Reference no: EM132406062
1. Consider two imaginary countries, Atlantis and Balagan. Atlantis' GDP per worker is 1.96 times that of Balagan. The ratio of physical investment to output is 0.35 in Atlantis, and in Balagan it is 0.25. Population and hence labour supply is constant over time in both countries. So is total factor productivity.
(a) Suppose output in each country i = A, B is produced according to
Yi(t) = ZiKθ i (t)L 1-θ i (t)
where Y is output, Z is total factor productivity, K is (physical) capital and L is labour. Meanwhile, capital is accumulated according to
K? i(t) = siYi(t) - δKi(t)
where an overdot represents a time derivative, i.e.
X? (t) := d/dtX(t).
(i) Output per worker (Y/L) in each country i will converge to a constant as t → ∞. Derive an expression for this constant in terms of Zi , si, δ and θ.
(ii) Suppose ZA = ZB. What must θ be in order for this model to fit the facts?
(iii) Suppose θ = 1/3. What must ZA/ZB be in order for the model to fit the facts?
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