<p>Notice that if you plug in $P=15$ into <em>either</em> of the $Q(P)$, you get</p>

<p>$$Q(P) = 700-40P = 700 - 40 \cdot 15 = 100$$</p>

<p>$$Q(P) = 400-20P = 400 - 20 \cdot 15 = 100$$</p>

<p>So you can take the exercise further and see that when $P &lt; 15$, then $Q &gt; 100$ (notice the direction of the inequality is changing; the more expensive a good, the less consumers buy of it)</p>

CC BY-SA 3.0
2015-12-12T05:53:25.080Z
2015-12-12T05:53:25.080Z
Kitsune Cavalry
<p>If I have demand functions</p>

<p>For $P&lt;15$:</p>

<p>$$
Q(P) = 700-40P
$$</p>

<p>For $P&gt;15$:
$$
Q(P) = 400-20P
$$</p>

<p>If I invert them, I get the price functions</p>

<p>For $Q&lt;100$:
$$
P(Q)=20 - (1/20)Q
$$</p>

<p>For $Q&gt;100$:
$$
P(Q)=17,5 – (1/40)Q
$$</p>

<p>I know how I get the expressions, for instance, $Q = 700 - 40P \Leftrightarrow 40P = 700 - Q \Leftrightarrow P = \frac{700}{40} - \frac{1}{40} Q$, but I don't how the conditions $P &lt; 15$ can change to $Q &lt; 100$.</p>

<supply-and-demand><production-function><price-level>
Inverting price functions and their conditions/intervals
Jamgreen
# Inverting price functions and their conditions/intervals

(Asked by: username_0 on 2015-12-12)

If I have demand functions

For $P<15$:

$$
Q(P) = 700-40P
$$

For $P>15$:
$$
Q(P) = 400-20P
$$

If I invert them, I get the price functions

For $Q<100$:
$$
P(Q)=20 - (1/20)Q
$$

For $Q>100$:
$$
P(Q)=17,5 – (1/40)Q
$$

I know how I get the expressions, for instance, $Q = 700 - 40P \Leftrightarrow 40P = 700 - Q \Leftrightarrow P = \frac{700}{40} - \frac{1}{40} Q$, but I don't how the conditions $P < 15$ can change to $Q < 100$.

**Tags:** supply-and-demand, production-function, price-level

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## 1 answers

### Answer by username_1 on 2015-12-12. Score: 2 | Accepted answer

Notice that if you plug in $P=15$ into *either* of the $Q(P)$, you get

$$Q(P) = 700-40P = 700 - 40 \cdot 15 = 100$$

$$Q(P) = 400-20P = 400 - 20 \cdot 15 = 100$$

So you can take the exercise further and see that when $P < 15$, then $Q > 100$ (notice the direction of the inequality is changing; the more expensive a good, the less consumers buy of it)


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