Assume that in the Solow model, a country\'s production function is: y=k^(0.5) w
ID: 1090817 • Letter: A
Question
Assume that in the Solow model, a country's production function is: y=k^(0.5) where y is per capita income and k is per capita stock. There is no population growth and no technological changes. The savings rate is 40%, the depreciation rate is 5%. In period 1, the country's investment is 2.8.
1) What is the value of the country's capital stock in period 1?
a) 4 b) 49 c) 64 d) none of the above
2) What is the value of the country's capital stock in period 2?
a) 4 b) 49 c) 64 d) none of the above
3) What is the value of the country's per capita consumption in steady state?
a) 4.8 b) 3.2 c) 64 d) 7.839
Explanation / Answer
s = 0.4*y is the savings function
ussually we start with the net investmetnt at 0 is 2.8 as the capital K
from the production function we have , y = k^(0.5) = 2.8^0.5
total savings equal = 0.4*(2.8)^0.5
annual depreciation of the capital = 0.05*k = 0.05*2.8
gross investment = savings - depreciated value = additional value used as new investment
= 0.4*(2.8)^0.5 - (0.05)*2.8 = 0.5293
a) so the capital stock in period 1 is 2.8 + 0.5293 = 3.3293 (none of the above )
b) gross investment in period 2 = savings(1) - depreciation value(1)
= 0.4*(3.3293)^0.5 -0.05*(3.3293) = 0.563389
net investment or totall capital in period 2 = 3.3293 + 0.563389 = 3.9 (close to 4)
c) value of percapita consumption in steady state should be
0.4*k^(0.5) = 0.05*k
==> 8 = k^(0.5) ==> k = 64