# Sellers and warranty

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?

• How does the warranty signal higher quality? I wish I could help but it’s difficult for me to understand your question. Commented Apr 5, 2023 at 23:00
• @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.
– user43302
Commented Apr 6, 2023 at 6:49

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 $$\frac{10000-8000}{500}=Y_{H}^{max} = 4$$ $$\frac{10000-5000}{1000}=Y_{L}^{max} = 5$$