3.8: Individual and market functions

Last updated
Save as PDF

Page ID: 108372

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

Markets are made up of many individual participants on the demand and supply side. The supply and demand functions that we have worked with in this chapter are those for the total of all participants on each side of the market. But how do we arrive at such market functions when the economy is composed of individuals? We can illustrate how, with the help of Figure 3.9.

Figure 3.9 Summing individual demands

At P₁ individual A purchases

and B purchases

. The total demand is the sum of these individual demands at this price (Q₁). At P₂ individual demands are summed to Q₂. Since the points Q₁ and Q₂ define the demands of the market participants it follows that market demand is the horizontal sum of these curves.

To concentrate on the essentials, imagine that there are just two buyers of chocolate cookies in the economy. A has a stronger preference for cookies than B, so his demand is greater. To simplify, let the two demands have the same intercept on the vertical axis. The curves D_A and D_B indicate how many cookies A and B, respectively, will buy at each price. The market demand indicates how much they buy together at any price. Accordingly, at P₁, A and B purchase the quantities and respectively. Thus . At a price P₂, they purchase and . Thus . The market demand is therefore the horizontal sum of the individual demands at these prices. In the figure this is defined by .

Market demand: the horizontal sum of individual demands.