Question

Write short notes on the following theories of investment: (a) Accelerator theory of investment (b) The flexible accelerator model (c) The \(q\) theory of investment

Short answer

Short Answer: The accelerator theory of investment states that investment in new capital goods is driven by expected increases in demand and is based on the relationship between investment and the rate of change of output or production. The flexible accelerator model, on the other hand, acknowledges that firms gradually adjust their capital stock over time due to various constraints. Finally, the \(q\) theory of investment focuses on the relationship between the market value of a firm's assets and their replacement cost, with firms investing when the market value of their assets is higher than their replacement cost.

Step-by-step solution

(a) Accelerator Theory of Investment)

The accelerator theory of investment is an economic concept that explains the relationship between the level of investment and the rate of change of output or production over time. According to this theory, firms invest in new capital goods (machinery, equipment, facilities) when they expect the demand for their goods or services to increase, and the additional capital goods will help them meet the growing demand. The main idea of the accelerator theory is that the rate of investment depends on the rate of change of production or output. The relationship is usually expressed by the equation: \( I_t = a(Y_t - Y_{t-1}) \) where \(I_t\) is the investment at time \(t\), \(a\) is the accelerator coefficient, \(Y_t\) is the output at time \(t\), and \(Y_{t-1}\) is the output at time \(t-1\). The higher the accelerator coefficient \(a\), the more sensitive firms are to changes in output.

(b) The Flexible Accelerator Model)

The flexible accelerator model, also known as the lags adjustment model or partial adjustment model, is a modification of the basic accelerator theory of investment. The flexible accelerator model recognizes that firms do not instantly adjust their capital stock to match the desired level of investment. Instead, they adjust their capital stock gradually over time to reach the desired level of investment. This is because firms usually face constraints, such as financial limitations, production capacity limits, and the need for planning and implementation. The flexible accelerator model is represented by the equation: \( I_t = b(K_{t}^{*} - K_{t-1}) \) where \(I_t\) is the investment at time \(t\), \(b\) is the speed of adjustment coefficient (between 0 and 1), \(K_{t}^{*}\) is the desired capital stock at time \(t\), and \(K_{t-1}\) is the actual capital stock at time \(t-1\). The higher the speed of adjustment coefficient \(b\), the faster firms adjust their capital stock to reach the desired level.

(c) The \(q\) Theory of Investment)

The \(q\) theory of investment, developed by James Tobin, is another approach to understanding investment behavior. The \(q\) theory focuses on the relationship between the market value of a firm's existing assets and the replacement cost of those assets. The \(q\) ratio refers to the ratio of the market value of a firm's assets to the replacement cost of those assets, and it is used as an indicator for firms to decide whether to invest in new assets. The main idea of the \(q\) theory is that a firm will invest in new capital when the \(q\) ratio is greater than 1, meaning that the market value of the firm's assets is higher than their replacement cost. Conversely, if the \(q\) ratio is less than 1, the firm will not invest in new capital, as it would be more profitable to buy existing assets rather than replace them. In summary, the three theories of investment covered in this exercise offer three different perspectives on investment behavior: - The accelerator theory focuses on the relationship between investment and the rate of change of output or production. - The flexible accelerator model considers the gradual adjustment of capital stock to reach the desired level of investment. - The \(q\) theory of investment emphasizes the role of the market value of a firm's assets and the replacement cost in investment decisions.

Key concepts

Accelerator Theory

The accelerator theory of investment is a concept in economics that describes how investment activity by firms is influenced by changes in production levels. Imagine a company that produces goods to meet consumer demands. If consumer demands increase, the company will need to ramp up its production.

This often requires additional investment in new capital goods, such as machinery and equipment. The connection between these demands and the company's investment decisions is captured by this theory. When production is expected to rise, investments also increase, as firms strive to ensure they have enough capacity to produce the demanded goods.

The relationship can be expressed with the formula: \( I_t = a(Y_t - Y_{t-1}) \) Here, \( I_t \) is the investment at time \( t \), \( a \) is the accelerator coefficient, \( Y_t \) is the output at time \( t \), and \( Y_{t-1} \) is the output at time \( t-1 \). A larger accelerator coefficient means that investment is more sensitive to changes in output, indicating rapid reactions to market changes.

Flexible Accelerator Model

The flexible accelerator model refines the basic accelerator theory by acknowledging that firms often can't immediately adjust their capital stock to match a desired level of investment. There are practical reasons for this delay:

• Financial limitations
• Production capacity constraints
• The need for detailed planning and implementation

Instead of immediate adjustment, firms gradually shift towards the desired investment level over time. This is described by the equation:\( I_t = b(K_{t}^{*} - K_{t-1}) \)In this equation, \( I_t \) is the investment at time \( t \), \( b \) represents the speed of adjustment (a fraction between 0 and 1), \( K_{t}^{*} \) is the desired capital stock at time \( t \), and \( K_{t-1} \) is the actual capital stock at \( t-1 \).

The closer \( b \) is to 1, the quicker the firm adjusts its capital stock to reach its desired level, indicating less friction in the adjustment process.

q Theory of Investment

The \( q \) theory of investment, attributed to James Tobin, provides another insightful perspective on how firms decide to invest. At its core, this theory links the firm's market performance to its investment decisions. Two essential components are compared:

• The market value of the firm's assets
• The cost of replacing those assets

This comparison is encapsulated in the \( q \) ratio. If \( q \) is greater than 1, it indicates that the market value of the firm's assets exceeds the cost of replacing them. In such a scenario, the firm finds it worthwhile to invest in new capital because the return from new investments is favorable.

Conversely, if \( q \) is less than 1, the market undervalues the firm's assets compared to its replacement cost, signalling to the firm to hold off on new investments and perhaps focus on acquiring pre-existing assets instead. This theory highlights the critical role of market valuations in guiding strategic investment decisions.