7
To increase the number of goods it produces, a firm invests in innovative effort, i.e. spends
resources on R&D. A firm’s R&D choice is twodimensional. Each instant, it chooses both
the frequency of arrival of new innovations
λ
t
∈
[0
,
¯
λ
] and the quality of new innovations
θ
t
∈
[0
,
1]. The arrival intensity of a new innovation
λ
t
determines the Poisson rate at which
innovations arrive. Conditional on an innovation, the number of new product lines that this
innovation generates is given by
X
t
= min (
Y
t
,
¯
p

P
t

)
with
Y
t
∼
Bin
(
n, θ
)
,
where
n
is an exogenous upper bound on the number of new product lines that can be
developed following an innovation,
θ
measures the expected quality of the innovation, and
Bin
(
n, θ
) is the binomial distribution. The expected number of new product lines is approx
imately given by
nθ
. Therefore, a higher quality
θ
leads to a higher expected number of new
product lines. Bounding the number of new product lines
X
t
from above by ¯
p

P
t

ensures
that
P
t
never exceeds ¯
p
. These assumptions imply that the total number of product lines the
firm has developed up to time
t
, denoted by
I
t
, evolves as
dI
t
=
X
t
dN
I
t
,
where
dN
I
t
is a Poisson process with intensity
λ
t
.
A firm’s existing product lines can become obsolete because some other firm innovates on
a good it is currently producing. In this case, the incumbent producer loses the good from its
portfolio due to creative destruction. Since any firm is infinitesimal, we can ignore the possi
bility that it innovates on a good it is currently producing. Because of creative destruction,
each product becomes obsolete at an exponentially distributed time with intensity
f
.
We
call
f
the rate of creative destruction, that each firm takes as given. Subsection
C
embeds
the singlefirm model into an industry equilibrium and endogenizes the rate
f
of creative
destruction. The total number
O
t
of product lines lost by the firm up to time
t
≥
0 because
of creative destruction evolves as
dO
t
=
dN
O
t
,
8
where
dN
O
t
is a Poisson process with intensity
fP
t

. The total number product lines in a
firm’s portfolio
P
t
is therefore given by
P
t
=
I
t

O
t
.
A firm with zero product lines exits the economy at time
τ
0
≡
inf
{
t >
0 :
P
t
= 0
}
.
A firm performing R&D with intensity and quality (
λ
t
, θ
t
) incurs flow costs
q
(
P
t
, λ
t
, θ
t
).
To ensure that shareholders are better off with more product lines we impose that the R&D
cost function does not increase too fast in the number of product lines, in that
q
(
p
+ 1
, λ, θ
)

q
(
p, λ, θ
)
<
1
.
(1)
An incumbent firm’s operating profit is the profit that comes from the operation of the
product lines minus the costs of performing R&D:
P
t

q
(
P
t
, λ
t
, θ
t
)
.
Profits are taxed at the constant rate
π >
0.
As a result, firms have an incentive to
issue debt to reduce corporate taxes.
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 Spring '17
 Enkhjin
 Debt, Test, The Natural