# Summing Demand Curves

To obtain the market demand curve, individual demand curves are summed horizontally, as we want to add the quantities demanded by each individual to find the total quantity demanded. This summation is only possible if each consumer faces the same price; otherwise, the sum is meaningless.

## Individual Demand vs. Market Demand

The total quantity demanded for a good or service at any price is the sum of the demand from each individual in the market. Therefore, to find the total or market demand, individual demand curves must be summed horizontally. This sum is only possible if all buyers face the same price.

## Graph: Summing Demand Curves

In the following graph, we illustrate the summation of two demand curves. Note that at a price of 2, the quantity demanded by one consumer is 6, and the quantity demanded by a second consumer is 9. Therefore, the total quantity demanded at a price of 2 is 15.

## Mathematically Summing Demand Curves

In the following example, we use the demand functions graphed earlier and sum them to find the total demand.

$$ \text{First demand curve:} \quad Q_1 = D^1(p) $$

$$ \text{Second demand curve:} \quad Q_2 = D^2(p) $$

$$ \text{Total demand:} \quad Q = Q_1 + Q_2 = D^1(p) + D^2(p) $$

$$ \text{Example of the first curve:} \quad Q_1 = 10 - 2p $$

$$ \text{Example of the second curve:} \quad Q_2 = 15 - 3p $$

$$ \text{Sum of the two demand curves:} $$

$$ Q = Q_1 + Q_2 $$

$$ Q = (10 - 2p) + (15 - 3p) $$

$$ Q = 10 - 2p + 15 - 3p $$

$$ Q = (10 + 15) - (2p + 3p) $$

$$ Q = 25 - 5p $$

This mathematical procedure can be generalized for three or more demand functions.