The demand curve for current labour is the
representative firm’s marginal product of
the labour schedule. Firms will hire current
labour until
MPN
equals the current wage
rate,
MPN = w
. The curve can be seen to
slope downwards because the marginal
product of labour declines as the labour
input increases. In this figure, we show the
representatives firm’s demand curve for
labour,
N
d
.
The Current Demand Curve for Labour Shifts Due to Changes in Current Total Factor
Productivity
z
and in the Current Capital Stock
K
The current demand curve for labour shifts
due to changes in current total factor
productivity
z
and in the current capital stock
K.
An increase in z or K shifts the curve to the
right reflecting the resulting increase in the
marginal product of labour. The frim chooses

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labour demand in the
future period in a similar way to its choice of current-period labour
demand.
The Representative Firm’s Investment Decision
A key principle in economic decision making is that the optimal level of an economic activity
is chosen so that the marginal benefit of the activity is equal to its marginal cost. We let
MC(I)
denote the marginal cost of investment for the firm where
MC(I)
= 1.
The marginal cost of investment is 1, as the firm gives up one unit of current profits for each
unit it invests. The marginal benefit from investment, denoted by
MB(I)
, is the marginal
product of future capital plus the quantity of capital that will be left in the future after
depreciation, all discounted back to the present value of profits,
V
.
MB(I)
=
MP'
K
+
1
−
d
1
+
r
Optimal Investment Rule for the Firm
The firm’s optimal investment rule is obtained by equating the marginal benefit and marginal
cost of investment:
MP'
K
+
1
−
d
1
+
r
= 1
This can be rewritten as
MP’
K
– d = r
The above equation states that the firm invests until the net marginal product of capital,
MP’
K
– d,
is
equal to the real interest rate. The net marginal product of capital is the marginal product of capital after

taking account of the depreciation of the capital stock. The intuition behind the optimal investment rule
is that the opportunity cost of investing in more capital is the real rate of interest, which is the rate of
return on the alternative assets in this economy.
In this model there are two assets:
1.
Bonds are traded in the credit market
2.
Capital held by representative firms
If the firm invests in capital, it is giving up the opportunity to lend in the credit market where
it can earn a real rate of return
?.
Effectively, the representative consumer holds the capital of the firm indirectly, because the
consumer owns the firm and receives its profits as dividend income. From the consumer’s point
of view, the rate of return that they receive between the current and future periods when the
firm engages in investment is the net marginal product of capital. As the firm acts in the
interests of the consumer, it would not be optimal for the firm to invest beyond the point where

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- Summer '18