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MANNE.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME MANNE
* Problem :
* *********
* A variable dimension econometric equilibrium problem
* suggested by A. Manne
* Source:
* B. Murtagh and M. Saunders,
* Mathematical Programming Studies 16, pp. 84-117,
* (example 5.12).
* SIF input: N. Gould and Ph. Toint, March 1990.
* classification OOR2-MN-V-V
* Number of periods
* The number of variables in the problem N = 3*T
*IE T 100 $-PARAMETER n = 300 original value
*IE T 365 $-PARAMETER n = 995
*IE T 1000 $-PARAMETER n = 3000
IE T 2000 $-PARAMETER n = 6000
* Problem parameters
RE GROW 0.03
RE BETA 0.95
RE XK0 3.0
RE XC0 0.95
RE XI0 0.05
RE B 0.25
RE BPROB 1.0
* Computed parameters
IE 1 1
IE 2 2
IA T-1 T -1
IA T-2 T -2
R( LOGXK LOG XK0
R* BLOGX LOGXK B
R( XK0**B EXP BLOGX
R+ NUM XC0 XI0
R/ A NUM XK0**B
RS 1-B B 1.0
RA 1+G GROW 1.0
R( LOG1+G LOG 1+G
R* SOME LOG1+G 1-B
R( GFAC EXP SOME
R* AT1 A GFAC
RA BT1 BETA 0.0
DO J 2 T
IA J-1 J -1
A* AT(J) AT(J-1) GFAC
A* BT(J) BT(J-1) BETA
ND
RS 1-BETA BETA 1.0
RD 1/1-BETA 1-BETA 1.0
A* BT(T) BT(T) 1/1-BETA
VARIABLES
DO I 1 T
X C(I) $ consumptions
X I(I) $ investments
X K(I) $ capitals
ND
GROUPS
N OBJ
* nonlinear constraints
DO I 1 T
XG NL(I) C(I) -1.0 I(I) -1.0
*XG NL(I) K(I) 0.1
ND
* linear constraints
DO I 1 T-1
IA I+1 I 1
XL L(I) K(I+1) 1.0 K(I) -1.0
XL L(I) I(I) -1.0
ND
ZL L(T) K(T) GROW
XL L(T) I(T) -1.0
RANGES
*X MANNE L(T-1) 10.0
*X MANNE L(T) 20.0
BOUNDS
FX MANNE K1 3.05
DO I 2 T
XL MANNE K(I) 3.05
ND
RE 1.04**T 0.05
DO I 1 T
RM 1.04**T 1.04**T 1.04
XL MANNE C(I) 0.95
XL MANNE I(I) 0.05
ZU MANNE I(I) 1.04**T
ND
START POINT
MANNE K1 3.05
DO I 2 T
IA I-1 I -1
RI RI-1 I-1
RM I-1/10 RI-1 0.1
RA VAL I-1/10 3.0
Z MANNE K(I) VAL
ND
DO I 1 T
X MANNE C(I) 0.95
X MANNE I(I) 0.05
ND
ELEMENT TYPE
EV LOGS C
EV POWER K
EP POWER B
ELEMENT USES
DO I 1 T
XT LOGC(I) LOGS
ZV LOGC(I) C C(I)
XT KS(I) POWER
ZV KS(I) K K(I)
ZP KS(I) B B
ND
GROUP USES
DO I 1 T
ZE OBJ LOGC(I) BT(I)
ZE NL(I) KS(I) AT(I)
ND
OBJECT BOUND
* Solution
*LO SOLTN -9.7457259D-01
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS MANNE
TEMPORARIES
M LOG
INDIVIDUALS
* Logarithmics
T LOGS
F LOG( C )
G C 1.0 / C
H C C -1.0 / C**2
* Powers
T POWER
F K**B
G K B * K**( B - 1.0 )
H K K B * ( B - 1.0 ) * K**( B - 2.0 )
ENDATA