where Cht, (j~pβ^ ,Hht,Lht are household h's consumption, end-of period
real money balances, hours worked, and leisure respectively, t is an index for
time, 0 < β < 1 is the discount factor, and each household has the same flow
utility function u, which is assumed to take the form
U(Ct) + δ ln(⅛) + V (1 - Hht)
ʃi
(11)
Each household-union belongs to a particular sector and wage-setting
cohort within that sector (recall, that each household is twinned with firm
f = h). Since the household acts as a monopoly union, hours worked are
demand determined, being given by the (7).
The household’s budget constraint is given by
PtCht + Mht + ^2 Q(st+1 I st)^h(st+1 ) ≤ Mht-I +Bht + WhtHht +Mt+Tht (12)
«t+1
where Bh(st+1) is a one-period nominal bond that costs Q(st+1 ∣ st) at
state st and pays off one dollar in the next period if st+1 is realized. Bht
represents the value of the household’s existing claims given the realized state
of nature. Mht denotes money holdings at the end of period t. Wht is the
nominal wage, πht is the profits distributed by firms and WhtHht is the labour
income. Finally, Tt is a nominal lump-sum transfer from the government.
The households optimization breaks down into two parts. First, there is
the choice of consumption, money balances and one-period nominal bonds to
be transferred to the next period to maximize expected lifetime utility (10)
given the budget constraint (12). The first order conditions derived from the
consumer’s problem are as follows:
uct = βRtEt ( -pp-uct+ι
p+t+ι
)
1
Rt
(13)
∑Q(st+1 I st)= βEtuct+p =
‰ uctpt+1
P _ Pt
δMt =uct - ^t ρt~uct+1
(14)
(15)
Equation (13) is the Euler equation, (14) gives the gross nominal inter-
est rate and (15) gives the optimal allocation between consumption and real