<p>The other answer is correct about the mechanism but I think this can be best explained using some simple algebra.</p>
<p>LM curve is given by equilibrium between money demand and money supply. We can use simple money demand: <span class="math-container">$L(Y,r) = a_0 + a_1Y – a_2r,$</span> and simple real money supply; <span class="math-container">$M/P= b_0 + b_1Y – b_2r$</span>. <span class="math-container">$Y$</span> is output, <span class="math-container">$r$</span> real interest rate (you could also rewrite everything in nominal interest rate using Fisher equation <span class="math-container">$r \approx i-\pi$</span>), <span class="math-container">$a$</span>'s and <span class="math-container">$b$</span>'s are parameters of money supply and money demand.</p>
<p>The LM curve is then given; <span class="math-container">$ r= \frac{(a_0 -b_0)}{(a_2 – b_2)} + \frac{(a_1-b_1)}{(a_2 – b_2)}Y$</span></p>
<p>How ca this LM curve shift? Mathematically this curve shifts up or down when you add (subtract) number from the constant or left (right) when you add (subtract) slope times constant, or it rotates when slope changes.</p>
<p>So to get any shifts or rotations of this curve we need some changes or additions to <span class="math-container">$a_0, a_1, a_2, b_0, b_1, b_3$</span>. Does shift in IS curve change this? Not really, <span class="math-container">$a_0$</span> is autonomous money demand (money demand that does not depend on anything so not on IS curve), <span class="math-container">$a_1$</span> tells us how much more money people demand when their income increases and <span class="math-container">$a_2$</span> tells us how much less money is demanded when interest rate increase (shifts in IS curve or fiscal policy should not change these fundamental behavioral preferences, you would have to make some behavioral story, like government spending that money on some propaganda that changes people's preferences about holding/borrowing money, and we abstract from that in simple classroom examples).</p>
<p>Continuing with supply curve parameters, <span class="math-container">$b_0$</span> is the autonomous money supply, you can think of it as coins and notes in circulation, <span class="math-container">$b_1$</span> tells us how central bank responds to output shocks and <span class="math-container">$b_2$</span> how central bank responds to real interest rates (and hence also indirectly to inflation). Shift in IS curve or fiscal policy itself again do not change this unless you add some extra assumptions and stories on top.  Fiscal policy should not affect the notes in circulation, and if there is clear central bank mandate, then it should not affect central bank policy function which dictates how central bank responds to output and inflation (of course IRL you could make stories where central bankers change their mind based on what government is doing, but in classroom we abstract from that).</p>
<p>So to sum it up, there is no clear way how IS curve or fiscal policy can shift LM curve, unless you are adding some ad hoc behavioral stories. IS curve and fiscal policy still interacts with LM curve. For example, fiscal policy can change <span class="math-container">$Y$</span>, but changes in either <span class="math-container">$Y$</span> or <span class="math-container">$r$</span> alone do not shift the LM curve, they represent movements along LM curve. To change shape of LM curve you need to change <span class="math-container">$a_0, a_1, a_2, b_0, b_1, b_3$</span> somehow.</p>

