The demand curves we studied in this chapter were constructed holding a person’s nominal income constant—hence, changes in prices introduced changes in real income (that is, utility). Another way to draw a demand curve is to hold utility constant as prices change. That is, the person is ‘‘compensated’’ for any effects that the prices have on his or her utility. Such compensated demand curves illustrate only substitution effects, not income effects. Using this idea, show that:

a. For any initial utility-maximizing position, the regular demand curve and the compensated demand curve pass through the same price/quantity point.

b. The compensated demand curve is generally steeper than the regular demand curve.

c. Any regular demand curve intersects many different compensated demand curves.

d. If Irving consumes only pizza and chianti in fixed proportions of one slice of pizza to one glass of chianti, his regular demand curve for pizza will be downward sloping but his compensated demand curve(s) will be vertical.