Download A consumption boom

A consumption boom.
Consider, first, what the effect on the economy will be if there is a sudden
consumption boom--if consumers become more optimistic about the
future (or less frugal), and so the parameter c0 in the consumption
function:
C  C(Y  T)  c 0  c(1 t)Y
rises by an amount c0, where "", the Greek letter capital delta, is a
standard symbol for "change."
If we remember that:
Private Savings + Government Savings + Capital Inflow = Investment(r)
Then it is clear what is going to happen in the flow-of-funds through
financial markets. More consumption means less private savings, means
an excess demand for investment financing. An excess demand for funds
to finance investment means that interest rates rise. As interest rates rise
demand for investment financing falls, and foreign speculators channel
their money into domestic financial markets as greed outweighs fear. The
flow-of-funds market settles down to equilibrium at a new, higher
equilibrium interest rate r with a new, lower level of investment and flow
of funds through financial markets.
On the loanable funds diagram, the flow-of-funds supply curve has
shifted to the left, and so the equilibrium position in the diagram has
moved up and to the left along the investment spending-as-a-function-ofthe-interest rate curve.
[Figure: A consumption boom and flow-of-funds equilibrium]
But by how much has the interest rate risen? And what are the effects on
the rest of the economy? To determine that we need to use our algebra.
Start with our national income identity in a full-employment economy:
C  I  G  NX  Y *
Note that since it must hold always, it holds for the changes in response to
this consumption boom increase in the parameter c0 by an amount c0 as
well:
C  I  G  NX  Y *
And note that since production is always equal to potential output in the
full employment economy of this chapter, that the right-hand-side is zero:
C  I  G  NX  0
On the left hand side the change in consumption will be simply the
change in the parameter c0:
C  c0  c(1  t)Y*  c0  c(1 t)(0)  c0
The change in investment spending will be simply the change in the real
interest rate r times how much a given change in interest rates affects
investment spending:
I  r
The change in government spending is--we assume--zero.
And--because neither domestic GDP nor foreign GDP will change--the
change in net exports will be simply the change in exports caused by the
shift in the exchange rate caused by the change in the real interest rate:
NX  GX  IM  xY f     Y *
    (r  r )
t
NX  x  0   (r  r t )    0
NX   r
Placing all of these parts of the national income identity together:
c0  r   r  0
From this equation it is straightforward to see that the change in the
equilibrium interest rate is:
r 
c0
  
And from this change in the equilibrium interest rate we can calculate the
changes in the equilibrium levels of the components of GDP, and of the
other price variable--the real exchange rate--in the model:
C  c0
I 

c
   0
G  0
NX 
 
 
c
   0

c
   0
The increase in consumption spending has led to a shortfall in savings and
a rise in real interest rates. The higher real interest rates have led to lower
investment, and to an appreciated dollar--using this definition of the
exchange rate, a lower level of . The appreciated dollar has led to a
decline in net exports. The declines in net exports and in investment
spending just add up to the increase in consumption, so the level of GDP
is unchanged at its full-employment level Y*--as we assumed that it would
be.
Note that the fall in investment is not as large as the rise in consumption
spending. It is true that the increase in consumption reduced the flow of
private domestic savings into financial markets dollar-for-dollar. But the
reduction in net exports from the appreciated dollar was associated with a
flow-of-funds into the country to take advantage of the new, higher
interest rates. This flow of foreign-owned capital into the country
provided financing for investment, and so kept the decline in investment
from being as large as the rise in consumption spending.
For a numerical example, suppose that the values of the parameters
describing the economy are as given in the table below:
t = 0.33
= 90
investment
c=0.75
x=0.1
=10
traditional
Tax rate of 1/3.
A 1 percentage point fall in the interest rate raises
spending by $80 billion a year.
A marginal propensity to consume of three-quarters.
One-tenth of changes in foreign GDP are spent on domestic
exports.
With an initial value for the real exchange rate  set at the
indexed value of 100, a 1 percentage point change in the
interest
=6
rate difference vis-à-vis abroad generates a 10% shift in the
exchange rate.
A 10% change in the exchange rate leads to a $60 billion a
year
change in exports.
And suppose that our initial consumption boom is a sudden increase in
consumption spending of $150 billion a year. Then this boom in
consumption increases the equilibrium real interest rate by one percentage
point:
r 
c0
$150
150


 1%
   90  6  10 150
And the equilibrium values of the other variables in the economy change
by:
C  c0  $150 billion
I 

90
c0 
$150  $90 billion
  
90  6  10
G  0
NX 
 
 
(6  10)
c0 
$150  $60 billion
  
90  6  10

10
c 0 
$150  10% change
  
90  6  10
The $150 billion increase in annual consumption spending, for this
economy with these parameter values, in this full-employment model,
shifts the economy's equilibrium by raising real interest rates by 1%,
appreciating the value of the dollar (remember: the initial value of the real
exchange rate  was set at 100) by 10%, reducing investment spending by
$90 billion a year and reducing net exports by $60 billion a year.