representing the speed of adjustment (1 ≥ x ≥ 0).

${\displaystyle I_{t}=\mu v\sum _{i=1}^{\infty }\left(1-\mu \right)^{i}\left(Y_{t-i}-Y_{t-i-1}\right)}$

The desired stock of capital goods is determined by such variables as the expected profit rate, the expected level of output, the interest rate (the cost of finance), and technology. Because the expected level of output plays a role, this model exhibits behavior described by the accelerator effect but less extreme than that of the simple accelerator. Because the existing capital stock grows over time due to past net investment, a slowing of the growth of output (GDP) can cause the gap between the desired K and the existing K to narrow, close, or even become negative, causing current net investment to fall.

Obviously, ceteris paribus, an actual fall in output depresses the desired stock of capital goods and thus net investment. Similarly, a rise in output causes a rise in investment. Finally, if the desired capital stock is less than the actual stock, then net investment may be depressed for a long time.

In the neoclassical accelerator model of Jorgenson, the desired capital stock is derived from the aggregate production function assuming profit maximization and perfect competition. In Jorgenson's original model (1963), [1] there is no acceleration effect, since the investment is instantaneous, so the capital stock can jump.

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## References

1. Jorgenson, Dale W. (1963). "Capital Theory and Investment Behavior". American Economic Review . 53 (2): 247–259. JSTOR   1823868.
• Knox, A. D. (1970). "The Acceleration Principle and the Theory of Investment: A Survey". In Shapiro, Edward (ed.). Macroeconomics: Selected Readings. New York: Harcourt, Brace & World. pp. 49–74. ISBN   0-15-551207-2.