Country A and Country B both have the same production function: Y t = K t 0.5 L
ID: 1162037 • Letter: C
Question
Country A and Country B both have the same production function:
Yt = Kt0.5L0.5
In the standard Solow model, the population and labor force are fixed (L). The capital accumulation equation is:
?Kt + 1 = sYt - dKt
where s is the savings rate and d is the depreciation rate.
B. Suppose that both countries start with a capital stock per worker of 1. What are the initial levels of output per worker and consumption per worker? Remembering that the change in the capital stock is investment less depreciation, use a calculator (or spreadsheet) to show how the capital stock per worker will evolve over time in both countries. For each year, calculate output per worker and consumption per worker as well. How many years will it take before consumption per worker in Country B is higher than consumption per worker in Country A? Explain the intuition behind this result. Why is consumption per worker in Country B initially lower than in Country A, but eventually surpasses consumption per worker in Country A?
Explanation / Answer
This is my answer
Countries Aand B have the same production function. It is given as
Yt=Kt0.5Lt0.5
Population and labour force L is fixed.
The capital accumulation equation is
Kt+1=sYt-dKt
where s is the savings rate and d is the depreciation rate.
Capital stock per worker is 1 for both countries.
Output per worker=Y/L=Kt0.5Lt0.5/Lt
Y/L=Kt0.5/Lt0.5
C+I=Y
C=Y-I
I=S=Kt
C=Kt0.5Lt0.5 - sYt - dKt
Thank you