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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!

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    $\begingroup$ 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? $\endgroup$ – ahorn May 19 '18 at 18:46
  • $\begingroup$ @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. $\endgroup$ – Hairy May 20 '18 at 0:52
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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.

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  • $\begingroup$ @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. $\endgroup$ – Hairy May 20 '18 at 15:11
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    $\begingroup$ @Hairy, you gave thanks to a wrong person. I just edited answer. ahorn wrote it $\endgroup$ – Ravshan S.K. May 20 '18 at 15:41
  • $\begingroup$ @Hairy pleasure. You can reward me by accepting the answer (the tick underneath the voting buttons), because then I will get reputation points. $\endgroup$ – ahorn May 21 '18 at 5:27

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