The name is absent

of the final good, r_t denotes the net real return on the one-period nominal bond, b_t, and Dt
denotes (in units of the final good) the lump-sum dividend that households receive from the
intermediate-good producing firms.

On the production side, a unit-continuum of monopolistically competitive intermediate-
good producing firms rent capital and hire labor in perfectly competitive markets. Indexing
firms by τ ∈ [0, 1], the τ’th firm chooses l_t (τ), k_t (τ), and its price, p_t (τ), to maximize its
value, subject to three things: the production technology

yt (τ) = e^w*kt (τ)^a lt (τ ,

where a ∈ (0,1); the demand schedule,

yt (τ)= ('"'/-) ^{εt γ}t,                                      (44)

where Y_t denotes aggregate output and ε_t ∈ (1, ∞) represents the (stochastic) elasticity of
substitution between goods; and a Calvo (1983) price rigidity. In the Calvo (1983) model,
randomly chosen firms of share 1 — ξ are able to make capital, labor, and pricing decisions
while the remaining share are only able to make capital and labor decisions. All firms make
their capital and labor decisions to minimize the real cost of producing a marginal unit of
output, mc_t, then those firms that can choose their prices do so to maximize

where Λ_t denotes the marginal utility of consumption, while the remaining firms keep their
prices unchanged. Profits are aggregated and returned to households (shareholders) in the
form of a lump-sum dividend.

The final-good producing firms also seek to maximize profits. They purchase intermediate
goods, aggregate them into a final good according to the technology

(1

Уу( (τ) ~ dτ
o

and sell these final goods to households in a perfectly competitive market. As is well known,
profit maximization by final-good producers gives rise to equation (44) while their zero-profit
condition implies

i

(¹                   ∖ ^{1 ε}t

P Pt (τ     dτ I .                               (47)

o                /

18

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