CAPACITY AND ASYMMETRIES IN MONETARY POLICY
under their full capacity level, firm’s actual market power is reduced, implying a
smaller mark-up rate. Notice that when no supply constraint is binding, π (v) = 1,
the pricing rule implies a constant mark-up over the marginal cost as in the standard
case.12 It is assumed that π (¢) > 1/e in order to prevent the input price being
zero.
The decision concerning the installment of the productive capacity of each input
firm has a dynamic nature. The objective of each firm is to maximize its divi-
dend, ∏{,, which is the amount of cash that remains after investment and fixed
costs expenditures are made, Pt (It + Φ), business loans (including wage payments),
WtLdjt(l + Rf), are repaid to financial intermediaries and input goods, PtYj,t, are
delivered for cash. More compactly,
(2.19) ∏∫t = PtYjtt - WtLdt(l + ⅛) - Pt (It + Φ)
Investment in new capital goods, It, is used to augment the future capital stock in
the intermediate business sector, according to the following law of motion, where δ
is the corresponding rate of depreciation,
(2.20) ⅛ι = Kt+1 -(1- δ)Kt
Firms choose a contingency plan {Kt+1, ʌ+∣ ∣ }4,1 to maximize the expected dis-
counted value of the dividend flow
∑∆t+1∏f
.t=o
(2.21) ¾,0
subject to (2.12), (2.15), (2.16), given the stochastic process for {Rt , Wt, ∆t}∑
and given K0 and A"o, with expectations formed rationally under the assumed
information structure. For firms to act in the best interests of their shareholders, the
stochastic discount factor ∆t+ι should correspond to the representative household’s
relative valuation of cash across time, which requires
Z9 99X ʌ _ βt+1Uc(Ctj-1,Ltj-1)
nt+ι — -----—--------
Pt+1
where β is the discount factor and Uc is the marginal utility for the household
of consumption, as will be explained later. Thus, the value of the firm for the
shareholder derives from the flow of dividends that are paid at the end of each period
with cash. The reason the subscript t +1 appears is because the shareholder has to
wait until next period to use this cash to buy consumption goods. Regarding the
optimal production plan of an intermediate-good firm, the next result summarizes
these decisions:
12In the standard case, π (7⅛) = 1, the pricing rule reduces to
∕e- 1∖ ^1 (1 + Rt) Wt
I e ) AtXf
which is similar to that in the paper of Christiano et al. (1997). In the sticky-price version of
their model, firms set their price equal to a constant mark-up over a weighted expectation of
the marginal cost. In the present model, firms can perfectly foresee R and W so that prices are
flexible in this respect. Notice that both models are not directly comparable since the production
function is Cobb-Douglas in Christiano et al. (1997) but Putty-Clay here.