<p>I don't have a question to "correctly interpret" , but I think the way you are calculating the demand function is correct. The demand curve in an oligopoly can be kinked (bowed out), as this one is. I think it is mathematically accurate to write the function split across the domains, as such:</p>

<p>$Q = \begin{cases} 
700 - P, &amp; 0  \leq P\leq 500 \\
2200 - 4P, &amp; 500&lt; P&lt; 550
\end{cases}$</p>

<p>where I have written quantity as a function of price, and assumed that the quantity is strictly positive. </p>

CC BY-SA 4.0
2018-05-20T15:11:22.587Z
@Ravshan S.K. This is what I was asking. This is what I got when I found the slope between the points and used point slope form. Thank you.
Hairy
CC BY-SA 4.0
2018-05-20T15:41:34.630Z
@Hairy, you gave thanks to a wrong person. I just edited answer. ahorn wrote it
Ravshan S.K.
CC BY-SA 4.0
2018-05-21T05:27:52.713Z
@Hairy pleasure. You can reward me by accepting the answer (the tick underneath the voting buttons), because then I will get reputation points.
ahorn
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2018-05-20T04:14:00.250Z
2018-05-20T04:18:56.337Z
2018-05-20T04:18:56.337Z
ahorn
<p>Here is the problem: </p>

<p>Suppose that an oligopolist charges a price of 500 and sells 200 units of output per day. If the oligopolist increases its price about 500, quantity demanded will decline by 4 units for every 1 increase in price. On the other hand, if the oligopolist lowers price below 500, quantity demanded will increase by only 1 unit for every 1 decrease in price. </p>

<p>Here is what I did: 
point 1: (200, 500)
point 2: (196, 501)</p>

<p>Then find slope using m=(y2-y1)/(x2-x1) and then use point-slope form for the line. I think I am interpreting the demand increase/decrease incorrectly, but am not sure?</p>

<p>Thanks!</p>

CC BY-SA 4.0
2018-05-19T18:46:39.173Z
What is the question? I do not understand what you are trying to do or what question you are trying to answer. Are you trying to find the function for the demand curve?
ahorn
CC BY-SA 4.0
2018-05-20T00:52:40.350Z
@ahorn Yes, I am trying to determine the demand functions. I believe the three points given are (201,499),(200,500),and(196,501). Then I found the slope between (201,499) and (200,500), and used point slope form to create one demand function. Then I found slope between (200,500) and (196,501), and used point slope form to create second demand function. I just don't know if I am correctly interpreting the question.
Hairy
<microeconomics><supply-and-demand><oligopoly>
Finding the demand function
Hairy
# Finding the demand function

(Asked by: username_0 on 2018-05-19)

Here is the problem:

Suppose that an oligopolist charges a price of 500 and sells 200 units of output per day. If the oligopolist increases its price about 500, quantity demanded will decline by 4 units for every 1 increase in price. On the other hand, if the oligopolist lowers price below 500, quantity demanded will increase by only 1 unit for every 1 decrease in price.

Here is what I did:
point 1: (200, 500)
point 2: (196, 501)

Then find slope using m=(y2-y1)/(x2-x1) and then use point-slope form for the line. I think I am interpreting the demand increase/decrease incorrectly, but am not sure?

Thanks!

**Tags:** microeconomics, supply-and-demand, oligopoly

> **Comments:**
> **username_1**: What is the question? I do not understand what you are trying to do or what question you are trying to answer. Are you trying to find the function for the demand curve?  
> **username_0**: @username_1 Yes, I am trying to determine the demand functions. I believe the three points given are (201,499),(200,500),and(196,501). Then I found the slope between (201,499) and (200,500), and used point slope form to create one demand function. Then I found slope between (200,500) and (196,501), and used point slope form to create second demand function. I just don't know if I am correctly interpreting the question.  

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## 1 answers

### Answer by username_1 on 2018-05-20. Score: 2

I don't have a question to "correctly interpret" , but I think the way you are calculating the demand function is correct. The demand curve in an oligopoly can be kinked (bowed out), as this one is. I think it is mathematically accurate to write the function split across the domains, as such:

$Q = \begin{cases}
700 - P, & 0 \leq P\leq 500 \\
2200 - 4P, & 500< P< 550
\end{cases}$

where I have written quantity as a function of price, and assumed that the quantity is strictly positive.

> **Comments:**
> **username_0**: @username_2 This is what I was asking. This is what I got when I found the slope between the points and used point slope form. Thank you.  
> **username_2**: @username_0, you gave thanks to a wrong person. I just edited answer. username_1 wrote it  
> **username_1**: @username_0 pleasure. You can reward me by accepting the answer (the tick underneath the voting buttons), because then I will get reputation points.  

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