1 +φ
t +秒
1 +φ
＃！
受名义预算约束
PtCt + Bt + Mt =（1 +它）Bt-1 + Mt-1 + WtNt +Πt
在哪里
以名义利率持有名义债券
，Wt
是名义上的
工资，铂
是价格指数和Ct
是消费。 Πt是名义利润（股息）
家庭从平等拥有的公司那里得到的收益。家庭请客
优化时给出的这些红利。
经济中存在单位数量的公司。我为每个公司选择的价格Pt（i）
提前期以最大化其预期利润
Et-1Πt（i）= Et-1 [Pt（i）Yt（i）-WtNt（i）]
受需求曲线向下倾斜的影响：
Yt（i）=
铂（i）
铂
-ε
t
在哪里
是总需求，Yt（i）是公司i的商品需求，并且ε>1。公司使用
仅需人工的CRS生产技术
Yt（i）= AtNt（i）
(a) Show that households choose their bond holdings Bt
, their labor supply Nt
, and
their real balances Mt/Pt to satisfy:
1
PtCt
= βEt (1 + it+1)
1
Pt+1Ct+1
Wt
Pt
1
Ct
= N
φ
t
1
PtCt
= βEt
1
Pt+1Ct+1
+ γ
1
Mt/Pt
1
Pt
Interpret these conditions in one sentence each. If a derivation is identical to
problem 2, you may simply state your result.
(b) Consider the firm’s problem.
i. Show that each firm’s marginal revenue is
MRt =
ε 1
ε
Pt (i)
Is marginal revenue above or below price Explain why marginal revenue is
not equal to price, as is the case in competitive markets.
ii. At the
optimum, a firm maximizing profits:
Et1Πt (i) = Et1 [Pt (i) Yt (i) WtNt (i)]
sets
MRt = Et1 {MCt}
Show that each firm in the economy thus chooses its price Pt (i) to satisfy:
Pt (i) = Et1 {μMCt}
where μ = ε/ (ε 1). Interpret μ and explain why it depends on ε.
2
iii. Show that the nominal marginal cost is:
MCt = Wt/At
and so:
Pt (i) = Et1 {μWt/At}
(c) Assume that the growth rate of technology satisfies
log At log At1 = v
A
t
where v
A
t
is a mean zero iid shock to the growth rate of technology. The monetary
authority sets the growth rate of money to satisfy
log Mt log Mt1 = v
M
t
where v
M
t
is a mean zero iid shock to the growth rate of money.
In equilibrium, labor, goods, output, and bond markets clear:
Nt (i) = Nt
Pt (i) = Pt
Yt (i) = Yt
Ct = Yt
Bt = 0
Show that in equilibrium these conditions imply
Mt = ΦPtYt
for some constant velocity of money Φ. Taking logs and differencing for periods
t and the expectation of period t at time t 1, what does this expression imply
about monetary neutrality in this model (I am looking for an expression for
log Yt Et1 log Yt
in terms of v
M
t
) Explain in a sentence why money is neutral
or non-neutral in this model.
(d) Show that in in equilibrium the quantity of labor satisfies
N
1+φ
t =
1
μ
Wt/At
Et1 (Wt/At)
Use this condition to argue that
Et1Nt = N