(3) Suppose the interest rate rises, starting from the situation in part (a). Will you save more or less in your working period? Discuss the change of your saving plan based on the substitution effect (SE) and income effect (IE), separately. (5 分)

3. The textbook Solow-Swan model gives you the following framework setup: \(\succ\) Aggregate production function: \(Y_{t} = AK_{t}^{\alpha}L_{t}^{1 - \alpha}\), where \(Y_{t}, K_{t}\), and \(L_{t}\) are aggregate output, aggregate physical capital, and total labor force at time \(t\), respectively. Total factor productivity \(A\) and the capital share \(\alpha\) are assumed constant. \(\succ\) Physical capital accumulation: \(K_{t + 1} = I_t + (1 - d)K_t\) , where \(I_{t}\) is the gross investment at time \(t\) and the capital depreciates at a constant rate of \(d\) > Labor force growth: \( L_{t+1} = (1 + n)L_t \), where \( n \) is a constant labor growth rate. > Aggregate output is distributed to aggregate consumption, \( C_t = (1 - s)Y_t \), and aggregate saving, \( S_t = sY_t \), where the saving rate \( s \) is constant. There is no government in this closed economy. Goods market is in equilibrium for all time. (1) Let \( k_{t} = K_{t} / L_{t} \) and \( y_{t} = Y_{t} / L_{t} \) be capital-labor ratio and output per worker, respectively, find the first-order difference equation for \( k_{t} \), that is \( k_{t + 1} = g(k_{t}) \). (5 分)

(3) Suppose the interest rate rises, starting from the situation in part (a). Will you save more or less in your working period? Discuss the change of your saving plan based on the substitution effect (SE) and income effect (IE), separately. (5 分)

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