Question

Tony likes to shop for soda at Wal-Mart. On his weekly shopping trip, he considers buying cans of either Wal-Mart brand soda (W) or Coke (C). His utility function can be expressed as U = 1.5C + W. In words, it takes one and a half cans of Wal-Mart brand soda to give Tony the same satisfaction he receives from one can of coke.

Tony's weekly income is $9. If the price of Coke of $0.50 and the price of Wal-Mart brand soda is $0.30, what is Tony's optimal consumption bundle?

Answer 1

Tony's utility function is U = 1.5C + W. This gives |MRS| = MUC/MUW = 1.5. Tony's weekly income is $9 and the price of Coke is PC = $0.50 and the price of Wal-Mart brand soda is PW = $0.30. Because tehe two goods are consumed as substitutes, Tony cares only about maximum utility. In these cases we compare |MRS| with price ratio. Here PC/PW = 0.50/0.30 = 5/3 = 1.67 while |MRS| = 1.5. Since |MRS| < PC/PW, Tony gets a higher utility from Wal-Mart brand soda. Hence he spends all his income inbuying only Wal-Mart brand soda. His chosen bundle is C = 0 and W = 9/0.3 = 30.