Introduction
We have explored the basic concept of demand and supply at the individual household and the individual supplier level. However, markets consist of collections of demanders and suppliers, so we need to understand the process of combining these individual agents’ behavior to arrive at market demand and supply functions.
The process could not be more straightforward: simply add all the buyers together and add all the sellers together. Suppose there are 1,000 identical gasoline buyers in our hypothetical example, and they represent the total market. At, say, a price of $3 per gallon, we find that one household would be willing to purchase 10 gallons per week (when income and price of automobiles are held constant at $50,000 and $20,000, respectively). So, 1,000 identical buyers would be willing to purchase 10,000 gallons collectively. It follows that to aggregate 1,000 buyers’ demand functions, simply multiply each buyer’s quantity demanded by 1,000, as shown in Equation 1-13:
where Qd x represents the market quantity demanded. Note that if we hold I and Py at their same respective values of 50 and 20 as before, we can collapse the constant terms and write the following Equation 1-14:
Equation 1-14 is just Equation 1-3 (an individual household’s demand function) multiplied by 1,000 households (Qd x represents thousands of gallons per week). Again, we can solve for Px to obtain the market inverse demand function:
The market demand curve is simply the graph of the market inverse demand function, as shown in Exhibit 1-5. It is important to note that the aggregation process sums all individual buyers’ quantities, not the prices they are willing to pay; that is, we multiplied the demand function, not the inverse demand function, by the number of households. Accordingly, the market demand curve has the exact same price intercept as each individual household’s demand curve. If, at a price of $28, a single household would choose to buy zero, then it follows that 1,000 identical households would choose, in aggregate, to buy zero as well. However, if each household chooses to buy 10 at a price of $3, then 1,000 identical households would choose to buy 10,000, as shown in Exhibit 1-5. Hence, we say that all individual demand curves horizontally (quantities), not vertically (prices), are added to arrive at the market demand curve.
Now that we understand the aggregation of demanders, the aggregation of suppliers is simple: We do exactly the same thing. Suppose, for example, that there are 20 identical sellers with the supply function given by Equation 1-8. To arrive at the market supply function, we simply multiply by 20 to obtain Equation 1-16:
Aggregate Weekly Market Demand for Gasoline as the Quantity Summation of All Households’ Demand Curves
Aggregate Market Supply as the Quantity Summation of Individual Sellers’ Supply Curves
And, if we once again assume W equals $15, we can collapse the constant terms, yielding Equation 1-17:
which can be inverted to yield the market inverse supply function (Equation 1-18):
Graphing the market inverse supply function yields the market supply curve in Exhibit 1-6.
We saw from the individual seller’s supply curve in Exhibit 1-3 that at a price of $3, an individual seller would willingly offer 500 gallons of gasoline. It follows, as shown in Exhibit 1-6, that a group of 20 sellers would offer 10,000 gallons per week. Accordingly, at each price, the market quantity supplied is just 20 times as great as the quantity supplied by each seller. We see, as in the case of demand curves, that the market supply curve is simply the horizontal summation of all individual sellers’ supply curves.
Related Links:
DEMAND AND SUPPLY ANALYSIS: INTRODUCTION
Demand Function and the Demand Curve
The Supply Function and the Supply Curve
0 Comments