the net marginal product of capital is equal to the real interest rate because this would imply
that the consumer was receiving a lower rate of return on his or her saving than could be
obtained by lending the credit market at the real interest rate
r
. Thus the real interest rate
represents the opportunity cost of investing for the representative firm.

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The Optimal Investment Schedule for the Representative Firm
This figure shows the optimal investment
schedule for the representative firm. The
optimal representative rule states that the
firm invests
MP
k
– d
=
r
. The future net
marginal product schedule
MP
k
– d
=
r
is
the representative firms optimal investment
schedule, because this describes how much
investment is required for the net marginal
product of future capital to equal the real
interest rate. It can be seen that the optimal investment schedule is the firm’s net marginal
product of capital, as a function of investment, given then initial quantity of capital K. If the
firm’s real interest rate is r
1
ten the firm wishes to invest I
1
.
The optimal investment schedule shifts to right if the future total factor productivity,
z’,
increases. If total factor productivity is expected to be higher in the future so that
z’
increases,
this increases the future marginal product of capital, and the firm is more willing to invest
during the current period. Higher investment in the current period leads to higher future
productive capacity, so that the firm can take advantage of high future total factor productivity.
The optimal investment schedule shifts to left if the current capital stock
K
is higher. A higher
capital stock at the beginning of the current period implies that for a given level of current
investment I, the future capital stock
K’
will be larger. That is, if
K
is larger, then there is more
of this initial capital left after the depreciation in the current period to use in future production.

Therefore, higher K implies that the future marginal product of capital,
MP’
K
, will decrease for
each level of investment, and the optimal investment will then shift to the left.
The Optimal Investment Schedule Shifts to the Right if Current Capital Decreases of Future
Total Fcator Productivity is Expected to Increase
This figure shows that the optimal
investment schedule shifts to the right if
current capital decreases or future total
factor productivity is expected to increase.
This is because either of these changes
causes the future marginal product of capital
to increase.
From the figure we can see a shift to the right in the optimal investment schedule which can be
caused by either an increase in future total productivity z’ or by a lower current quantity of
capital K.
An increase in z’ causes firms capitalize on higher future productivity and invest
more now
.

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- Summer '18