Addendum:
Parametrization of equilibrium curves
◮
Example: The IS curve represents all (i, Y )-combinations for
which the demand plans on the goods market can be realized
= equilibrium on the goods market.
◮
This curve in the (i, Y )-space is parametrized by other
variables such like governmental expenditures or – in case of
Mundell-Fleming – exchange rate or foreign income.
◮
If we change a parameter, the entire curve shifts to another
position.
p.1
Example: IS curve for a closed economy:
Y = C a + cY + I (i) + G
(1 − c)Y − C a = I (i) + G
◮
The curve in (i, Y )-space is parametrized by G .
◮
Let G increase. Then the right hand side increases, and the equality
does not hold true anymore, i.e. the old IS curve is not valid
anymore.
◮
Question: Does the IS curve shift to the left or to the right? In
other words: which (i, Y )-combinations establish a new equilibrium?
◮
Answer: For a given Y we need a higher i (and thus lower I (i)) in
order to equalize left and right hand side (because this compensates
the higher G on the right side). Alternatively, for a given i we need
a higher Y (because this increases the left side so that both sides
are equal again). Graphically, this means that the IS curve shifts to
the right.
p.2
◮
Note: These considerations have nothing to do with
economic causalities as a consequence of the increased
G ! We simply do not know what happens with Y or i in the
economy as a consequence of increased G (this would require
a model analysis e.g. including a LM curve).
◮
We are just analysing the location of an equilibrium condition!
◮
On the subsequent slide we consider the case of an open
economy where the IS curve is additionally parametrized by
the foreign income Y f and the exchange rate τ .
◮
Algebraically, this can be done by looking whether a shift of
e.g. dY f > 0 would require a higher income (dY > 0) or a
lower income (dY < 0) in order to have a goods market
equilibrium if we keep the interest rate constant (di = 0).
Alternatively, we could also investigate whether with a given
income (dY = 0) a goods market equilibrium requires a higher
interest rate (di > 0) or a lower (di < 0).
p.3
◮
Change of Y f :
dY = CY dY + Ii di + XY f dY f + XY dY
Keep i constant (di = 0):
⇒
XY f
dY
=
>0
dY f
1 − CY − XY
If Y f increases: right-shift of IS curve!
◮
Change of τ :
dY = CY dY + Ii di + Xτ dτ + XY dY
Keep i constant (di = 0):
⇒
Xτ
dY
=
>0
dτ
1 − CY − XY
If τ increases: right-shift of IS curve!
p.4