一个关于Blassa-Samuelson的计算问题

题中变量后面的T和N都是脚标，表示tradable和non-tradable。

Consider the Samuelson-Balassa model. The production function in the tradable sector is:
YT= AT * KT^0.5 * LT^0.5 ,
where YT is output in the tradable sector, AT is total factor productivity in the tradable sector, KT is the capital stock in the tradable sector and T L is the labour in the tradable sector.
The production function in the nontradable sector is:

YN= AN * KN^0.5 * LN^0.5 ,
where YN is output in the nontradable sector, AN is total factor productivity in the nontradable sector, KN is the capital stock in the nontradable sector and LN is the labour in the non-tradable sector.

Assume that the world interest rate is r =1 (note that r is strictly 1, donot unitize it by dividing it by 100). Set AT = AN = 2.


a. Work out the capital/labour ratio in the tradable sector (kT) and the real wage, (w).
Present your work clearly and explain your answer.

b. Work out the capital/labour ratio in the nontradable sector (kN) and the relative price of non-tradables relative to tradables (p).
Present your work clearly and explain your answer.

c. Determine the effects on the price of nontradables relative to tradables (p) and the capital/labour ratio in the nontradable sector (kN) if:
(i) AT doubles and AN does not change.
(ii) AT does not change and AN increases by 50%.
(iii) AT triples and AN doubles.

参考公式：
YT=AT F(KT, LT)
YN=AN F(KN,LN)
yT=YT/LT =AT f(kT)
yN=YN/LN =AN f(kN)
kT=KT/LT
kN=KN/LN
p relative price of non-tradable in terms of tradable
r=AT f'(kT)
w=AT [f(kT)-f'(kT)kT]
r=AN g'(kN)
w=AN [g(kN)-g'(kN)kN]