8. Consider the flexible accelerator model of economic theory. Nerlove postulates the following hypothesis, known as the partial adjustment hypothesis \( J_{t}=\partial\left(K_{t}-K_{t-1}\right) \) interpret the foregoing relationship between actual investment, \( I_{t} \), the coefficient of adjustment, \( \partial,\{0<\partial \leq 1\} \) and the desired investment, \( \left(K_{t}-K_{t-1}\right) \), for that period (4 marks)

In the context of the flexible accelerator model, the relationship \( J_{t}=\partial\left(K_{t}-K_{t-1}\right) \) illustrates how actual investment \( I_{t} \) adjusts over time towards a desired level of investment. Here, \( J_{t} \) represents the current period's actual investment made by firms, while \( K_{t}-K_{t-1} \) signifies the gap between the desired capital stock and the previous year's stock. The coefficient \( \partial \), which ranges between 0 and 1, indicates the speed of this adjustment. A value closer to 1 suggests that firms react more rapidly to changes in desired investment, while a value closer to 0 implies a slower response due to various frictions or constraints. Understanding this model can help in real-world economies by predicting how companies allocate their investments in response to expected changes in demand or market conditions. For example, if firms anticipate an uptick in consumer demand leading to higher desired capital stock, they will increase their actual investments accordingly. The flexibility captured in the model thus helps policymakers gauge how investment behavior can affect overall economic growth, allowing them to create strategies that stimulate investment during economic downturns or transitions.