Assuming individual firms' production technology, $f(k) = Ak^{\alpha}$ \\
$\alpha \in (0, 1)$ \\
Goods Price: $P = 1$ \\
Investment adjustment costs: $C(I) = \frac{h}{2}I^2$ \\
Parameter h reflects the speed of investment adjustment \\
The dynamic equation for investment $\dot{k}(t) = I - \delta k$ \\
Parameter $\delta$ reflects the capital depreciation rate. The number of \\
firms is N. Please answer the following questions based on Tobin's \\
investment theory: \\
(4) Analyze the entire adjustment process of the economic system's \\
capital stock (K) and the price of capital goods (q) as it moves \\
towards a new equilibrium when the firm faces an unexpected \\
temporary increase in interest rates. Please calculate (solve the \\
differential equation) and provide an explanation with economic \\
intuition.