Consider two imaginary countries, Arcadia and Brigadoon. Arcadia\'s GDP per work
ID: 1178926 • Letter: C
Question
Consider two imaginary countries, Arcadia and Brigadoon. Arcadia's GDP per worker is 1.44 times that of Brigadoon. The ratio of physical investment to output is 0.3 in Arcadia, and in Brigadoon it is 0.25. Population and hence labour supply is constant over time in both countries. So is total factor productivity. Moreover, total factor productivity is the same in both countries. Suppose output in each country i is produced according to where Y is output, K is (physical) capital and L is labour. Meanwhile, capital is accumulated according to Output per worker (Y/L) in each country i will converge to a constant. Derive an expression for this constant in terms of si, delta and theta. What must theta be in order for this model to fit the facts?Explanation / Answer
here, i m using x in place of theta
y(t) = [k^x]*[L^1-x]
for contry Arcadia
K = .3Y
so,
y = (.3^x)*(y^x)*L^(1-x)
y^(1-x) = (.3^x)*L^(1-x)
y/L = .3^(x/1-x)
similary for Brigadoon
y/L = .25^(x/1-x)