This post goes over the economic intuition of horizontal and vertical IS and LM curves in the IS/LM model. It develops the associated graphs, and talk about the fiscal policy and monetary policy implications of such slopes for the IS and LM curves.

First let's review what to look for in the relevant equations:

Fiscal Policy can result in: higher/lower taxes, or higher/lower
government spending

So we need to look for the influence of T and G in the
following models to see what kind of impacts fiscal policy will have.

Monetary policy can result in: higher/lower money supply, or
higher/lower interest rates (if we assume discount rates affect the national
interest rate).

Let’s consider the following situations:

**Economy A, where:**Consumption function: C = 5 + 2(Y-T);

Investment function: I = 3 + 4Y– 2i

Government spending = G

Money demand: Md = 6 – 2i

Money supply: Ms = M

**Economy B, where:**

Consumption function: C = 5 + 2(Y-T);

Investment function: I = 3 + 4Y

Government spending = G

Money demand: Md = 5Y – 2i

Money supply: Ms = M

**Economy C, where:**

Consumption function: C = 5 + 2(Y-T);

Investment function: I = 3 + 4Y – 2i

Government spending = G

Money demand: Md = 5Y

Money supply: Ms = M

Investment function: I = 3 + 4Y – 2i

Government spending = G

Money demand: Md = 5Y

Money supply: Ms = M

For descriptions of the variables check out this
introduction to the IS/LM model. Note
that lower case letters followed by numbers are arbitrary constants or
coefficients.

We need to identify which equations have T and G in them,
and whether the effect is positive or negative.
We see that each economy has T enter negatively and G enter positively
which is what we would expect, so the standard impacts of fiscal policy apply. The key difference occurs in Economy B where Investment spending is independent of the interest rate. This means that the amount of private
investment in the economy does not change as the national interest rate
changes. This means that no “crowding
out” will occur due to fiscal policy meaning that the full impact of the policy
will be felt on the economy.

Economy B is also
unique, in that the IS curve will be vertical because no variable is dependent
on the interest rate. Typically
investment and/or consumption depend negatively on the interest rate which is
what gives the IS curve its downward slope.
Without this relationship, Y is just Y regardless of i hence the
vertical IS.

This same sort of logic can be applied to the monetary
policy side of things. Typically the
money demand equation (which looks like L(Y,i)) is a function of both real GDP
(Y) and the interest rate (i). This
holds true for Economy A and we get our normal upward sloping LM curve. However, when we look at Economy A and C, we
see that i and Y are absent respectively.
What implications does this have?

In Economy C money demand only depends on Y. This will result in a vertical LM curve,
because whatever the interest rate is, only a certain amount of money will be
demanded. However, if there is any change
in Y, the LM curve will have to shift (meaning an associated change in money
supply or the price level has to take place).
With respect to monetary policy, this implies that any change in the
money supply will have a direct effect on real GDP since no adjustment in the
interest rate will have an effect.
Basically, if the Federal Reserve increases the money supply by $100,
real GDP will have to increase by $100 to compensate. It is also possible that the price level, P
could adjust, but I am assuming it doesn’t in this scenario.

Finally, in Economy A money demand depends only on i. This will result in a horizontal LM curve,
because whatever the real GDP level is, only a certain amount of money will be
demanded. If there is any change in i,
the LM curve will have to shift (meaning an associated change in the money
supply or the price level has to take place).
With respect to monetary policy, this implies that any change in the
money supply will have a direct effect on the interest rate since no adjustment
in Y will have an effect.

**Now that we know the three scenarios, we can summarize the possible fiscal and monetary policy effects on equilibrium Y and i:**

In Economy A with the horizontal LM curve, a change in
fiscal policy shifts the IS curve and we will see a movement along the LM curve. Because the LM curve is horizontal, we will
see only a change in Real GDP. This
means that fiscal policy is super effect at changing real GDP because there is
no change in the interest rate causing crowding out. A change in monetary policy will shift the LM
curve, with an associated movement along the IS curve as normal.

In Economy B with the vertical IS curve, a change in fiscal
policy shifts the IS curve and we see a movement along the LM curve. A change in monetary policy shifts the LM
curve and we see a movement along the IS curve which will ONLY change the
interest rate, not real GDP. This means
monetary policy is ineffective at increasing or decreasing real GDP.

In Economy C with the vertical LM curve, a change in fiscal
policy shifts the IS curve and we will see a movement along the LM curve. Because the LM curve is vertical, we will see
only a change in interest rates, no change in real GDP. This means that fiscal policy is ineffective
at changing real GDP in this situation.
A change in monetary policy will shift the LM curve, with an associated
movement along the IS curve as normal.