Answer :
Country A would converge to the steady-state faster because its current output per worker is closest to the calculated steady-state output per worker.
Using the production function y = [tex]Ak^{1/2[/tex] and the provided parameters, we calculate the steady-state for each country.
The formula for the steady-state level of capital (k*) is given by: investment rate / depreciation rate
For all countries, the investment rate is 10% (0.10) and the depreciation rate is 2% (0.02). Thus, k* = 0.10/0.02 = 5.
Steps to calculate steady-state output per worker
- Country A: k* = 5 → y* = √5 ≈ 2.24
- Country B: k* = 5 → y* = √5 ≈ 2.24
- Country C: k* = 5 → y* = √5 ≈ 2.24
- Country D: k* = 5 → y* = √5 ≈ 2.24
Since all countries converge to the same steady-state level of output per worker (approximately 2.24), the time it takes to reach that state depends on how far each country is currently from this level:
- Country A: Starting at 2, close to 2.24
- Country B: Starting at 3, further than Country A but still reasonably close
- Country C: Starting at 4, further than B
- Country D: Starting at 5, furthest among all
Country A is closest to its steady-state output level, implying it would converge faster to the steady-state compared to the other countries
