<p>So you want to find $\partial p / \partial k$</p>

<p>By implicit differentiation what they mean is let $p=p(k)$ so p is a function of k. </p>

<p>Take your equilibrium condition $Q_s-Q_d=0$ and now differentiate with respect to k. </p>

CC BY-SA 3.0
2016-09-05T18:49:50.847Z
@BNA You were able to solve it?
VCG
CC BY-SA 3.0
2016-09-05T18:28:14.600Z
2016-09-05T18:28:14.600Z
VCG
<p>By the implicit function theorem, when we have an equilibrium <em>equation</em> $F$</p>

<p>$$F \equiv   Q^s - Q^d = 0   \implies F\equiv   kp^2-D(p)=0$$</p>

<p>the equilibrium change of, in this case, $p$ when $k$ changes is given by </p>

<p>$$\frac {dp}{dk} = -\frac {\partial F/\partial k}{\partial F/ \partial p}$$</p>

<p>Since $D(p)$ is not given explicitly, you won't get a fully parametric answer of course, but the sign of $D'(p)$ will help you determine the direction of movement.</p>

CC BY-SA 3.0
2016-09-06T17:55:22.933Z
2016-09-06T17:55:22.933Z
Alecos Papadopoulos
<p><a href="https://i.sstatic.net/7xS8A.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/7xS8A.png" alt="enter image description here"></a></p>

<p>To find the equilibrium price I understand you set $$ Q^s = Q^d $$ 
and then solve for p. But as P is not indpendently labeled in $$Q^d$$ I am slightly confused how you would go about writing this equation? Thanks! </p>

<supply-and-demand><general-equilibrium>
Question about Equilibrium Price
BNA
# Question about Equilibrium Price

(Asked by: username_0 on 2016-09-05)

[![enter image description here](https://i.sstatic.net/7xS8A.png)](https://i.sstatic.net/7xS8A.png)

To find the equilibrium price I understand you set $$ Q^s = Q^d $$
and then solve for p. But as P is not indpendently labeled in $$Q^d$$ I am slightly confused how you would go about writing this equation? Thanks!

**Tags:** supply-and-demand, general-equilibrium

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## 2 answers

### Answer by username_1 on 2016-09-05. Score: 1

So you want to find $\partial p / \partial k$

By implicit differentiation what they mean is let $p=p(k)$ so p is a function of k.

Take your equilibrium condition $Q\_s-Q\_d=0$ and now differentiate with respect to k.

> **Comments:**
> **username_1**: @BNA You were able to solve it?  

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### Answer by username_2 on 2016-09-06. Score: 0

By the implicit function theorem, when we have an equilibrium *equation* $F$

$$F \equiv Q^s - Q^d = 0 \implies F\equiv kp^2-D(p)=0$$

the equilibrium change of, in this case, $p$ when $k$ changes is given by

$$\frac {dp}{dk} = -\frac {\partial F/\partial k}{\partial F/ \partial p}$$

Since $D(p)$ is not given explicitly, you won't get a fully parametric answer of course, but the sign of $D'(p)$ will help you determine the direction of movement.


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