<p>The key to problems like this is that it cannot be simplified to one representative buyer and one representative seller.</p>

<p>You have shown that a buyer will not buy for more than <span class="math-container">$\$48$</span> 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?</p>

CC BY-SA 4.0
2019-04-23T17:31:17.940Z
I fail to see what the first sentence has to do with anything.
Giskard
CC BY-SA 4.0
2019-04-22T11:26:16.247Z
2019-04-22T11:26:16.247Z
Xabu
<p>Ask yourself a few questions: </p>

<p>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!</p>

CC BY-SA 4.0
2019-02-19T21:34:09.063Z
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.
armara
CC BY-SA 4.0
2019-02-20T10:21:10.583Z
I would then suggest the the equilibrium lies in between the two values that you have calculated!
user22485
CC BY-SA 4.0
2019-02-20T12:15:00.237Z
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.
armara
CC BY-SA 4.0
2019-02-21T09:48:07.027Z
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.
user22485
CC BY-SA 4.0
2019-02-19T11:50:17.630Z
2019-02-19T11:50:17.630Z
user22485
<p>On a perfectly competitive market, a buyer wants to buy a used good. He is willing to pay <span class="math-container">$30$</span> for a badly used good, and <span class="math-container">$60$</span> for a nicely used good.</p>

<p>The seller is willing to sell a badly used good for a minimum of <span class="math-container">$30$</span>, and a nicely used good for a minimum of <span class="math-container">$50$</span>.</p>

<p>The buyer can't distinguish which goods are badly/nicely used, but he knows that <span class="math-container">$40\%$</span> of the goods are badly used, and <span class="math-container">$60\%$</span> are nicely used. <strong>What is the market equilibrium for a used good, and is it an efficient outcome?</strong> </p>

<p>When talking about equilibrium, I try to use <span class="math-container">$supply = demand$</span>. But this doesn't apply to this question If I were to calculate the expected value, I would get;</p>

<p><span class="math-container">$$EV[buyer]=0.4*30+0.6*60=48 $$</span>
<span class="math-container">$$EV[seller]=0.4*30+0.6*50=42 $$</span></p>

<p>But <span class="math-container">$EV[buyer]$</span> can't be put equal to <span class="math-container">$EV[seller]$</span>, so I don't know how to go about it.</p>

<microeconomics><competitive-equilibrium>
What's the market equilibrium price for the used good?
armara
# What's the market equilibrium price for the used good?

(Asked by: username_0 on 2019-02-18)

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.

**Tags:** microeconomics, competitive-equilibrium

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## 2 answers

### Answer by username_1 on 2019-04-22. Score: 0

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?

> **Comments:**
> **username_2**: I fail to see what the first sentence has to do with anything.  

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### Answer by username_3 on 2019-02-19. Score: 0

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!

> **Comments:**
> **username_0**: 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.  
> **username_3**: I would then suggest the the equilibrium lies in between the two values that you have calculated!  
> **username_0**: 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.  
> **username_3**: 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.  

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