3. The unit cost function,Cj(.) has three basic properties: it is negatively sloped
and its slope is equal to -Kj/Lj , it is concave and it is linearly homogenous in
factor prices(see Khan and Naqvi,1983).
4. We find this type of capital mobility in Chandra and Khan(1993).
Appendix
The total differentials of Equations (10),(11) and (12) are given by:
WudLu +WidLi +WrdLr = (L- Lr)dWr - LidWi - LudWu ..........................(15);
kudLu + kidLi +krdLr = dK -Lu dku -Li dki -Lr dkr .........................(16); and
dLu +dLi + dLr = --dU ...................................................... (17).
The matrix form of these equations is :
W Wi Wr dL
uir u
Ku Ki Kr dLi
1 1 1 JL dLr
(L Lr) dWr Li dWi Lu dWu
dK Lu dku Lidki Lr dkr
--dU
Let D be the determinant of the co-efficient matrix of the endogenous variables in the
system. So,we can write,
D = (Wr -Wi) ku -(Wu - Wi)kr + (Wu - Wr) ki
If ku > ((Wu- Wi)/(Wr -Wi))kr, then, D >0
Hence, dLu = 1/D(((L -Lr) dWr -Li dWi - Lu dWu) (ki -kr) -(dK -Lu dku -Li dki -
Lrdkr) (Wi -Wr) - dU (Wi kr -Wr ki)).................................(A.1)
dLi = 1/D (((dK - Lu dku -Li dki -Lr dkr )(Wu -Wr) + (Wukr -Wrku ) dU -
((L -Lr) dWr -LidWi -Lu dWu) (ku -kr)..............................(A.2)
dLr = 1/D (((L -Lr) dWr -- Li dWi -LudWu ) -(dK - Ludku -Lidki -
Lrdkr)(Wu -Wi) + (Wiku - Wuki ) dU)............................(A.3)
Effect of a change in Pi
Put dWi =dK =0 in the expressions (A.1), (A.2) and (A.3) and we get,