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Suppose there are two sellers $\{H, L\}$ such that $H$ sells high quality products at $\\\$ 8000$ and $L$ sells low quality products at $\\\$ 5000$. The customers value the products at prices $\\\$10000$ and $\\\$7000$ respectively but they don't know who is selling which product (or at least, they don't trust what the sellers say). Each customer has $50\%$ chance of buying a high quality product and $50 \%$ chance of buying a low quality one. If warranty costs $500Y$ for the high-quality product seller and $1000Y$ for the low-quality product seller where $Y =$ number of years of warranty, what's the optimal warranty (in years) that $H$ will set to signal that his quality of product?

If the customers get the right signal, they'll pay $\\\$10000$ for the high quality product. $H$ can provide a max of $\frac{10000 - 8000}{500} = 4$ years warranty while $L$ can provide a max of $2$ years' warranty. I think $H$ will give $2 + \epsilon $ (where $\epsilon \in (0, 2]$ years warranty. Is that correct? Or do I have to consider the expected price the customers will pay somewhere for this?

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  • $\begingroup$ How does the warranty signal higher quality? I wish I could help but it’s difficult for me to understand your question. $\endgroup$ Commented Apr 5, 2023 at 23:00
  • $\begingroup$ @NicolasTorres I think OP means that a longer warranty would make his customers believe that the product is of high quality (as a low quality product won't last long and so it's not in the seller's best interest to offer a long-time warranty). This is my interpretation which may not be fully correct. $\endgroup$
    – user43302
    Commented Apr 6, 2023 at 6:49

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IF the cost of production for $H$ is $\\\$8000$ and the cost of production for $L$ is $\\\$5000$ (as you seem to be assuming), then $$ \frac{10000-8000}{500}=Y_{H}^{max} = 4 $$ $$ \frac{10000-5000}{1000}=Y_{L}^{max} = 5 $$

However, I think there must be more to this question than you have included. For instance, what is the valuation of warranty length by the customers? Are those numbers really the cost of production?

(Not sure if this response follows protocol, but I cannot post comments yet).

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