<p>Given your equations, you can find</p>

<p>$$Y = C + 50 + 20 \implies Y = C + 70$$</p>

<p>You can then substitute $Y$ for its equal into your other equation</p>

<p>$$C = 100 + 0.5(C + 70 - T)$$</p>

<p>Finally, given a balanced buget, you know that $G = T$, which should be enough for you to solve for $C$.</p>

CC BY-SA 3.0
2016-08-30T21:34:15.773Z
2016-08-30T21:34:15.773Z
Kitsune Cavalry
<p>Consider a simple closed economy model where <strong>Y = C + I + G</strong>, consumption is given by the function <strong>C = 100 + 0.5 (Y - T)</strong>, investment is <strong>I = 50</strong>, government purchases are <strong>G = 20</strong>, and the government’s 
budget is balanced. </p>

<p>How do I work out what tax is, to work out the amount of autonomous spending? Is there something obvious I'm missing?</p>

CC BY-SA 3.0
2016-08-30T10:58:35.663Z
Figure out what tax is equivalent to from 'budget balance' and autonomous spending is the spending not related income, so think what the spending level is when wealth is zero.
VCG
<macroeconomics>
Simple closed economy problem
Jason Huang
# Simple closed economy problem

(Asked by: username_0 on 2016-08-30)

Consider a simple closed economy model where **Y = C + I + G**, consumption is given by the function **C = 100 + 0.5 (Y - T)**, investment is **I = 50**, government purchases are **G = 20**, and the government’s
budget is balanced.

How do I work out what tax is, to work out the amount of autonomous spending? Is there something obvious I'm missing?

**Tags:** macroeconomics
> **Comments:**
> **username_1**: Figure out what tax is equivalent to from 'budget balance' and autonomous spending is the spending not related income, so think what the spending level is when wealth is zero.  

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## 1 answers

### Answer by username_2 on 2016-08-30. Score: 0 | Accepted answer

Given your equations, you can find

$$Y = C + 50 + 20 \implies Y = C + 70$$

You can then substitute $Y$ for its equal into your other equation

$$C = 100 + 0.5(C + 70 - T)$$

Finally, given a balanced buget, you know that $G = T$, which should be enough for you to solve for $C$.


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