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Giovanni Ganelli and Juha Tervala - page 10 / 32

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8

D*

D*

t

=

t 1

Et

Et

* M t t + δ

  • +

    M*

t 1

  • +

    (1 τ

I t

*

* * 1 ( ) ( ) t t z l w + τ

C t

*

* * * * * ) t t t t t T P C P + + π

(5)

where foreign variables are denoted by asterisks. A global asset-market clearing condition 0 ) 1 ( * = + t t D n n D a l s o h o l d s .

Domestic households maximize (1) subject to (4), and an analogous optimization problem holds for foreign households. The resulting first order conditions are

t δ

(1 + τ

C t

) Pt + 1 C t + 1

= β (1+τ

C t +1

t t C P )

(6)

t δ

(1 + τ

C* t

t P * 1 ) +

t * C 1 +

Et +1

= β(1+τ

C* t +1

t E C P t t * * )

(7)

ν t

l=

I t C t

(1τ ) wt (1+τ ) C P

tt

*ν t

l=

*

I* t C t

(1τ ) wt (1+τ ) Ct P*

*

t

(8)

(9)

Mt t M P* P * t

t

δ τ χ 1 ) 1 ( ( t t C t C + =

=(

τ χ * * ) 1 ( C t C t +

δ 1 t t E 1+

)

1 ε

)

1 ε

(10)

(11)

Et

Equations (6) and (7) are the Euler equations for optimal domestic and foreign consumption including taxes, they reduce to standard Euler equations if the tax rate on consumption is kept constant. Equations (8) and (9) are the domestic and foreign optimal labor supply equations, which equate the disutility of supplying an extra unit of labor with the marginal utility of the extra private consumption that can be bought due to the marginal increase in labor supply. Equations (8) and (9) show that higher labor or consumption taxes reduce labor supply for given levels of the real wage and consumption. Finally, equations (10) and (11) show that households’ optimal money demand is an increasing function of private consumption (including taxes) and a decreasing function of the interest rate.

B. The Government

We assume that all government spending is for public transfers to households, which can be financed through income and consumption taxes or seignorage.8 We therefore abstract from government spending for public consumption and investment. Taking into account symmetry across agents, the government budget constraint in per-capita terms can therefore be written as

8

In what follows we will keep money supply constant, therefore abstracting from seignorage in practice.

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