<p>Notice that the elasticity can be written as </p>

<p><span class="math-container">$$\frac{\Delta C}{\Delta Y}\cdot\frac{Y}{C}$$</span></p>

<p>So for category <span class="math-container">$1$</span> you have <span class="math-container">$$\frac{\Delta C_1}{\Delta Y}\cdot\frac{Y}{C_1}=0.5$$</span> and <span class="math-container">$$MPC_1=\frac{\Delta C_1}{\Delta Y}=0.1$$</span></p>

<p>This gives you 
<span class="math-container">$$0.1\cdot\frac{Y}{C_1}=0.5$$</span>
which by reordering yields to
<span class="math-container">$$\frac{C_1}{Y}=\frac{1}5$$</span></p>

<p>Similarly <span class="math-container">$$\frac{C_2}{Y}=\frac{3}{10}$$</span></p>

<p>Finally notice that <span class="math-container">$C=C_1+C_2=1000$</span> and <span class="math-container">$Y=2000$</span>, hence we must have that <span class="math-container">$\frac{C}{Y}=\frac{C_1+C_2}{Y}=0.5$</span> which is satisfied since
<span class="math-container">$$\frac{1}5+\frac{3}{10}=0.5$$</span></p>

<p>(Since we have that <span class="math-container">$2C=Y$</span> and <span class="math-container">$100\%$</span> of revenue comes from <span class="math-container">$C$</span> is straightforward to see that the <span class="math-container">$\%$</span> of revenue associated with each category are twice this numbers)</p>

CC BY-SA 4.0
2019-05-14T16:31:22.607Z
2019-05-14T19:42:11.960Z
2019-05-14T19:42:11.960Z
Chaos
<p>Given a total consummation of 1000 and a total revenue of 2000 with </p>

<p>Cat 1 => elasticity of 0.5; MPC of 0.1</p>

<p>Cat 2 => elasticity of 1, MPC of 0.3</p>

<p>How would I go about to calculating the % of the total revenue for each category?</p>

<hr>

<p>I tried using both these formulas</p>

<p><img src="https://chart.googleapis.com/chart?cht=tx&amp;chl=%5C%5CMPC%3D%5Cfrac%7B%5CDelta%20C%7D%7B%5CDelta%20Y%7D" alt="mpc"></p>

<p><img src="https://chart.googleapis.com/chart?cht=tx&amp;chl=Elasticity%3D%5Cfrac%7B%5Cfrac%7B%5CDelta%20C%7D%7BC%7D%7D%7B%5Cfrac%7B%5CDelta%20Y%7D%7BY%7D%7D" alt="elasticity"></p>

<p>and tried to figure out the first category by assuming the variation of revenue to be 2000 (2000-0) and the initial consummation to be 0.  </p>

<p><img src="https://chart.googleapis.com/chart?cht=tx&amp;chl=0.5%3D%5Cfrac%7B%5Cfrac%7BC_%7B2%7D-0%7D%7B1000%7D%7D%7B%5Cfrac%7B2000-0%7D%7B2000%7D%7D" alt="whatidid"></p>

<p>which gives me a value of 500 for c2. But then, using the MPC formula, it does not seem to make any sense</p>

<p><img src="https://chart.googleapis.com/chart?cht=tx&amp;chl=0.1%5Cneq%20%5Cfrac%7B500-0%7D%7B2000-0%7D" alt="hmm"></p>

<macroeconomics>
Finding the % of the total consummation by category using elasticity and MPC
Mohammed
# Finding the % of the total consummation by category using elasticity and MPC

(Asked by: username_0 on 2019-05-14)

Given a total consummation of 1000 and a total revenue of 2000 with

Cat 1 => elasticity of 0.5; MPC of 0.1

Cat 2 => elasticity of 1, MPC of 0.3

How would I go about to calculating the % of the total revenue for each category?

---

I tried using both these formulas

![mpc](https://chart.googleapis.com/chart?cht=tx&chl=%5C%5CMPC%3D%5Cfrac%7B%5CDelta%20C%7D%7B%5CDelta%20Y%7D)

![elasticity](https://chart.googleapis.com/chart?cht=tx&chl=Elasticity%3D%5Cfrac%7B%5Cfrac%7B%5CDelta%20C%7D%7BC%7D%7D%7B%5Cfrac%7B%5CDelta%20Y%7D%7BY%7D%7D)

and tried to figure out the first category by assuming the variation of revenue to be 2000 (2000-0) and the initial consummation to be 0.

![whatidid](https://chart.googleapis.com/chart?cht=tx&chl=0.5%3D%5Cfrac%7B%5Cfrac%7BC_%7B2%7D-0%7D%7B1000%7D%7D%7B%5Cfrac%7B2000-0%7D%7B2000%7D%7D)

which gives me a value of 500 for c2. But then, using the MPC formula, it does not seem to make any sense

![hmm](https://chart.googleapis.com/chart?cht=tx&chl=0.1%5Cneq%20%5Cfrac%7B500-0%7D%7B2000-0%7D)

**Tags:** macroeconomics


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## 1 answers

### Answer by username_1 on 2019-05-14. Score: 0 | Accepted answer

Notice that the elasticity can be written as

$$\frac{\Delta C}{\Delta Y}\cdot\frac{Y}{C}$$

So for category $1$ you have $$\frac{\Delta C\_1}{\Delta Y}\cdot\frac{Y}{C\_1}=0.5$$ and $$MPC\_1=\frac{\Delta C\_1}{\Delta Y}=0.1$$

This gives you
$$0.1\cdot\frac{Y}{C\_1}=0.5$$
which by reordering yields to
$$\frac{C\_1}{Y}=\frac{1}5$$

Similarly $$\frac{C\_2}{Y}=\frac{3}{10}$$

Finally notice that $C=C\_1+C\_2=1000$ and $Y=2000$, hence we must have that $\frac{C}{Y}=\frac{C\_1+C\_2}{Y}=0.5$ which is satisfied since
$$\frac{1}5+\frac{3}{10}=0.5$$

(Since we have that $2C=Y$ and $100\%$ of revenue comes from $C$ is straightforward to see that the $\%$ of revenue associated with each category are twice this numbers)


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