Public goods

Governments often use money to purchase things which private markets do not provide. In order to implement government into a model, we have to add $DEMAND:GOVT

· tax revenue collected in the economy is assigned to the government

· government spends this revenue on purchasing public goods

Similar to households, there are few ways to represent public consumption:

1) simple way:

   Markets  |    X       Y        W   | GOVT   CONS
   ------------------------------------------------------
       PX   |  100   -95 | -5
       PY   |    100 -85 | -15
       PW   |                      180|       -180
       PL   |  -20      -60               |        80
       PK   |  -60      -40               |         100
 tax  |  -20         | 20 
    ------------------------------------------------------

$DEMAND:GOVT

D:PX Q: 5

D:PY Q: 15

2) a good called G (price PG), which represent the consumption composite of goods X and Y by the government:

   Markets  |    X       Y     G   W  | GOVT   CONS
   ------------------------------------------------------
       PX   |  100    -5 -95 | 
       PY   |    100  -15 -85 |
 PG |  20  | -20 
       PW   |                      180|       -180
       PL   |  -20      -60               |        80
 PK   |  -60      -40               |        100
 tax  |  -20         | 20 
    ------------------------------------------------------

$PROD:G s:1

O:PG Q: 20

I:PX Q: 5

I:PY Q: 15

$DEMAND:GOVT

D:PG

No need to define Q: for D:PG, if GOVT is the only agent demanding PG in the model Þ MPSGE automatically fulfills market clearing condition in such case.

3) a good called G (price PG), which is produced from capital and labor like private goods:

   Markets  |    X       Y     G   W   | GOVT   CONS
   ------------------------------------------------------
       PX   |  100   -100|
       PY   |    100 -100|
 PG |  25  | -25 
       PW   |                      200|       -200
       PL   |  -20      -60     -10       |        90
 PK   |  -60      -40     -10       |        110
 tax  |  -20      -5    | 25 
    ------------------------------------------------------

$PROD:G s:1

O:PG Q: 25

I:PL Q: 10

I:PK Q: 10 P:1.5 A:GOVT T:TAX

$DEMAND:GOVT

D:PG

Transfers from the government

Consumer may receive the full benefit of the public good without paying for it. To do this, we introduce the “rationing variable” (as an auxiliary variable) and “rationing constraint”:

$PROD:W s:1

O:PW Q:225

I:PX Q: 100

I:PY Q: 100

I:PG Q: 25 ! public goods

$DEMAND:CONS

D:PW Q:225

E:PL Q: 90 ! labor

E:PK Q: 110 ! capital

E:PG Q: 25 R:LGP ! transfers

$CONSTRAINT:LGP

LGP =E= G;

The above notation means that consumer has an endowment of L=90, K=110, and G=25*LGP. The value of LGP (like any auxiliary variable) is set by a constraint: rationing variable (LGP) transfers the public good (PG) to consumer (CONS)

Note: G is a multiplier of the public activity and 25 is the reference (benchmark) quantity for the G (i.e. when G=1). When G changes in counterfactual equilibrium, transfers to household changes appropriately.

   Markets  |    X       Y     G   W   | GOVT   CONS
   ------------------------------------------------------
       PX   |  100   -100|
       PY   |    100 -100|
 PG |  25 -25 | -25 25
       PW   |                      225|       -225
       PL   |  -20      -60     -10       |        90
       PK   |  -60      -40     -10       |        110
 tax  |  -20             -5    | 25 
    ------------------------------------------------------

When government has his own consumption, the transfer to households also can be implemented:

$PROD:W1 s:1

O:PW Q:185

I:PX Q: 95

I:PY Q: 90

$DEMAND:CONS

D:PW Q:185

E:PL Q: 80 ! labor

E:PK Q: 100 ! capital

E:PW Q: 5 R:LGP ! transfers

$DEMAND:GOVT

D:PG

E:PW Q:(-5) R:LGP

$CONSTRAINT:LGP

G =E= 1;

   Markets  |    X       Y     G   W  | GOVT   CONS
   ------------------------------------------------------
       PX   |  100    -5 -95 | 
       PY   |    100  -10 -90 |
 PG |  15  | -20  5
       PW   |                     185|       -185
       PL   |  -20      -60               |        80
 PK   |  -60      -40               |        100
 tax  |  -20         | 20 
    ------------------------------------------------------