Tax reforms that yield the government the same amount of revenue

Hold the labor tax rate TXL exogenous, but change its value, in each case solving for the value of the capital tax TXK that yields the same value of revenue as the

original tax. Þ TXK now become a variable, not a parameter.

Note: replacing one tax with another rarely yields the same welfare in general equilibrium

New fields in the model:

$AUXILIARY - the new class of MPSGE variables in order to implement additional constraints into the model (by default, auxiliary variables are set to zero in MPSGE)

$CONSTRAINT – additional constraint in the model

N: - standing for endogenous tax rate (T: specifies exogenous tax rate)

.

Equal yield constraint:

TLX*PL*X*20 + TKX*PK*X*60 =E= 20 * (PX + PY)/2;

· the left-hand side is tax revenue from TXL and TXK.

· the right-hand side specifies the target revenue. What is meant by “constant” revenue? It depends. Here we assume that tax revenue is spent on X and Y in equal proportions: the initial tax revenue of 20 is spent (at prices for X and Y equal to one) on 10 X and 10 Y. Price of goods will change due to changes in tax rate, but X = Y = 10 must hold

Note: government is not actually buying anything in this simple model, it is just redistributing the revenue back to the agents. The point is that the modeler must specify what the revenue target is in real terms, and then allow the nominal value of that to adjust with prices.

$TITLE Model M33.GMS: Closed 2x2 Economy - Equal Yield Tax Reform

$ONTEXT

   Markets  |    X       Y        W   |       CONS
   ------------------------------------------------------
       PX   |  100   -100|
       PY   |    100 -100|
       PW   |                      200|       -200
       PL   |  -20      -60               |        80
       PK   |  -60      -40               |        100
 tax  |  -20         |  20
    ------------------------------------------------------

$OFFTEXT

SETS S /1*5/;

PARAMETERS

WELFARE(S) Welfare,

REALCONS(S) Real consumption of goods,

LABSUP(S) Labor supply,

CAPTAX(S) Capital tax rate,

ref tax reform activation /0/

TLX Ad-valorem tax on labor inputs to X /1/;

$ONTEXT

$MODEL:M33

$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

$AUXILIARY:

*when Auxilary variable is not active at the benchmark,

*the condition “$” is necessary

TKX$ref ! Endogenous capital tax

$PROD:X s:1

O:PX Q:100

I:PL Q: 20 P:2 A:CONS T:TLX

I:PK Q: 60 A:CONS$ref N:TKX$ref

$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: 80

E:PK Q:100

$CONSTRAINT:TKX$ref

TLX*PL*X*20 + TKX*PK*X*60 =E= 20 * (PX + PY)/2;

$OFFTEXT

$SYSINCLUDE mpsgeset M33

PW.FX = 1;

M33.ITERLIM = 0;

$INCLUDE M33.GEN

SOLVE M33 USING MCP;

M33.ITERLIM = 2000;

* hold TXL exogenous, but change its value

*(in each case solving for the value of TXK that yields the same value of revenue as the original tax)

LOOP(S,

TLX = 1 - 0.05*ORD(S);

$INCLUDE M33.GEN

SOLVE M33 USING MCP;

* welfare (value of leisure)

WELFARE(S) = W.L;

* real consumption

REALCONS(S) = (PX.L*X.L*100 + PY.L*Y.L*100)

/(PX.L**0.5*PY.L**0.5*200);

LABSUP(S) = TLX;

CAPTAX(S) = TKX.L;

);

DISPLAY WELFARE, REALCONS, LABSUP, CAPTAX;

$ontext

Exercises:

a) Explain the formula for REALCONS

b) Compare the above results with the alternative reform, where TXK for Y (instead of X) will be applied

c) Assume now that TXL in sector X will decrease, while TXL in sector Y will increase. How this reform will influence the results?

$offtext