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In my text book, many theories are explained using ad unitary demand curve: a consumer can buy 1 quantity of the product, or none. The example of the demand function is $ p(q) = 1- q $

but that means if I want to sell one quantity the price should be 0? I did simply p(q=1) = 1- 1 = 0

What does it mean?

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    $\begingroup$ I think you are mixing up concepts. But to try to address your main question: If your demand function is $p = 1-q$ then that does not mean $q=1$ means one unit, it could mean one billion or 550. $\endgroup$ – snoram Jul 2 '16 at 22:57
  • $\begingroup$ How q =1 could mean 550 quantities ? $\endgroup$ – sparkle Jul 2 '16 at 23:13
  • $\begingroup$ Yes. In that case one unit is $q = \frac{1}{550} = 0.0018$. What is important is the relationship between price and quantity. $\endgroup$ – snoram Jul 2 '16 at 23:25
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This demand function is just normalized to unit. If you are not interested in the concrete quantity of your demand function, but you are interested how the demand of the specific market is distributed between firms, you can use this simple demand function.

For example, you can consider a normalized demand function in a Bertrand's game. Let's assume the firms are symmetric, there's no capacity constraints. The demand ($D(p_i,p_{-i})$) of firm $i$ is the following:

$$ D(p_i,p_{-i}) = \begin{cases} 0 & \quad \text{if } p_i > p_{-i} \\ 1/2 & \quad \text{if } p_i = p_{-i} \\ 1 & \quad \text{if } p_i < p_{-i} \\ \end{cases} $$

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  • $\begingroup$ Admins, how can I write $D(p_i, p_{-i})$ beside the array? $\endgroup$ – Übel Yildmar Jul 3 '16 at 19:26
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    $\begingroup$ Just edited and implemented that exact change. $\endgroup$ – snoram Jul 4 '16 at 2:59

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