<p>I'm not sure about this, can I ask you if I'm wrong? Thanks.</p>
<p><strong>Data:</strong>
<span class="math-container">$$Q_{s}=P/2$$</span>
<span class="math-container">$$Q_{d}=P-42$$</span></p>
<p><strong>Questions:</strong></p>
<p><em>a) How many units will be traded at 35 dollars? At $14 dollars?</em></p>
<p><em>b) What quantity at what price will be in equilibrium?</em></p>
<p><em>c) What is the total revenue from sales?</em></p>
<p><strong>Answer a</strong></p>
<p><span class="math-container">$$Q_{s}=P/2 =&gt; P=2Q_{s}$$</span>
<span class="math-container">$$Q_{d}=P-42 =&gt; P=Q_{d}+42$$</span>
<span class="math-container">$$P/2=P-42$$</span>
<span class="math-container">$$P_{eq}=84$$</span></p>
<p>35 dollars is below 84 dollars, therefore, there is a shortage (we should plug the 35 dollars into the supply equation)</p>
<p>=&gt; 17 units will be sold at that price (am I correct to round down?)</p>
<p><span class="math-container">$$Q_{s}=35/2 = 17.5$$</span></p>
<p>14 dollars also is below 84 dollars, therefore, there is a shortage too (we should plug the 14 dollars into the supply equation)</p>
<p>=&gt; 7 units will be sold at that price</p>
<p><span class="math-container">$$Q_{s}=14/2 = 7$$</span></p>
<p><strong>Answer b</strong></p>
<p><span class="math-container">$$P_{eq}=84$$</span>
<span class="math-container">$$Q_{eq}=P_{eq} /2 = P_{eq}-42$$</span>
<span class="math-container">$$Q_{eq}= 42$$</span></p>
<p><strong>Answer c</strong></p>
<p>The total revenue would be, respectively:
<span class="math-container">$$84*42 = 3528$$</span>
<span class="math-container">$$35*17 = 595$$</span>
<span class="math-container">$$14*7 = 98$$</span></p>
<p>I know it's supposed to be simple but not sure if I'm rounding correctly (17.5 to 17) and if those dramatic drops in revenue are to be expected.</p>
<p>Thank you.</p>

CC BY-SA 4.0
2021-02-22T12:07:10.820Z
Check your demand function, it should be decreasing.
VARulle
CC BY-SA 4.0
2021-02-22T12:12:30.077Z
Thanks for your reply. Not sure I follow you. A demand function is always decreasing. Do you mean by that that I'm incorrect somewhere? I would like more assurance, not less so I would be grateful if you can be more specific.
1) I'm not sure if I should use 17 instead of 17.5. Is 17 correct?
2) I only used the supply function to plug my variables as there is a shortage not a surplus. Therefore I never used the demand function here. Am I wrong then?
Thanks.
Bachir Messaouri
CC BY-SA 4.0
2021-02-22T12:59:46.907Z
Your demand is $Q_d=P-42$, which is increasing in price. I guess it should be $42-P$. Then your calculations will change accordingly. And in general you shouldn't round to integers (if not instructed to do so) since units could well be divisible.
VARulle
CC BY-SA 4.0
2021-02-22T13:07:33.663Z
Ok, I got it ! super thanks.
Strange because the original data is part of the question. So this would mean there is an issue there.
Bachir Messaouri
<supply-and-demand><equilibrium>
Simple supply and demand problem
Bachir Messaouri
# Simple supply and demand problem

(Asked by: username_0 on 2021-02-21)

I'm not sure about this, can I ask you if I'm wrong? Thanks.

**Data:**
$$Q\_{s}=P/2$$
$$Q\_{d}=P-42$$

**Questions:**

*a) How many units will be traded at 35 dollars? At $14 dollars?*

*b) What quantity at what price will be in equilibrium?*

*c) What is the total revenue from sales?*

**Answer a**

$$Q\_{s}=P/2 => P=2Q\_{s}$$
$$Q\_{d}=P-42 => P=Q\_{d}+42$$
$$P/2=P-42$$
$$P\_{eq}=84$$

35 dollars is below 84 dollars, therefore, there is a shortage (we should plug the 35 dollars into the supply equation)

=> 17 units will be sold at that price (am I correct to round down?)

$$Q\_{s}=35/2 = 17.5$$

14 dollars also is below 84 dollars, therefore, there is a shortage too (we should plug the 14 dollars into the supply equation)

=> 7 units will be sold at that price

$$Q\_{s}=14/2 = 7$$

**Answer b**

$$P\_{eq}=84$$
$$Q\_{eq}=P\_{eq} /2 = P\_{eq}-42$$
$$Q\_{eq}= 42$$

**Answer c**

The total revenue would be, respectively:
$$84\*42 = 3528$$
$$35\*17 = 595$$
$$14\*7 = 98$$

I know it's supposed to be simple but not sure if I'm rounding correctly (17.5 to 17) and if those dramatic drops in revenue are to be expected.

Thank you.

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

> **Comments:**
> **username_1**: Check your demand function, it should be decreasing.  
> **username_0**: Thanks for your reply. Not sure I follow you. A demand function is always decreasing. Do you mean by that that I'm incorrect somewhere? I would like more assurance, not less so I would be grateful if you can be more specific. 1) I'm not sure if I should use 17 instead of 17.5. Is 17 correct? 2) I only used the supply function to plug my variables as there is a shortage not a surplus. Therefore I never used the demand function here. Am I wrong then? Thanks.  
> **username_1**: Your demand is $Q_d=P-42$, which is increasing in price. I guess it should be $42-P$. Then your calculations will change accordingly. And in general you shouldn't round to integers (if not instructed to do so) since units could well be divisible.  
> **username_0**: Ok, I got it ! super thanks. Strange because the original data is part of the question. So this would mean there is an issue there.  

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