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🖥️ Console Model leisure.gms

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$TITLE Model M1_4S: Close 2x2 economy with labor-leisure choice

$ontext

November, 1995 (revised)

In this model, the consuer is endowed with 200 units of time.  In
the benchmark equilibrium, 100 units of time are provided to the
market and 100 units are "purchased" by the consumer.  This formulation
provides an elastic labor supply.

Production Sectors          Consumers
    Markets   |    X       Y        W    |       CONS
    ------------------------------------------------------
         PX   |  100             -100    |
         PY   |          100     -100    |
         PW   |                   300    |       -300
         PL   |  -40     -60     -100    |        200
         PK   |  -60     -40             |        100
    ------------------------------------------------------

$offtext

*       GAMS parameters which we will use in model specification:

SCALAR  TX      Ad-valorem tax rate for X sector inputs /0/,
      ESUBL Elasticity of substitution for leisure vs consumption /0.5/;

$ONTEXT

$MODEL: M1_4S

$SECTORS:
        X       ! Activity level for sector X
        Y       ! Activity level for sector Y
        W       ! Activity level for sector W (Hicksian welfare index)

$COMMODITIES:
        PX      ! Price index for commodity X
        PY      ! Price index for commodity Y
        PL      ! Price index for primary factor L
        PK      ! Price index for primary factor K
        PW      ! Price index for welfare (expenditure function)

$CONSUMERS:
        CONS    ! Income level for consumer CONS

$PROD:X s:1
        O:PX  Q:100
        I:PL   Q:40  A:CONS T:TX
        I:PK   Q:60  A:CONS T:TX

$PROD:Y s:1
        O:PY  Q:100
        I:PL  Q: 60
        I:PK  Q: 40

$PROD:W s:ESUBL  a:1
        O:PW  Q:300
        I:PX  Q:100  a:
        I:PY  Q:100  a:
        I:PL  Q:100

$DEMAND:CONS
        D:PW  Q:300
        E:PL  Q:200
        E:PK  Q:100
$OFFTEXT
$SYSINCLUDE mpsgeset M1_4S

*       Replicate the benchmark:

M1_4S.ITERLIM = 0;
$INCLUDE M1_4S.GEN
        SOLVE M1_4S USING MCP;
        M1_4S.ITERLIM = 2000;

*       Solve a counterfactual: 100% tax on X:

TX = 1;
$INCLUDE M1_4S.GEN
        SOLVE M1_4S USING MCP;

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🖥️ Console Model leisure.gms

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