$TITLE:  Solution to Exercise 2

SCALAR
        X       QUANTITY OF X FOR WHICH THE MRS IS TO BE EVALUATED
        Y       QUANTITY OF Y FOR WHICH THE MRS IS TO BE EVALUATED
        MRS     COMPUTED MARGINAL RATE OF SUBSTITUTION
        PX0     PRICE OF X
        PY0     PRICE OF Y;

X = 1;
Y = 1;
PX0 = 1/4;
PY0 = 1;

$ONTEXT

$MODEL:MRSCAL

$COMMODITIES:
        PX      ! PRICE INDEX FOR GOOD X
        PY      ! PRICE INDEX FOR GOOD Y

$CONSUMERS:
        RA      ! REPRESENTATIVE AGENT

$DEMAND:RA      s:1
        D:PX    Q:1     P:PX0
        D:PY    Q:1     P:PY0
        E:PX    Q:X
        E:PY    Q:Y

$OFFTEXT
$SYSINCLUDE mpsgeset MRSCAL

$INCLUDE MRSCAL.GEN
SOLVE MRSCAL USING MCP;


MRS = PX.L / PY.L;


OPTION MRS:8;
DISPLAY MRS;



*-----------------------------------------------------------------------------
* EXERCISE (a): Show that the demand function is homothetic by uniform scaling
*       of the X and Y endowments.  The resulting MRS should remain unchanged.

X = 20;
Y = 20;

$INCLUDE MRSCAL.GEN
SOLVE MRSCAL USING MCP;

*       Compute the MRS using the new solution values:
MRS = PX.L / PY.L;

DISPLAY MRS;


*-----------------------------------------------------------------------------
* EXERCISE (b):  Modify the demand function calibration point so that the
*       reference price of both X and Y equal unity.

PX0 = 1;
PY0 = 1;

$INCLUDE MRSCAL.GEN
SOLVE MRSCAL USING MCP;

*       Compute the MRS using solution values:
MRS = PX.L / PY.L;

DISPLAY MRS;