<blockquote>
<p>I assumed that I would have to calculate the equilibrium price here by equating supply and demand <span class="math-container">$S(p)=D(p)$</span>.</p>
<p>Is this the correct approach?</p>
</blockquote>
<p>Yes.</p>

CC BY-SA 4.0
2022-02-26T22:06:49.670Z
2022-02-26T22:06:49.670Z
Giskard
<p><strong>Problem</strong>: Consider  a partial equilibrium of a good x and the composite good m. Consumers have a quasi-linear utility function of <span class="math-container">$u(x)+m$</span> with <span class="math-container">$u(x)=-5(x-6)^2$</span>. Furthermore a single producer produces the good x with a cost function <span class="math-container">$c(x)=5x^2$</span></p>
<hr />
<p>From that I computed first the consumer's demand, resulting in the following <span class="math-container">$D(p)=6-\frac{p}{10}$</span> (by differentiating <span class="math-container">$u(x)$</span> like that <span class="math-container">$\frac{d u(x)}{dx}$</span>)</p>
<p>Next I computed the supply in a similar manner by differentiating <span class="math-container">$p*x - c(x)$</span> resulting in <span class="math-container">$S(p)=\frac{p}{10}$</span></p>
<hr />
<p><strong>Unsolved Problem</strong>: And now I have to compute the market outcome (price, quantity) as (<span class="math-container">$p^{*}, x^{*}$</span>) when the monopolist does not exercise its market power but behaves as a price taker.</p>
<hr />
<p>And at this point I am not sure how to proceed, as I do not entirely understand what I have to do. Maybe the monopolist price taker is irritating me.</p>
<p><strong>Approach</strong>: I assumed that I would have to calculate the equilibrium price here by equating supply and demand <span class="math-container">$S(p)=D(p)$</span>.</p>
<p>Is this the correct approach?</p>

<microeconomics>
Computing the market outcome of a monopolist that behaves as a price taker
niszlo
# Computing the market outcome of a monopolist that behaves as a price taker

(Asked by: username_0 on 2022-02-26)

**Problem**: Consider a partial equilibrium of a good x and the composite good m. Consumers have a quasi-linear utility function of $u(x)+m$ with $u(x)=-5(x-6)^2$. Furthermore a single producer produces the good x with a cost function $c(x)=5x^2$

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From that I computed first the consumer's demand, resulting in the following $D(p)=6-\frac{p}{10}$ (by differentiating $u(x)$ like that $\frac{d u(x)}{dx}$)

Next I computed the supply in a similar manner by differentiating $p\*x - c(x)$ resulting in $S(p)=\frac{p}{10}$

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**Unsolved Problem**: And now I have to compute the market outcome (price, quantity) as ($p^{\*}, x^{\*}$) when the monopolist does not exercise its market power but behaves as a price taker.

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And at this point I am not sure how to proceed, as I do not entirely understand what I have to do. Maybe the monopolist price taker is irritating me.

**Approach**: I assumed that I would have to calculate the equilibrium price here by equating supply and demand $S(p)=D(p)$.

Is this the correct approach?

**Tags:** microeconomics


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## 1 answers

### Answer by username_1 on 2022-02-26. Score: 2

> I assumed that I would have to calculate the equilibrium price here by equating supply and demand $S(p)=D(p)$.
>
> Is this the correct approach?

Yes.


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