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

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.

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.

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.