Unitary demand curve: p = 1 - q

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?

• 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. – snoram Jul 2 '16 at 22:57
• How q =1 could mean 550 quantities ? – sparkle Jul 2 '16 at 23:13
• Yes. In that case one unit is $q = \frac{1}{550} = 0.0018$. What is important is the relationship between price and quantity. – snoram Jul 2 '16 at 23:25

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:
$$D(p_i,p_{-i}) = \begin{cases} 0 & \quad \text{if } p_i > p_{-i} \\ 1/2 & \quad \text{if } p_i = p_{-i} \\ 1 & \quad \text{if } p_i < p_{-i} \\ \end{cases}$$
• Admins, how can I write $D(p_i, p_{-i})$ beside the array? – Übel Yildmar Jul 3 '16 at 19:26