$ONTEXT
The SAM


        X1        X2        CONS1        CONS2
X1                           40           70        110
X2                           60           30        90
CONS1    50        50                           100
CONS2    60        40                           100
        110        90        100          100


$OFFTEXT

*Calibration

* We have to declare some initial parameters

PARAMETERS
ALPHA1
ALPHA2
A1
A2
;

* Lets calibrate those
ALPHA1 = 40 / (50 + 50);
ALPHA2 = FILL_IN;

A1 = 100 / ( 40**ALPHA1 * 60**(1 - ALPHA1) );
A2 = FILL_IN;


* Now lets introduce our vars

VARIABLES
C1X1   Consumption of X1 by consumer 1
C1X2   Consumption of X2 by consumer 1
C2X1   Consumption of X1 by consumer 2
C2X2   Consumption of X2 by consumer 2

W1     Consumer 1 utility
W2     Consumer 2 utility

P1     Price of X1
P2     Price of X2

PW1    Consumer 1 price index
PW2    Consumer 2 price index

INC1     Consumer 1 income
INC2     Consumer 2 income

TRICK    A trick variable
;


EQUATIONS
      MKT_X1    Market clearing for X1
      MKT_X2    Market clearing for X1

      MKT_W1   Market clearing for W1
      MKT_W2   Market clearing for W2

      PW1_IDX  Consumer 1 price index
      PW2_IDX  Consumer 2 price index

      I_INC1   Income balance 1
      I_INC2   Income balance 2

      TRCK   A trick equation
;

MKT_X1.. 50 + 60 =E= alpha1 * W1 * PW1 / P1 + alpha2 * W2 * PW2 / P1;
MKT_X2.. FILL_IN

MKT_W1.. INC1 =E= PW1*W1;
MKT_W2.. FILL_IN

PW1_IDX.. PW1 =E= FILL_IN
PW2_IDX.. PW2 =E= FILL_IN

I_INC1.. P1 * 50 + P2 * 50 =E= INC1;
I_INC2.. FILL_IN =E= INC2;

TRCK..  TRICK=E=1;

MODEL EXCHANGE
/
MKT_X1
MKT_X2

MKT_W1
MKT_W2

PW1_IDX
PW2_IDX

I_INC1
I_INC2

TRCK
/;

$ONTEXT
Here is the SAM again so it is easier to input starting values


        X1        X2        CONS1        CONS2
X1                           40           70        110
X2                           60           30        90
CONS1    50        50                           100
CONS2    60        40                           100
        110        90        100          100


$OFFTEXT

C1X1.L=40;
C1X2.L=60;
C2X1.L=70;
C2X2.L=30;

W1.L=100;
W2.L=100;

P1.L=1;
P2.L=1;

PW1.L=1;
PW2.L=1;

INC1.L=100;
INC2.L=100;

TRICK.L=1;

option nlp = pathnlp ;

SOLVE  exchange USING NLP maximizing TRICK;

* Exercises 1:
* 1. Fill in the gaps so that the model is calibrated.
* 2. Introduce a numeraire and see if the Walras Law holds
* 3. Increase endowment of good X1 of consumer 1. What happens?
* 4. Introduce a lump sum transfer between consumers. How this transfer affects equlibrium variables?
* 5. Rewrite the whole model in the vector form (with sets)