1. **Problem statement:** We have three types of watches sold at price $p$: new originals (100 units, reservation price 775), used (200 units, reservation price 400), and fakes (300 units, reservation price 40). Buyers cannot distinguish types but know quantities and valuations: new originals worth 1700, fakes worth 30, and used watches valued between 30 and 1700. 2. **Goal:** Determine which statement (a-e) about market outcomes is correct given buyer valuations and seller reservation prices. 3. **Key concepts:** - Sellers sell only if $p \geq$ their reservation price. - Buyers buy if $p \leq$ their willingness to pay. - Market equilibrium price $p^*$ balances supply and demand. 4. **Analyze statement (a):** "If buyer valuation for used watches is between 955 and 1075, only used watches are sold." - Sellers of used watches require $p \geq 400$. - Sellers of new originals require $p \geq 775$. - Buyers value used watches between 955 and 1075, so $p$ must be $\leq$ that. - If $p$ is between 955 and 1075, sellers of new originals will sell (since $p \geq 775$), so new originals would also be sold. - Therefore, only used watches sold is false. 5. **Analyze statement (b):** "If buyers pay at least 1425 for used watches, all watches are sold in equilibrium." - Sellers of fakes require $p \geq 40$, buyers value fakes at 30. - Since buyer valuation for fakes is 30, less than 40, fakes won't sell regardless of $p$. - So not all watches are sold. 6. **Analyze statement (c):** "Equilibrium price depends only on sellers' reservation prices." - Equilibrium price depends on both supply (reservation prices) and demand (buyers' willingness to pay). - So this is false. 7. **Analyze statement (d):** "None of the other statements is correct." - We have found (a), (b), and (c) false. 8. **Analyze statement (e):** "Since sellers' reservation price for fakes (40) is higher than buyers' willingness to pay (30), fakes are never sold." - This is true because $40 > 30$. **Final answer:** Statement (e) is correct.