Horizontal Versus Vertical Summation
When adding individual demand curves it is critical that the summation be horizontal rather than vertical. The derivation of the market demand function involves adding quantities. The conventional graphical representation is of the inverse demand function. Adding inverse demand equations involves adding prices. In order to add the demand functions algebraically one must first convert the inverse equation to the standard demand function where quantity demanded is a function of price. For example, assume that there are two consumers in a given market and their respective demand functions are P = 30 - 2Q and P = 30 - 6Q. To sum these functions to obtain the market demand curve we must first convert to standard form, that is Q = 15 - (P/2) and Q = 5 - (P/6). Then, adding Q1 and Q2 yields 15 - (P/2) + 5 - (P/6) = 20 - (4P/6)= 20 - 2P/3.
Read more about this topic: Demand (economics), From Individual To Market Demand Curve
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