Deriving a market demand curve

In my most recent post, I quickly defined what demand is in economics. However, my readers might ask; How does someone build such demand curves? My answer is that one shall add the quantities at each price point for all the consumers in the market. This process is known as horizontal summation.

Consider this problem: you are tasked with finding the demand for a market that only contains two  consumers; consumer A and consumer B. If their demand schedules can be respectively modeled by the following equations:

Then, find a formula by summing the Q's, we get:

The last step consists of re-arranging the equation in terms of P. This equation corresponds to the market demand when  .

Now let's graph that:

The market demand above P=3 (the dotted line) is just consumer A's demand curve since it is the only consumer buying products above the price of three in the market.