Suppose you have $200 in discretionary income that you would like to spend on ABBA CDs and Arnold Schwarzenegger DVDs.
A. On the way to work, you take your $200 to the Wal-Mart and buy 10 CDs and 5 DVDs at CD prices of $10 and DVD prices of $20.
(a) On a graph with DVDs on the horizontal and CDs on the vertical, illustrate your budget constraint and your optimal bundle A.
(b) On the way home, you drive by the same Wal-Mart and see a big sign: “All DVDs half-price — only $10!” You also know that Wal-Mart has a policy of either refunding returned items for the price at which they were bought if you provide them with a Wal-Mart receipt — or, alternatively, giving store credit in the amount that those items are currently priced in the store if you have “lost” your receipt. What is the most in store credit that you could get?
(c) Given that you have no more cash and only a bag full of DVDs and CDs, will you go back into Wal-Mart and shop?
(d) On the way to work the next day, you again drive by Wal-Mart — and you notice that the sale sign is gone. You assume that the price of DVDs is back to $20 (with the price of CDs still unchanged), and you notice you forgot to take your bag of CDs and DVDs out of the car last night and have it sitting right there next to you. Will you go back into the Wal-Mart store (assuming you still have an empty wallet)?
(e) Finally, you pass Wal-Mart again on the way home—and this time sees a sign: “Big Sale—All CDs only $5, All DVDs only $10!” With your bag of merchandise still sitting next to you and your wallet still empty, will you go back into Wal-Mart?
(f) If you are the manager of a Wal-Mart with this “store credit” policy, would you tend to favor —all else being equal—across the board price changes or sales on selective items?
(g) True or False: If it were not for substitution effects, stores would not have to worry about people gaming their “store credit” policies as you did in this example.
B. Suppose your tastes for DVDs (x1) and CDs (x2) can be characterized by the utility function u(x1,x2) = x10.5 x20.5 . Throughout, assume that it is possible to buy fractions of CDs and DVDs.
(a) Calculate the bundle you initially buy on your first trip to Wal-Mart.
(b) Calculate the bundle you buy on your way home from work on the first day (when p1 falls to 10).
(c) If you had to pay the store some fixed fee for letting you get store credit, what’s the most you would be willing to pay on that trip?
(d) What bundle will you eventually end up with if you follow all the steps in part A?
(e) Suppose that your tastes were instead characterized by the function u(x1,x2) = (0.5x1−ρ
+0.5x2−ρ)−1/ρ. Can you show that your ability to game the store credit policy diminishes as the elasticity of substitution goes to zero (i.e. as ρ goes to ∞)?