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.