Filene’s Basement, a Boston-based department store, has a policy of marking down the price of sale items each week that they go unsold. You covet an expensive brand of winter coat that is on sale for $100. In fact, you would be willing to pay as much as $120 for it. Thus, you can buy it now (for a profit of $120 - $100 = $20) or wait until next week, when the price will be reduced to $75 if the coat is still available. The chances of its being available next week are 2/3. If it is available in week 2, you can buy or wait until week 3. There is a 1/2 chance it will be sold between weeks two and three and a 1/2 chance it will be available at a reduced price of $60. Finally, if it is available in week 3, you can buy or wait until week 4. There is a 1/4 chance it still will be available, at a price of $50 (and a 3/4 chance it will be sold in the meantime). Week 4 is your last chance to buy before the coat is withdrawn.
a. How long should you wait before buying? Illustrate via a decision tree.
b. Filene’s has 120 of these winter coats for sale. What is its expected total revenue from the pricing scheme in part (a)? (One-third of the coats sell in the first week, one-half of the remaining coats in the second week, and so on. All coats in week 4 are sold for $50.)
c. Alternatively, Filene’s can set a single price for all coats. Its demand curve is P = 180 - Q. Would it prefer a common-price method or the price-reduction method in part (b)? Explain.