CC BY-SA 4.0
2024-10-30T13:27:57.737Z
2024-10-30T13:34:23.780Z
2024-10-30T13:34:23.780Z
csilvia
<blockquote>
<p>At the same time, my prof has mentioned that fiscal policies do not change the LM curve (assuming the rate of interest remains constant.) Why is this so? If the curves are interdependent, would not a shift in the IS curve, say by increasing government expenditure, shift the LM curve as well?</p>
</blockquote>
<p>No, just because the system is interdependent it does not mean shift in one curve has to shift another curve. This is similar to classic supply &amp; demand. Supply and demand is interdependent system but, for example, change in consumer preferences will only shift demand. There will be change in quantity supplied but not supply curve per se.</p>
<p>Similarly, when shift in IS occurs, there will be new equilibrium on money market so. However, this is not the same as whole LM curve shifting, since LM curve is constructed from all possible money market equilibria (see picture below from Blanchard et al Macroeconomics pp 86). Hence for LM curve to shift, you need to have a new set of possible money market equilibria.  Shift in LM curve means that at the same output interest rate is always lower, or higher. Not that for example, we have higher interest rate with higher output (movement along the LM curve).</p>
<p>Moreover, I choose the picture below, because I think it is actually better explanation than what your professor gave you. In the picture below you see increase in <span class="math-container">$Y$</span> which would correspond to expansionary fiscal policy. But because real money supply is held constant, you get higher interest rate, we move to new equilibrium <strong>along</strong> the LM curve with higher interest rate and output (here is the interdependency with IS), but there is no shift in LM curve.  An alternative is to say what your professor said. If you assume interest rate does not depend on fiscal policy (e.g. you could assume perfectly elastic money demand) you will also get no shifts in LM curve (although I do not have picture for this scenario), however, this extra assumption is not even strictly speaking necessary, unless in your class some other assumptions were relaxed (e.g. in your class you used endogenous instead of exogenous money supply etc).</p>
<p><a href="https://i.sstatic.net/Yospc1x7.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Yospc1x7.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2024-10-30T12:26:25.897Z
2024-10-30T12:26:25.897Z
1muflon1
<p>We have been studying the IS-LM model in class, and while I understand how to derive these curves, I am struggling to understand what the model really represents. I am aware that the model implies an interconnectedness between the goods and money markets.  But how? It seems to me that the model implies that fiscal policies that are expansionary may have countervailing effects because of the LM curve, that is, the increase in income may be offset by changes in the money market if a fiscal policy is implemented?</p>
<p>At the same time, my prof has mentioned that fiscal policies do not change the LM curve (assuming the rate of interest remains constant.) Why is this so? If the curves are interdependent, would not a shift in the IS curve, say by increasing government expenditure, shift the LM curve as well?</p>
<p>Any help is appreciated since I am aware my confusion is based on some fundamental misunderstanding of this model.</p>

CC BY-SA 4.0
2024-10-30T11:41:41.777Z
Always be aware that the IS-LM model is imperfect and does not explain the real world very well. The LM curve is better modelled as horizontal since short term interest rates are central bank policy, not determined in money markets. I don't see huge pedagogical function in still teaching it at undergrad but clearly it is.
Jamie Smith
CC BY-SA 4.0
2024-10-30T12:47:09.737Z
This comment is absolutely unhelpful. First, OP does not say he is puzzled by realism of IS-LM model but by its internal mechanism. You might as well go to physics se and write on any question about undergraduate physics about how unrealistic their problems are. Second, IS-LM model works fine and is completely compatible with short term interest rates being set by central bank, and mentioning it does not help with the above question. This is borderline trolling.
csilvia
<macroeconomics><monetary-policy><fiscal-policy><keynesian-economics>
Why do fiscal policies only shift the IS curve?
mayu
# Why do fiscal policies only shift the IS curve?

(Asked by: username_0 on 2024-10-30)

We have been studying the IS-LM model in class, and while I understand how to derive these curves, I am struggling to understand what the model really represents. I am aware that the model implies an interconnectedness between the goods and money markets. But how? It seems to me that the model implies that fiscal policies that are expansionary may have countervailing effects because of the LM curve, that is, the increase in income may be offset by changes in the money market if a fiscal policy is implemented?

At the same time, my prof has mentioned that fiscal policies do not change the LM curve (assuming the rate of interest remains constant.) Why is this so? If the curves are interdependent, would not a shift in the IS curve, say by increasing government expenditure, shift the LM curve as well?

Any help is appreciated since I am aware my confusion is based on some fundamental misunderstanding of this model.

**Tags:** macroeconomics, monetary-policy, fiscal-policy, keynesian-economics

> **Comments:**
> **username_1**: Always be aware that the IS-LM model is imperfect and does not explain the real world very well. The LM curve is better modelled as horizontal since short term interest rates are central bank policy, not determined in money markets. I don't see huge pedagogical function in still teaching it at undergrad but clearly it is.  
> **username_2**: This comment is absolutely unhelpful. First, OP does not say he is puzzled by realism of IS-LM model but by its internal mechanism. You might as well go to physics se and write on any question about undergraduate physics about how unrealistic their problems are. Second, IS-LM model works fine and is completely compatible with short term interest rates being set by central bank, and mentioning it does not help with the above question. This is borderline trolling.  

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## 2 answers

### Answer by username_2 on 2024-10-30. Score: 2

The other answer is correct about the mechanism but I think this can be best explained using some simple algebra.

