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Giovanni Ganelli and Juha Tervala - page 9 / 32

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7

Ut =

s=t

β st [logCs +

χ 1ε

(

Ms P s

)1ε

ls (z)ν +1 ν +1

]

(1)

where 0 < β < 1 is the discount factor, Cs is a composite good representing private c o n s u m p t i o n a n d s P i s t h e p r i c e i n d e x a s s o c i a t e d w i t h i t . s M d e n o t e s n o m i n a l m o n e balances and ls (z) the household’s supply of labor; ε > 0 is the inverse of the consumption y

elasticity of money demand, ν is the elasticity of the marginal disutility of producing output with respect to output, and χ is a positive parameter.

The composite private consumption good is defined in the following equation as an aggregate across the individual goods produced by firms

1

θ 1

θ

t Ct = [c (z)

θ

dz]

θ 1

0

(2)

where θ is the elasticity of substitution between any pair of individual goods. The associated

price index is

n

= ) ( [ z p P t t

1

θ + * 1 ) ) ( ( z p E d z t t

1θ dz]

1 1θ

(3)

  • 0

    n

w h e r e ) ( z p t i s t h e p r i c e o f g o o d z e x p r e s s e d i n d o m e s t i c c u r r e n c y , ) ( * z p t i s t h e f o r e i g n

currency price of foreign good z and E is the nominal exchange rate, defined as the price of the foreign currency in terms of the domestic currency.

The budget constraint of the domestic representative household is given by

t t t t D D M = + δ 1

  • +

    Mt1

t t t t t C t t t I t T P C P z l w + + + + π τ τ ) 1 ( ) ( ) 1 (

(4)

where D denotes the household’s holding of nominal bonds. Bonds are denominated in the currency of the domestic country and account for international shifts in wealth, δ is the price of a bond (the inverse of one plus the nominal interest rate), wt is the nominal wage paid to

the household in a competitive labor market, π is the household’s share of profits received f r o m f i r m s , I t τ a n d C t τ a r e t h e t a x r a t e s o n h o u s e h o l d i n c o m e a n d c o n s u m p t i o n , a n d t T d e n o t e s

real transfers from the government.7 Given that bonds are denominated in domestic currency, the budget constraint of the foreign representative household is

7 The fact that bonds are denominated in domestic currency does not introduce any asymmetry across countries, since we assume open capital markets so that nominal interest rates are equalized internationally. Furthermore, PPP holds under PCP.

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