Transcript Investment

Before we consider investment in the
model however, we should very briefly
look at what is happening to money here
ys
r0
yd
y0
First notice that the
market for goods
determines
real income (y)
and the
real interest rate (r)
•So the money market determines the
nominal variables in the economy:
•The price level
P,
•Inflation
p
•Nominal interest rate
R= r+ p

First consider the Demand for
Money
MD = P L (y, R)
L (+,-)
That is, the demand for money depends
on the level of real income and the
NOMINAL interest rate
Why Nominal?
Because lose R on all money held
First consider the Demand for
Money
P
MD = P L (Y, R)
e.g Suppose we figure out L(y, R)= 8
then
MD = 8P
MD
M
Finding Money Market Equilibrium
For simplicity assume for now that there
is no inflation, p=0
and thus R=r (that is there is no
distinction)
Money Demand must equal Money
supply
 M D  MS  
Money Market Equilibrium
IF
M D  MS  
Then
 M D  P.L( y, r )    MS
L( y , r )

P

Money Market Equilibrium
P
MD
L( y 0 , r0 )
 P0


Money Market Equilibrium
MD
P0
MbD

What happens
now if there is a
Boom?
MD rises as y
rises and r goes
down L(+,-)
So at every P
more is
demanded
Money Market Equilibrium
MD
P0
MbD
P1

So where is the
new
Equilibrium?
So the price
level has fallen
in a boom as
predicted by
the stylised
facts
Money Market Equilibrium
MrD
P1
MD
P0
Similarly in a
recession MD falls
as y falls and r
goes up
Md =PL(y

,r )
And the price
level rises in a
recession
Money Market Equilibrium
Inflation!
P1
MD
P0
0
1
What happens if
the monetary
authority increases
the money supply
It just
causes P to
rise!
Business Cycle Model with Investment
y=f(kt-1,Lt)
y
y=f(kt-1)
y=f(+,+)
Note
production
depends on the
capital stock in
place at the end
of last period
kt-1
y=f(kt-1)
y
Note we are
treating L as a
constant here
y=f(kt-1,Lt)
kt-1
MPk t-1
Marginal
Product of
Capital is
decreasing
kt-1
y
y=f(kt-1)
Note we are
treating L as a
constant here
y=f(kt-1,Lt)
kt-1
y=f(L)
L
But we are
treating kt-1
as a constant
here
y=f(kt-1,Lt)
y
y=f(kt-1)
kt-1
y=f(L)
L
And both
functions
exhibit
decreasing
returns to scale
More generally could consider
changes in K & L and then would
expect something more like:
2y
y
k&L
2k & 2L
However,
right now we
want to
focus on the
investment
decision so
we need to
focus on
capital in
isolation
y=f(kt-1)
y
MPk t-1
kt-1
And on the
MPkt-1 in
particular
Why?
kt-1
However,
right now we
want to
focus on the
investment
decision so
we need to
focus on
capital in
isolation
y=f(kt-1)
y
kt-1
MPk t-1
kt-1
Because the
MPkt-1 tells
us the
additional
output we
get from one
more unit of
Capital
MPk t-1
What other
consideration do we
need to think about
with capital?
Depreciation!
kt-1
MPk t-1
So true return from
capital is MPkt-1 less
depreciation, d.
What is its cost?
The real rate of
interest r
MPk t-1-d
kt-1
MPk t-1
So we should equate
the real return on
capital, MPkt-1-d,
with the real rate of
interest r
r
MPk t-1-d
kt-1
k̂
*
t 1
k̂
MPk t-1
*
t 1
Is the desired
capital stock
r
MPk t-1-d
kt-1
k̂
*
t 1
MPk t-1
Note a rise in r or
d results in a
lower desired
capital stock
r
MPk t-1-d
kt-1
k̂
*
t 1
Higher r
MPk t-1
r
MPk t-1-d
kt-1
k̂
*
t 1
Higher d
MPk t-1
r
MPk t-1-d
kt-1
k̂
*
t 1
MPk t-1
k̂ (r, d )
*
t 1
k̂ (,)
*
t 1
r
MPk t-1-d
kt-1
k̂
*
t 1
k̂
*
t 1
Desired Capital Stock
But we are interested in investment, not
desired capital stock
How do we get from desired capital
stock to investment?
Investment is the difference between the
desired capital stock, and the existing
capital stock
Investment is the difference between
the desired capital stock, and the
existing capital stock
Existing Capital Stock:
Capital in place last period less
whatever wore out.
(1-d)kt-1
Investment is the difference between
the desired capital stock, and the
existing capital stock
i  k̂
*
t 1
 (1  d )k t 1
i  k̂
*
t 1
 (1  d )k t 1
i  k̂ (r, d )  (1  d )k t 1
*
t 1
(-,-)
i(r, d , k t1 )
i(, ,)
But what about d?
i  k̂
*
t 1
 (1  d )k t 1
i  k̂ (r, d )  (1  d )k t 1
*
t 1
(-,-)
i(r, d , k t1 )
i(, ? ,)
r
i(r, d , k t1 )
id
i
r
Empirically we know that:
di dc

dr dr
And…
id
i
r
c i
: : is approximat ely 4 : 1
y y
Id
I
So what does the aggregate
economy look like now?
r
Notice id is
flatter than
cd
r0
cd
id
i0
c0
And total aggregate
demand is id plus cd
r
r0
cd
id
i0
yd=cd + id)
c0
y0
r
And equilibrium depends on
aggregate demand and supply
ys
r0
cd
id
i0
yd=cd + id)
c0
y0
So now we have described the model with
Investment..
r
ys
r0
id
cd
yd=cd + id)
i0
c0
y0
And we are now in a position to return to our
business cycle shocks.