We now need to present both stock (asset market) and flow
(commodity market) equilibrium on the same graph. The conventional
way to do this is to put the real interest rate on the vertical axis
and output (income and employment) on the horizontal one.
First, we present again the equations of stock and flow equilibrium.

The conditions of asset (stock) and goods market (flow) equilibrium as presented in the previous topic are, respectively

1. M/P = γ − θ ( r + τ ) + ε Y

and

2. Y
= ( a + δ
+ Φ_{BT} + DSB)/(s + m)
− μ/(s + m) r
+ m* /(s + m) Y*
− σ/(s + m) Q

where we express the domestic interest rate simply as r without regard to the role of world capital market conditions in determining it---that will be incorporated later. If you are not completely familiar with the derivation and meaning of these equations you should review the previous two topics again.

The combinations of r and Y for which Equation 2 holds can be presented as a negative relationship between income and the real interest rate as shown in Figure 1. The downward sloping flow-equilibrium curve---normally not a straight line as here portrayed---is called the IS curve in textbooks and we will follow that naming convention here.

The label IS comes from the fact that in a closed economy
(one with no trade) the curve gives the combinations of income and
the interest rate for which desired savings equals desired investment.
In an open economy this curve gives the combinations of income and the
interest rate for which the desired net capital outflow, represented by
savings minus investment, equals the the desired current account
balance---that is, for which S − I =
B_{T} + DSB. When there is no international
trade, this condition becomes simply S − I
= 0 .

**A fall in the interest rate leads to an expansion of investment, causing
equilibrium output, income and emloyment to increase as we move
down along the IS curve. A fall in the real exchange rate shifts
world demand onto domestic goods, increasing income at each level
of the real interest rate and shifting IS to the right. An
increase in rest-of-world income, or exogenous increase in consumption
or investment or net exports at any given level of the real interest rate
also causes the IS line to shift to the right and the equilibrium level
of output, income and employment to increase.**

To portray asset equilibrium in terms of the relationship it implies between the real interest rate and the level of income, it is useful to rearrange Equation 1 to put r on the left side:

1a. r = − (1/θ) M/P + γ/θ − τ + (ε/θ) Y

Since ε/θ in this equation is preceded by a positive
sign, the equation defines a positive relationship between the real interest
rate and level of income, holding everything else constant, and can be
portrayed as the upward sloping curve LM (portrayed as a straight line) in
Figure 2. (The name LM, meaning liquidity-money, is also traditional.) **The
LM curve gives the combinations of income and the interest rate for which the
demand for money (or desired liquidity) equals the money supply and hence for
which the domestic economy is in asset or stock equilibrium.
**

The intuition behind the positive slope of LM is as follows: An increase in the interest rate reduces the demand for money and an increase in income increases it. To keep the demand for money equal to a constant money supply as the interest rate rises and we move along the LM curve, the level of income must increase.

An increase in the money supply holding the real interest rate constant requires a higher level of income to make the demand for money equal to that greater supply, shifting LM to the right. The combinations of income and the real interest rate at which the demand for money equals the supply now lie farther to the right. An increase in the expected inflation rate at a given level of the real interest rate increases the cost of holding money and reduces the quantity people chose to hold. This requires that the level of income rise at the given world real interest rate to bring desired money holdings back into line with the unchanged money supply and preserve asset equilibrium---the LM curve shifts to the right.

**
Overall equilibrium will occur where the IS and LM curves cross. In a
an economy that is closed to international trade, an increase in the money
supply in Figure 2 will shift LM to the right causing the interest rate
to fall as the public tries to reestablish portfolio equilibrium by
purchasing assets. The fall in the interest rate will cause output,
income and employment to increase. The interest rate will fall and income
will increase until the quantity of money demanded has increased by an
amount equal to the increase in the money supply.** The new equilibrium will
be at point **b** in Figure 2.

Full portrayal of equilibrium also requires that we add a vertical line
Y_{F} to portray the full-employment level of income
which the equilibrating process will eventually achieve in the long-run.
This is shown in Figure 3.

Starting with a full-employment situation where IS and LM cross, let us
assume that there is a decline in desired investment so that the IS curve
shifts downward to IS'. In the short run before the price level can adjust
the real interest rate will fall from r_{1} to
r_{2} and output and income fall from their
full-employment levels to Y_{1} . As time passes the
price level will fall, increasing the real money stock and shifting the
LM curve down to LM'. As a result, the real interest rate will fall from
r_{2} to r_{3} and income and
employment will return to their full-employment levels.

The above analysis assumes, unrealistically, that our economy is closed to international trade and capital movements. When we incorporate these elements an additional line has to be added to the graph---the horizontal rZ line in Figure 4.

**The rZ line imposes on our small open economy the effect of world market
conditions on the determination of the domestic real interest rate.** Since
domestic assets are owned world-wide and the domestic economy is small, the
interest rate on those assets will be determined by the willingness of world
residents to hold them. The domestic real interest rate will thus equal the
foreign real interest rate plus a premium that reflects the risk of holding
domestic assets rather than rest-or-world assets. The domestic interest rate
will also differ from the foreign interest rate by an amount to compensate for any
expected capital gain or loss on domestic assets resulting from expected
future changes in the domestic real exchange rate.

Overall full-employment equilibrium of the small open economy will occur,
of course, where the IS and LM curves cross at the point at which the
vertical Y_{F} line and the horizontal rZ also cross.
But suppose now that the IS curve shifts down to IS'. Given the fact that
the domestic interest rate cannot change, how will a new equilibrium be
established in the short and long runs?
The next two topics will develop the answer to this question. First, however,
it is time for a test. As always think up your own answers to the questions
before looking at the answers provided.

Question 1

Question 2

Question 3

Choose Another Topic in the Lesson