Questions / Quant trading, Markets & quotes
Optimize a one-period offer
Choose an offer a between 100 and 102. One buyer’s reservation value is uniform on [100,102]; a sale yields a−100 and otherwise zero. Ignore inventory and costs. What offer maximizes expected profit?
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Answer: 101 price
- Expected profit is (a−100)(102−a)/2. This concave quadratic is maximized halfway between its roots, at a=101.
Interview shortcut. Monopoly price: midway between cost (100) and the top value (102).
In the app this has a follow-up where one thing about the setup changes. Try the follow-up.