LM curve is given by equilibrium between money demand and money supply. We can use simple money demand: $L(Y,r) = a\_0 + a\_1Y – a\_2r,$ and simple real money supply; $M/P= b\_0 + b\_1Y – b\_2r$. $Y$ is output, $r$ real interest rate (you could also rewrite everything in nominal interest rate using Fisher equation $r \approx i-\pi$), $a$'s and $b$'s are parameters of money supply and money demand.

The LM curve is then given; $ r= \frac{(a\_0 -b\_0)}{(a\_2 – b\_2)} + \frac{(a\_1-b\_1)}{(a\_2 – b\_2)}Y$

How ca this LM curve shift? Mathematically this curve shifts up or down when you add (subtract) number from the constant or left (right) when you add (subtract) slope times constant, or it rotates when slope changes.

So to get any shifts or rotations of this curve we need some changes or additions to $a\_0, a\_1, a\_2, b\_0, b\_1, b\_3$. Does shift in IS curve change this? Not really, $a\_0$ is autonomous money demand (money demand that does not depend on anything so not on IS curve), $a\_1$ tells us how much more money people demand when their income increases and $a\_2$ tells us how much less money is demanded when interest rate increase (shifts in IS curve or fiscal policy should not change these fundamental behavioral preferences, you would have to make some behavioral story, like government spending that money on some propaganda that changes people's preferences about holding/borrowing money, and we abstract from that in simple classroom examples).

Continuing with supply curve parameters, $b\_0$ is the autonomous money supply, you can think of it as coins and notes in circulation, $b\_1$ tells us how central bank responds to output shocks and $b\_2$ how central bank responds to real interest rates (and hence also indirectly to inflation). Shift in IS curve or fiscal policy itself again do not change this unless you add some extra assumptions and stories on top. Fiscal policy should not affect the notes in circulation, and if there is clear central bank mandate, then it should not affect central bank policy function which dictates how central bank responds to output and inflation (of course IRL you could make stories where central bankers change their mind based on what government is doing, but in classroom we abstract from that).

So to sum it up, there is no clear way how IS curve or fiscal policy can shift LM curve, unless you are adding some ad hoc behavioral stories. IS curve and fiscal policy still interacts with LM curve. For example, fiscal policy can change $Y$, but changes in either $Y$ or $r$ alone do not shift the LM curve, they represent movements along LM curve. To change shape of LM curve you need to change $a\_0, a\_1, a\_2, b\_0, b\_1, b\_3$ somehow.


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### Answer by username_3 on 2024-10-30. Score: 1

> At the same time, my prof has mentioned that fiscal policies do not change the LM curve (assuming the rate of interest remains constant.) Why is this so? If the curves are interdependent, would not a shift in the IS curve, say by increasing government expenditure, shift the LM curve as well?

No, just because the system is interdependent it does not mean shift in one curve has to shift another curve. This is similar to classic supply & demand. Supply and demand is interdependent system but, for example, change in consumer preferences will only shift demand. There will be change in quantity supplied but not supply curve per se.

Similarly, when shift in IS occurs, there will be new equilibrium on money market so. However, this is not the same as whole LM curve shifting, since LM curve is constructed from all possible money market equilibria (see picture below from Blanchard et al Macroeconomics pp 86). Hence for LM curve to shift, you need to have a new set of possible money market equilibria. Shift in LM curve means that at the same output interest rate is always lower, or higher. Not that for example, we have higher interest rate with higher output (movement along the LM curve).

Moreover, I choose the picture below, because I think it is actually better explanation than what your professor gave you. In the picture below you see increase in $Y$ which would correspond to expansionary fiscal policy. But because real money supply is held constant, you get higher interest rate, we move to new equilibrium **along** the LM curve with higher interest rate and output (here is the interdependency with IS), but there is no shift in LM curve. An alternative is to say what your professor said. If you assume interest rate does not depend on fiscal policy (e.g. you could assume perfectly elastic money demand) you will also get no shifts in LM curve (although I do not have picture for this scenario), however, this extra assumption is not even strictly speaking necessary, unless in your class some other assumptions were relaxed (e.g. in your class you used endogenous instead of exogenous money supply etc).

[![enter image description here](https://i.sstatic.net/Yospc1x7.png)](https://i.sstatic.net/Yospc1x7.png)


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