# What's the market equilibrium price for the used good?

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.

• 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. Feb 20 '19 at 12:15
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?