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.