Accelerator Model

The Accelerator Model: Investment Driven by Changes in Output

The accelerator model links the level of investment in an economy to the rate of change of output. It asserts that firms adjust their capital stock in response to changes in demand and output. The underlying assumption is that firms strive to maintain a relatively stable capital-output ratio, denoted by the accelerator coefficient (‘v’).

Investment is a function of the change in output:

• If output increases, firms will need to invest in additional capital to meet the rising demand, leading to a positive level of net investment.
• If output remains constant, firms only need to invest to replace worn-out capital (replacement investment), resulting in zero net investment.
• If output declines, firms will reduce their investment spending, as they don’t need to replace all depreciated capital, leading to negative net investment.

The formula for the accelerator model is:

$$I_t=v(Y_t-Y_{t-1})$$

Where:

• $I_t$ represents net investment in period $t$.
• $v$ is the accelerator coefficient (capital-output ratio).
• $Y_t$ is output in period $t$.
• $Y_{t-1}$ is output in the previous period $(t-1)$.

The accelerator model can be illustrated through a simple example:

Suppose a firm has a capital-output ratio of $2$ $(v=2)$. If output increases by 10 units, the firm needs to invest in 20 units of capital $(2\times 10)$ to maintain its desired capital-output ratio. Conversely, if output decreases by $5$ units, the firm will reduce its investment by $10$ units $(2\times -5)$

The sources provided do not go into detail about the accelerator model itself, but they do discuss the interaction of the accelerator with the multiplier. The multiplier-accelerator interaction suggests that changes in autonomous spending (like government spending or exports) can trigger a magnified effect on national income through a combined multiplier and accelerator process.

• An initial increase in autonomous spending leads to a rise in income through the multiplier effect.
• The increase in income, in turn, induces further investment through the accelerator effect, leading to a further rise in income, and so on.

This interaction can result in:

• Damped fluctuations: Where the income fluctuations gradually diminish over time.
• Constant amplitude fluctuations: Where the income fluctuations remain stable over time.
• Explosive cycles: Where the income fluctuations become increasingly larger over time.

Limitations of the Accelerator Model:

The accelerator model offers a simplified view of investment behavior and is subject to limitations:

• Assumes Constant Capital-Output Ratio: The accelerator coefficient (‘v’) might not be constant and could change due to factors like technological advancements or shifts in the composition of output.
• Ignores Other Determinants of Investment: The model overlooks factors like interest rates, business expectations, and the availability of credit, which also influence investment decisions.
• Focuses Only on Induced Investment: It does not account for autonomous investment, driven by factors unrelated to changes in output, such as technological innovations or government infrastructure projects.

Despite these limitations, the accelerator model provides a useful framework for understanding how changes in output can influence investment decisions and potentially amplify economic fluctuations.