# With the graph of the demand curve shown in figure m1

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With the graph of the demand curve shown in Figure M.1- 4(b), however, the story is a bit different. Normally, economists say that the quantity demanded of a good is a function of its price : Q D = f ( P ). In this way of expressing the relationship, price should be the independent variable, and appear on the horizontal axis. Indeed, some economists (notably Léon Walras and Frank Knight) did draw the graphs of demand functions in this way. Who is to blame for the “backward” way that economists draw demand curves? The culprit is Alfred Marshall, one of the great economists, who pioneered the use of demand and supply curves in economics in Books 3 and 5 of his classic text, Principles of Economics. Why would Marshall, a solid mathematician, put quantity on the horizontal axis? There are a number of reasons, but we will mention only one: in his ini- tial discussion of demand functions, Marshall dealt with the short-short run (or “tem- porary”) equilibrium in a single market on a single market-day. Although he allowed for some variation in the quantity supplied at different prices and also for some trading at disequilibrium prices, if the supply brought to market that day were perfectly inelas- tic (a vertical line), so that the same quantity would be supplied regardless of the price, then the quantity brought to market would determine the equilibrium market price. Regardless of the reasons, however, it has become conventional to draw market demand and supply curves with quantity on the horizontal axis and price on the verti- cal axis, even when implicitly or explicitly we are assuming that the quantity demanded of a good is a function of its price : Q D = f ( P ). In Figure M.1- 4(c) we have depicted the budget constraint for an individual who has a budget of M dollars and spends it all on only two goods, X and Y , which have ±xed prices P X and P Y , respectively. The equation for the budget line can be written in a number of ways, including M = P X X + P Y Y, or equivalently, Y = M/P Y –P X /P Y X, (M.1.7) where M/P Y is the vertical intercept and X /P Y is the slope. The term P X X represents the total amount spent on X , and similarly P Y Y represents the total amount spent on Y . In this case, if we know the total budget M and how much has been spent on X , we can then calculate how much has been spent on Y , and therefore (if we also know P Y ) how many units of Y have been purchased. But we can also reverse the procedure: if we know how much has been spent on Y , we can then calculate how much has been spent on X , and therefore (if we know P X ) how many units of X have been purchased. Hence in Figure M.1- 4(c), the “causal” arrows can run in both directions. The message of this section is not that “anything goes” in the placement of variables on axes. In fact, economists have adopted certain conventions (and assume them) in the graphical depiction of some of the basic economic relations. The message is rather that it is important to learn these conventions, and what is being assumed about “causality” in the standard diagrams.

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