<p>Take your two beginning expressions and cross multiply them:</p>

<p>$$p_1 c_1^F = p_2 c_2^F$$</p>

<p>$$p_1 c_1^H = p_2 c_2^H$$</p>

<p>Then subtract each right hand side for both equations. Multiply one of the expressions by $-1$ on each side:</p>

<p>$$p_1 c_1^F - p_2 c_2^F = 0$$</p>

<p>$$-p_1 c_1^H + p_2 c_2^H = 0$$</p>

<p>And set each expression equal to each other:</p>

<p>$$p_1 c_1^F - p_2 c_2^F = -p_1 c_1^H + p_2 c_2^H$$</p>

<p>Put the $p_1$ and $p_2$ terms together:</p>

<p>$$p_1 c_1^F + p_1 c_1^H = p_2 c_2^F + p_2 c_2^H$$</p>

<p>Factor the $p_1$ and $p_2$ terms and rearrange:</p>

<p>$$p_1 (c_1^F + c_1^H) = p_2 (c_2^F + c_2^H) \implies \frac{p_1}{p_2} = \frac{c_2^F + c_2^H}{c_1^F+ c_1^H}$$</p>

CC BY-SA 3.0
2016-03-06T04:53:34.573Z
2016-05-16T04:25:53.823Z
2016-05-16T04:25:53.823Z
Kitsune Cavalry
<p>Suppose I have two markets, Home and Foreign. Suppose that </p>

<p>$$\frac{p_1}{p_2} = \frac{c_2^F}{c_1^F}$$</p>

<p>$$\frac{p_1}{p_2} = \frac{c_2^H}{c_1^H}$$</p>

<p>Supposedly I am supposed to be able to show </p>

<p>$$\frac{p_1}{p_2} = \frac{c_2^F + c_2^H}{c_1^F+ c_1^H}$$ </p>

<p>But by rules of simple algebra, it would seem </p>

<p>$$\frac{p_1}{p_2} = \frac{c_2^Fc_1^H+c_1^Fc_2^H}{2c_1^Fc_1^H}$$</p>

<p><strong>MY QUESTION:</strong>
What step am I missing to get
$$\frac{p_1}{p_2} = \frac{c_2^F + c_2^H}{c_1^F+ c_1^H}$$ ?</p>

<macroeconomics><international-trade>
How does one derive relative demand?
Stan Shunpike
# How does one derive relative demand?

(Asked by: username_0 on 2016-03-05)

Suppose I have two markets, Home and Foreign. Suppose that

$$\frac{p\_1}{p\_2} = \frac{c\_2^F}{c\_1^F}$$

$$\frac{p\_1}{p\_2} = \frac{c\_2^H}{c\_1^H}$$

Supposedly I am supposed to be able to show

$$\frac{p\_1}{p\_2} = \frac{c\_2^F + c\_2^H}{c\_1^F+ c\_1^H}$$

But by rules of simple algebra, it would seem

$$\frac{p\_1}{p\_2} = \frac{c\_2^Fc\_1^H+c\_1^Fc\_2^H}{2c\_1^Fc\_1^H}$$

**MY QUESTION:**
What step am I missing to get
$$\frac{p\_1}{p\_2} = \frac{c\_2^F + c\_2^H}{c\_1^F+ c\_1^H}$$ ?

**Tags:** macroeconomics, international-trade

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## 1 answers

### Answer by username_1 on 2016-03-06. Score: 2 | Accepted answer

Take your two beginning expressions and cross multiply them:

$$p\_1 c\_1^F = p\_2 c\_2^F$$

$$p\_1 c\_1^H = p\_2 c\_2^H$$

Then subtract each right hand side for both equations. Multiply one of the expressions by $-1$ on each side:

$$p\_1 c\_1^F - p\_2 c\_2^F = 0$$

$$-p\_1 c\_1^H + p\_2 c\_2^H = 0$$

And set each expression equal to each other:

$$p\_1 c\_1^F - p\_2 c\_2^F = -p\_1 c\_1^H + p\_2 c\_2^H$$

Put the $p\_1$ and $p\_2$ terms together:

$$p\_1 c\_1^F + p\_1 c\_1^H = p\_2 c\_2^F + p\_2 c\_2^H$$

Factor the $p\_1$ and $p\_2$ terms and rearrange:

$$p\_1 (c\_1^F + c\_1^H) = p\_2 (c\_2^F + c\_2^H) \implies \frac{p\_1}{p\_2} = \frac{c\_2^F + c\_2^H}{c\_1^F+ c\_1^H}$$


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