SCALAR  TX      Ad-valorem tax rate for X sector inputs /0/;

$ONTEXT

$MODEL:M1_7S

$SECTORS:
        X       ! Activity level for sector X
        Y       ! Activity level for sector Y
        W       ! Activity level for sector W (Hicksian welfare index)
        Z       ! Alternative activity for producing X.

$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

*       Note that at the benchmark (when all prices equal unity), the
*       cost of Z inputs equals 1.1 and the value of outputs equals 1.0.
*       An economic equilibrium prevails provided that this sector is
*       idle:

$PROD:Z s:1
        O:PX    Q: 1.00
        I:PL    Q: 0.44
        I:PK    Q: 0.66

$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
        E:PK    Q:100

$OFFTEXT
$SYSINCLUDE mpsgeset M1_7S

*       Check the benchmark calibration --- after setting the activity
*       level for Z equal to 0:

        Z.L = 0;

        M1_7S.ITERLIM = 0;
$INCLUDE M1_7S.GEN
        SOLVE M1_7S USINCP MCP;
        M1_7S.ITERLIM = 2000;


*       Lets levy a high tax on sector X and see what happens:

        TX = 1.00;
$INCLUDE M1_7S.GEN
        SOLVE M1_7S USINCP MCP;


$ontext
Exercises:

(a) Plot the Laffer curve for TX in this model. Compare your
results with the curve from a model in which sector Z does
not exist.

Hint:
An activity may be omitted from the model by fixing its value to 0,
that is by specifying: Z.FX=0;

If you subsequently want to compute an equilibrium in which Z is not
fixed, you may enter: Z.LO = 0;
                      Z.UP = +INF;

(b) Consider another model where sectoral capital stocks are differentiated
(replace PK by PKX and PKY). Repeat steps from exercise (a).

(c) Compare results form model (a) and (b). Do the same comparison plotting
welfare cost versus TX.

$offtext