Sam spends $6/wk on orange juice and apple juice. Orange juice costs $2/cup while apple juice costs $1/cup. Sam views 1 cup of orange juice as a perfect substitute for 3 cups of apple juice. Find Sam’s optimal consumption bundle of orange juice and apple juice each week. Suppose the price of apple juice rises to $2/cup, while the price of orange juice remains constant. How much additional income would Sam need to afford his original consumption bundle?
Bruce has the same income and faces the same prices as Sam in Problem 1, but he views 1 cup of orange juice as a perfect substitute for 1 cup of apple juice. Find Bruce’s optimal consumption bundle. How much additional income would Bruce need to be able to afford his original consumption bundle when the price of apple juice doubles?