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Giovanni Ganelli and Juha Tervala - page 11 / 32

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9

t T = τ

I t

wt

t C lt +τ Ct +

Mt Mt 1

t P

t P

(12)

w h e r e t T d e n o t e s r e a l t r a n s f e r s .

C. Firms

Technology

Each firm produces a differentiated good according to the simple production function

yt (z) = lt (z)

(13)

where yt (z) is the output of firm z and lt (z) the labor input used by firm z .

Profits

We assume that each firm enjoys a certain degree of monopolistic power in the production of its differentiated good. Under this assumption, demand for the output of firm z is given by

d t z y = ( ) (

pt (z) t P

t C θ W )

(14)

w h e r e W t C i s w o r l d a g g r e g a t e c o n s u m p t i o n g i v e n b y C

W t

= nCt + (1n)C

* t

(15)

P r o f i t s a r e d e f i n e d a s t t t t t l w z y z p z = ) ( ) ( ) ( π . U s i n g ( 1 3 ) , ( 1 4 ) a n d ( 1 5 ) p r o f i t s c a n written as b e

) ( ) ( ) ( ( ) ( t t t t t P z p w z p z = π

) ) 1 ( ( ) * t t C n n C + θ

(16)

Price Setting

In the absence of price rigidities, the profit maximization process would imply that the price of each differentiated good is given by a simple mark-up over wages, according to the formula

θ pt (z) = θ 1

wt

(17)

However, following Calvo (1983), we introduce nominal rigidities by assuming that each firm resets its price with a probability 1γ in each period, independently of other firms and

independently of the time elapsed since the last adjustment. Each firm has to take into account, when setting its profit-maximizing price, that in every subsequent period there is a probability 0 < γ < 1 that it will not be able to revise its price setting decision. When setting a

new price in period t , each firm seeks to maximize the present value of profits weighting

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