Summing Supply Curves
To obtain the market supply curve, individual supply curves are added horizontally. This procedure sums the quantities offered by each supplier at any given price to find the total supply.
Individual Supply vs. Market Supply
The total quantity supplied of a good or service at any given price is the sum of the supply from each supplier in the market. Therefore, to obtain the total or market supply, individual supply curves are summed horizontally. This sum is only possible if all suppliers face the same market price; otherwise, it does not make sense.
Graph of Summing Supply Curves
The graph shows the sum of two supply curves. Note that at a price of 6, the first supplier offers 4 units and the second supplier offers 6 units. Therefore, on the total supply curve at a price of 6, the quantity supplied is 12.
Mathematically Summing Supply Curves
In this example, the sum of the two supply functions graphed earlier is done mathematically. Note that although the inverse supply function is graphed, the horizontal summation of supply functions is done using the direct functions, i.e., quantities expressed as a function of prices.
$$ \text{First supply curve:} \quad Q_1 = S^1(p) $$
$$ \text{Second supply curve:} \quad Q_2 = S^2(p) $$
$$ \text{Total supply:} \quad Q = Q_1 + Q_2 = S^1(p) + S^2(p) $$
$$ \text{Example of the first supply curve:} \quad Q_1 = P - 2 $$
$$ \text{Example of the second supply curve:} \quad Q_2 = 2P - 4 $$
$$ \text{Sum of the two supply curves:} $$
$$ Q = Q_1 + Q_2 $$
$$ Q = (P - 2) + (2P - 4) $$
$$ Q = P - 2 + 2P - 4 $$
$$ Q = (P + 2P) - (2 + 4) $$
$$ Q = 3P - 6 $$