SCALAR  TX      Ad-valorem tax rate for x sector inputs /0/,
        LENDOW  Labor endowment multiplier              /1/;

$ONTEXT

$MODEL:M1_1S

$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

* Taxes are always applied on a value-added basis in an MPSGE modeling.
* Here, the user cost of labor inputs is then PL(1+TX).

$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:1
        O:PW    Q:200
        I:PX    Q:100
        I:PY    Q:100


$DEMAND:CONS
        D:PW    Q:200
        E:PL    Q:(100*LENDOW)
        E:PK    Q:100

$OFFTEXT
$SYSINCLUDE mpsgeset M1_1S

*       An equilibrium in this model determines only relative prices -
*       there is no "money illusion" and the absolute price level is
*       irrelevant.  This must be considered when reporting induced
*       changes in relative prices.  It is convenient to select one
*       good as numeraire and fix its price as unity.  Labor is
*       a traditional choice as numeraire, so we use it:

        PL.FX=1;

*       N.B.  Fixing a price instructs MPSGE to omit the corresponding
*       equation -- In equilibrium, this equation will be satisfied
*       automatically through Walras' law.

*       It is not necessary to fix a numeraire, however if a numeraire
*       is not specified, the normalization of prices is arbitrary.
*       (When no price is exogenously fixed, the system uses one consumer
*       income as normalization, and this income level is determined by the
*       initial price vector).

*        In the folowing statements we declare to check the calibaration.
*        ITERLIM means number of iterations.

* Replicate the benchmark
        M1_1S.ITERLIM = 0;

$INCLUDE M1_1S.GEN
        SOLVE M1_1S USING MCP;
        M1_1S.ITERLIM = 2000;

*       Solve a counterfactual: 50% tax on inputs to X production.
*       LENDOW=1 means labor endowment=100%

        TX = 0.5;
        LENDOW = 1;

$INCLUDE M1_1S.GEN
        SOLVE M1_1S USING MCP;

*       Solve a counterfactual: 100% increase in labor endowment (TX=0)

        TX = 0;
        LENDOW = 2;

$INCLUDE M1_1S.GEN
        SOLVE M1_1S USING MCP;

***********
* Exercises:
*
*(a) Verify that relative prices are the same no matter of normalization method
*that we will use in a CGE model.
*
*(b) Introduce a "typo" in a setor X output and then examine the benchmark
* replication results to see how this error is manifested in the output.