The name is absent

PEDRO PABLO ALVAREZ LOIS

a symmetric equilibrium in prices, avoiding in this manner price aggregation dif-
ficulties. It is worthwhile to point out that this assumption on the price behavior
of input firms should not have important implications on the manner in which the
economy responds to aggregate shocks: since prices are announced at the time
shocks are known, they are perfectly flexible in this sense.

The price decision is static and the same rule will be followed by all firms given
that, ex-ante, all of them are identical; that is, P_t = Pj_d- Consequently, each firm
chooses a price in order to maximize current period expected profits,

(2.13)            P_t ≡ arg max E_υ [P_tYfi_t -(1 + ⅛ ) W_tL^d_jd]

which by (2.12) is
(2.14)
where Yj_d is the level of inputs-goods produced by firm j. The particular amount of
those input-goods produced will depend on the demand shock faced by each firm.
Such a demand is derived from expression (2.2) or more specifically

P_t ≡ arg max E_v

(1 + O∏q∖

Λ¾ ^j'^t

.   . hPΛ f^vt . .    - Γ

(2.15)         E_v(Y_jd) = ₅¹ Yt vdF(v) + Y_t dF (t>)

∖¹f√ √v             Jvt

Taking into account these considerations, the optimal price decision can be charac-
terized by the following result:

Lemma 2 (Intermediate-Goods Pricing). The price decision of any input firm j
at date t adopts the following expression:

F_t = fl _ ¹ A ^¹ (^{1 +} ⅞) ^W*
^t ∖    eπ (¾) J      A_tXfi

where π (¾) represents the probability of excess capacity in the economy, that is,
π (¾) is a weight measure of the proportion of firms for which demand is smaller
than their productive capacity,

E_v (Yt)

Vt

vdF(v)

Notice that π (v) depends only on v, as becomes clear from the combination of
equations (2.15) and (2.3) above,

Γ «dF (t>)
(2.18)                π ¾ =       ⅛-------=------

f^vt t>dF (v) + v_t f.^v dF (v)

The pricing mechanism resulting from (2.16) implies that intermediate firms set
their price as a mark-up over the marginal cost.¹¹ The mark-up rate depends
negatively on the (absolute) value of the price elasticity of expected sales, which
is defined as the elasticity of expected sales to expected demand, π (v), times the
price elasticity of expected demand, e. This means that when π (v), the probability
of a sales constraint, is large, that is, when more input firms are Iikelely to produce

¹¹The derivation of this condition supposes that each monopolistic firm only considers the
direct effect of its price decision on demand and neglects all indirect effects (e.g. the effects
through y_t). This approximation is reasonable in a context where there is a continuum of firms.

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