I am working on a model and I am encountering the error ‘error in square system: pivot too small’ when I use CNS. When I use NLP, I get a solution but also a message like ‘Optimal solution. Reduced gradient less than tolerance.’ The model I am using is an adaptation of the PEP 1-t model, and it worked fine before I introduced the elements to adapt it for my SAM. I didn’t add or remove any equations or variables. I just added one exogenous variable that allowed for the calibration of government income and the savings of the rest of the world. Can someone please help me find the problem? Here is the summary of the model resolution with CNS:

```
**** REPORT SUMMARY : 0 INFEASIBLE
1 DEPENDENT (DEPND)
2 ERRORS ( ****)
BLOCKS OF EQUATIONS 108 SINGLE EQUATIONS 1,699
BLOCKS OF VARIABLES 125 SINGLE VARIABLES 1,699
NON ZERO ELEMENTS 7,201 NON LINEAR N-Z 3,693
CODE LENGTH 10,923 CONSTANT POOL 747
SINGLE =E|X= EQUS 1,699 SINGLE UNFIXED VARS 1,699
GENERATION TIME = 0.000 SECONDS 8 MB 45.4.0 19dc3313 WEX-WEI
L O O P S TIME 10
GAMS 45.4.0 19dc3313 Nov 27, 2023 WEX-WEI x86 64bit/MS Windows - 09/15/24 07:14:23 Page 103
PEP standard model 1-t, version 2.0
Solution Report SOLVE PEP1T Using CNS From line 2079
S O L V E S U M M A R Y
MODEL PEP1T
TYPE CNS
SOLVER CONOPT FROM LINE 2079
**** SOLVER STATUS 1 Normal Completion
**** MODEL STATUS 17 Solved Singular
RESOURCE USAGE, LIMIT 0.015 10000000000.000
ITERATION COUNT, LIMIT 1 2147483647
EVALUATION ERRORS 0 0
C O N O P T 3 version 3.17O
Copyright (C) ARKI Consulting and Development A/S
Bagsvaerdvej 246 A
DK-2880 Bagsvaerd, Denmark
** Warning ** The value of LFITER is out of range.
LFITER is decreased from 2147483647 to 1000000000.
** Warning ** The variance of the derivatives in the initial
point is large (= 5.9 ). A better initial
point, a better scaling, or better bounds on the
variables will probably help the optimization.
Pre-triangular equations: 246
Post-triangular equations: 20
** Error in Square System: Pivot too small.
CONOPT time Total 0.009 seconds
of which: Function evaluations 0.007 = 77.8%
1st Derivative evaluations 0.000 = 0.0%
**** ERRORS/WARNINGS IN EQUATION EQ44(10)
1 error(s): Pivot too small.
**** ERRORS/WARNINGS IN VARIABLE IR(10)
1 error(s): Pivot too small.
---- EQU EQ44 Rest-of-the-world income
LOWER LEVEL UPPER
1 . . . DEPND
LOWER LEVEL UPPER
1 -INF 0.0400 +INF DEPND
```