Intermediate Microeconomics and Its Application 12th Edition by Walter Nicholson,Christopher Snyder

Exercise 41

The residents of Uurp consume only pork chops (X) and Coca-Cola (Y). The utility function for the typical resident of Uurp is given by
In 2012, the price of pork chops in Uurp was $1 each; Cokes were also $1 each. The typical resident consumed 40 pork chops and 40 Cokes (saving is impossible in Uurp). In 2013, swine fever hit Uurp and pork chop prices rose to $4; the Coke price remained unchanged. At these new prices, the typical Uurp resident consumed 20 pork chops and 80 Cokes.
a. Show that utility for the typical Uurp resident was unchanged between the two years.
b. Show that using 2012 prices would show an increase in real income between the two years.
c. Show that using 2013 prices would show a decrease in real income between the years.
d. What do you conclude about the ability of these indexes to measure changes in real income?