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On a perfectly competitive market, a buyer wants to buy a used good. He is willing to pay $30$ for a badly used good, and $60$ for a nicely used good.

The seller is willing to sell a badly used good for a minimum of $30$, and a nicely used good for a minimum of $50$.

The buyer can't distinguish which goods are badly/nicely used, but he knows that $40\%$ of the goods are badly used, and $60\%$ are nicely used. What is the market equilibrium for a used good, and is it an efficient outcome?

When talking about equilibrium, I try to use $supply = demand$. But this doesn't apply to this question If I were to calculate the expected value, I would get;

$$EV[buyer]=0.4*30+0.6*60=48 $$ $$EV[seller]=0.4*30+0.6*50=42 $$

But $EV[buyer]$ can't be put equal to $EV[seller]$, so I don't know how to go about it.

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Ask yourself a few questions:

1). If the buyer doesn't know, does the seller. If so why would they have the same probabilities? 2). Is the scenario realistic in a perfectly competitive market (absolutely no!) 3). In another type of market surely the seller decides what they want to receive and it is up to the buyer whether they buy it or not. It's surely not the case where a buyer can demand to pay a certain price!

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  • $\begingroup$ Hi and thanks for the help. I forgot to mention it, but yes the seller absolutely knows what he is selling. The percentage is solely for the buyer, he has heard that 40% are badly used and 60% are nicely used. $\endgroup$ – armara Feb 19 '19 at 21:34
  • $\begingroup$ I would then suggest the the equilibrium lies in between the two values that you have calculated! $\endgroup$ – user22485 Feb 20 '19 at 10:21
  • $\begingroup$ Ok, so maybe I should just pick $\frac{48+42}{2}=45$ as the equilibrium, but what about the question "Is this an efficient outcome?" How do I answer that question, I don't even know their utility functions so I can't know how "happy" they are with the deals they made. Maybe it's not an efficient outcome, because the buyer paid 45 but could only get a badly used good? Since the nicely used good cost 50. $\endgroup$ – armara Feb 20 '19 at 12:15
  • $\begingroup$ I think the tricky thing in this question is that it is not a perfectly competitive market. I would also be unsure of using 45 as the price without more details. $\endgroup$ – user22485 Feb 21 '19 at 9:48
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The key to problems like this is that it cannot be simplified to one representative buyer and one representative seller.

You have shown that a buyer will not buy for more than $\$48$ assuming that all sellers are in the market. How will good sellers react to this price? How will bad sellers react to this price? Who is left in the market after deciding whether they are willing to sell? How does the buyer update their expectations given this knowledge and what is their new expected value?

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  • $\begingroup$ I fail to see what the first sentence has to do with anything. $\endgroup$ – Giskard Apr 23 '19 at 17:31

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