Changes in the price of a good lead the budget constraint to shift. A shift in the budget constraint means that when individuals are seeking their highest utility, the quantity that is demanded of that good will change. In this way, the logical foundations of demand curves - which show a connection between prices and quantity demanded - are based on the underlying idea of individuals seeking utility. Figure 6.5 (a) shows a budget constraint with a choice between housing and "everything else". (Putting "everything else" on the vertical axis can be a useful approach in some cases, especially when the focus of the analysis is on one particular good). The preferred choice on the original budget constraint that provides the highest possible utility is labeled M0. The other three budget constraints represent successively higher prices for housing of P1, P2, and P3. As the budget constraint rotates in, and in, and in again, the utility-maximizing choices are labeled M1, M2, and M3, and the quantity demanded of housing falls from Q0 to Q1 to Q2 to Q3.
Figure 6.5 The Foundations of a Demand Curve: An Example of Housing (a) As the price increases from P0 to P1 to P2 to P3, the budget constraint on the upper part of the diagram shifts to the left. The utility-maximizing choice changes from M0 to M1 to M2 to M3. As a result, the quantity demanded of housing shifts from Q0 to Q1 to Q2 to Q3, ceteris paribus. (b) The demand curve graphs each combination of the price of housing and the quantity of housing demanded, ceteris paribus. Indeed, the quantities of housing are the same at the points on both (a) and (b). Thus, the original price of housing (P0) and the original quantity of housing (Q0) appear on the demand curve as point E0. The higher price of housing (P1) and the corresponding lower quantity demanded of housing (Q1) appear on the demand curve as point E1.
So, as the price of housing rises, the budget constraint shifts to the left, and the quantity consumed of housing falls, ceteris paribus (meaning, with all other things being the same). This relationship - the price of housing rising from P0 to P1 to P2 to P3, while the quantity of housing demanded falls from Q0 to Q1 to Q2 to Q3 - is graphed on the demand curve in Figure 6.5 (b). Indeed, the vertical dashed lines stretching between the top and bottom of Figure 6.5 show that the quantity of housing demanded at each point is the same in both (a) and (b). The shape of a demand curve is ultimately determined by the underlying choices about maximizing utility subject to a budget constraint. And while economists may not be able to measure "utils," they can certainly measure price and quantity demanded.