We now demonstrate that if a good rises in price, the quantity demanded of it is likely to fall. A geometric analysis of maximising utility subject to a budget constraint is used. Begin with a situation in which a consumer is currently in a utility maximising position, at the point indicated by “a” in Figure 3.10. Money income is m, prices are Py1 and Px1, and maximised utility is U1.
Now suppose that the price of good x falls from Px1 to Px2, but money income and the price of good y remain unchanged. This rotates the individual’s budget constraint anti-clockwise; its position changes from the line connecting the points (m/ Py1) and (m/ Px1) to the line (m/ Py1) to (m/ Px2). The set of feasible consumption choices is now enlarged, and the consumer attains a new utility maximum at the point “b” on the indifference curve U2.
What has happened to the quantity of good x that the consumer demands as the price of good x falls? It has increased, from x1 to x2 . The individual’s demand curve for x is, therefore, negatively sloped (at least in this region) as a lower price has resulted in a greater quantity demanded.