<p>Your friend is right. If you look at the initial investment equation, and comparing it to your definition, you have:
<span class="math-container">$$I=900+(0)Y-50i$$</span>
So <span class="math-container">$d_{1}=0$</span> and <span class="math-container">$c_{1}=0.8(0.75)$</span> and thats why you get the spending multiplier as <span class="math-container">$\frac{1}{0.4}$</span></p>

CC BY-SA 4.0
2019-07-09T11:50:47.497Z
but wouldn't c1 just be 0.8 and not 0.8 times 0.75?
Sara Saletti
CC BY-SA 4.0
2019-07-09T14:23:02.517Z
$C=0.8(1-t)Y$ where $t$ is exogenously given. Further, if you look at your IS curve you derive, $c_1$ is that chunk that appears before $Y$. I believe it isn’t just the $0.8$
Brennan
CC BY-SA 4.0
2019-07-09T16:37:24.977Z
what does t being exogenous imply?? i didnt quite get it
Sara Saletti
CC BY-SA 4.0
2019-07-09T17:24:10.247Z
It just means that it is computed **outside** of the model and should be taken as given. Its an assumption that simplifies the model. It is like assuming government expenditures, $G=800$ so it is easier to compute. Im sure you could dig deep into where $t$ comes from in reality.
Brennan
CC BY-SA 4.0
2019-07-09T04:26:29.303Z
2019-07-09T04:26:29.303Z
Brennan
<p>So i have this question:<a href="https://i.sstatic.net/46iWx.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/46iWx.png" alt="enter image description here"></a></p>

<p>I go along and get 
<a href="https://i.sstatic.net/1Vfxk.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/1Vfxk.png" alt="enter image description here"></a></p>

<p>Then i need to calculate the effect on the optimal output is G increases by 80:<a href="https://i.sstatic.net/NwMJg.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/NwMJg.png" alt="enter image description here"></a></p>

<p>And on the answer sheet it states that the spending multiplier is:</p>

<p><a href="https://i.sstatic.net/DTxX7.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/DTxX7.png" alt="enter image description here"></a></p>

<p>From my knowledge i know that 
<a href="https://i.sstatic.net/WBEtx.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/WBEtx.png" alt="enter image description here"></a></p>

<p>Now how come that the spending multiplier is 1/0.4? Where are they getting the 0.4, which should be 1-c1-d1 from the original equations?</p>

<p>A friend told me that the 1/0.4 is derived from 1/1-c1(1-t) </p>

<p>then 1/1-0.8(0.75)= 1/0.4. He said that since there is no d1 in the equations ( in the investment equation) we don't use it.</p>

<p>Can somebody explain the meaning behind this 1/0.4) Thanks!</p>

<macroeconomics><general-equilibrium>
How to calculate the spending multiplier from a given set of equations?
Sara Saletti
# How to calculate the spending multiplier from a given set of equations?

(Asked by: username_0 on 2019-07-08)

So i have this question:[![enter image description here](https://i.sstatic.net/46iWx.png)](https://i.sstatic.net/46iWx.png)

I go along and get
[![enter image description here](https://i.sstatic.net/1Vfxk.png)](https://i.sstatic.net/1Vfxk.png)

Then i need to calculate the effect on the optimal output is G increases by 80:[![enter image description here](https://i.sstatic.net/NwMJg.png)](https://i.sstatic.net/NwMJg.png)

And on the answer sheet it states that the spending multiplier is:

[![enter image description here](https://i.sstatic.net/DTxX7.png)](https://i.sstatic.net/DTxX7.png)

From my knowledge i know that
[![enter image description here](https://i.sstatic.net/WBEtx.png)](https://i.sstatic.net/WBEtx.png)

Now how come that the spending multiplier is 1/0.4? Where are they getting the 0.4, which should be 1-c1-d1 from the original equations?

A friend told me that the 1/0.4 is derived from 1/1-c1(1-t)

then 1/1-0.8(0.75)= 1/0.4. He said that since there is no d1 in the equations ( in the investment equation) we don't use it.

Can somebody explain the meaning behind this 1/0.4) Thanks!

**Tags:** macroeconomics, general-equilibrium


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## 1 answers

### Answer by username_1 on 2019-07-09. Score: 1 | Accepted answer

Your friend is right. If you look at the initial investment equation, and comparing it to your definition, you have:
$$I=900+(0)Y-50i$$
So $d\_{1}=0$ and $c\_{1}=0.8(0.75)$ and thats why you get the spending multiplier as $\frac{1}{0.4}$

> **Comments:**
> **username_0**: but wouldn't c1 just be 0.8 and not 0.8 times 0.75?  
> **username_1**: $C=0.8(1-t)Y$ where $t$ is exogenously given. Further, if you look at your IS curve you derive, $c_1$ is that chunk that appears before $Y$. I believe it isn’t just the $0.8$  
> **username_0**: what does t being exogenous imply?? i didnt quite get it  
> **username_1**: It just means that it is computed **outside** of the model and should be taken as given. Its an assumption that simplifies the model. It is like assuming government expenditures, $G=800$ so it is easier to compute. Im sure you could dig deep into where $t$ comes from in reality.  

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