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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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closed as off-topic by Giskard, Herr K., Brythan, JoaoBotelho, Kitsune Cavalry Sep 11 '18 at 14:39

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question does not meet the standards for homework questions as spelled out in the relevant meta posts. For more information, see our policy on homework question and the general FAQ." – Giskard, Herr K., Brythan, JoaoBotelho, Kitsune Cavalry

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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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