Answer :
The change in capital per worker during the year of 2100 is 16 units of capital per worker per year. capital per worker at the beginning of 2101 would be 165.62 units of capital per worker. If population growth rate is 2% then 15.62 units of capital per worker per year
In the Solow model, an economy's output, as well as its level of capital and labor, determines its rate of economic growth. The Solow model predicts that the per capita growth rate of a country is determined by capital accumulation until it reaches its steady-state level, which occurs when capital stock is constant.
The change in capital per worker is calculated as follows: dK/dt = sY/L - δK/Lwhere: s is the investment rate, Y/L is the output per worker, δ is the depreciation rate, and K/L is the capital per worker.In year 2100, the quantity of capital per worker is 150 and the quantity of output per worker is 100.
Given that the fraction of output invested was 25%, and the depreciation rate was 6%, the change in capital per worker during the year of 2100 is calculated as follows = 0.25, Y/L = 100, δ = 0.06, K/L = 150dK/dt = sY/L - δK/L= (0.25 x 100) - (0.06 x 150)= 25 - 9 = 16 units of capital per worker per year
Therefore, the change in capital per worker during the year of 2100 is 16 units of capital per worker per year. The capital per worker at the beginning of year 2101 would be:K/L2101 = K/L2100 + dK/dt= 150 + 16= 166 units of capital per worker
Assuming the population growth rate is 2%, the capital per worker equation becomes:dK/dt = sY/(L (1 + n)) - δK/Lwhere n is the population growth rate. In this case,n = 0.02dK/dt = 0.25 x 100/(1 + 0.02) - 0.06 x 150/ (1 + 0.02)= 24.5 - 8.88= 15.62 units of capital per worker per year
Thus, the capital per worker at the beginning of 2101 would be:K/L2101 = K/L2100 + dK/dt= 150 + 15.62= 165.62 units of capital per worker In conclusion, population growth decreases the capital per worker, and this decrease becomes more significant when the population growth rate is higher.
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