<blockquote>
<p>If there are 24 apartments to rent, why isn't it the case that the equilibrium price is also in a range, like the 25 and 26 cases (Varian's answer is just 500)?</p>
</blockquote>
<p>The equilibrium price is given by intersection of demand and supply curve. With supply being 24 there is only one intersection of supply and demand at the point where P=500.  If you want some economic intuition you can ask yourself, why would suppliers charge less than P=500 on this market? For charity?</p>
<p>Here we assume people are self interested and rational. If suppliers see that all houses sell for 500 why would they offer lower price? Unless you assume some sort of charitableness or masochistic preferences it makes absolutely no sense for suppliers to offer lower price than 500. That price will be acceptable to all buyers and sellers get as much as they can from their goods.</p>
<p>When the number of houses is 25 or 26 the price will be bid lower (or in 24 case there will be range) because if it would stay 500 some houses would be left unsold.</p>
<blockquote>
<p>What if the supply is even lower than 24? In the extreme case, with just one apartment being supplied, how can the value of 500 be called an equilibrium price (or the range ]200, 500] if I was correct) if there are a total of 25 people willing to pay the maximum value of 500, but only one person getting the apartment and 24 left out?</p>
</blockquote>
<p>There are at least 4 distinct notions/concepts of equilibrium in economics (see my past answer <a href="https://economics.stackexchange.com/a/50699/15517">here</a> for details). In this case you call it equilibrium either because there are no endogenous tendencies to change (notion 1 in my old answer), or that no agents have any incentive to deviate from their behavior (notion 4 in my old answer).</p>

CC BY-SA 4.0
2022-04-13T07:52:12.363Z
@Rick 1. but here there are no information asymmetries between buyers and sellers, in this simple model supply and demand are common knowledge 2. You asked why the situation above can be called equilibrium. From economic perspective this is justified because equilibrium is not simply defined as situation where quantity demanded equals quantity supplied. You can always invent new terminology if you want, heck you can even call demand equilibrium instead of demand that’s up to you but i personally don’t see reason why we should make up new terminologies when the current ones work fine
1muflon1
CC BY-SA 4.0
2022-04-14T01:27:03.413Z
1 - If you assume that, is it correct to say that you disagree with the answers of both links I sent (for the cases where the supply curve is fixed in 25 and 26)? You don't think that there is a range in any case, because the seller would always know the maximum price accepted by the buyers. 2 - The author makes right in the beginning some caveats about the notion of equilibrium, but says that this is accepted "The equilibrium principle: Prices adjust until the amount that people
demand of something is equal to the amount that is supplied."
Rick
CC BY-SA 4.0
2022-04-14T06:50:59.270Z
@Rick no there is range on 24 because sellers can see demand not reservation prices. Look this is simple model do not over think it, there is no negotiation in place, none, suppliers and customers just look at where demand intersects supply and instantly arrive at price. There are no iterations no guessing as to what correct price is. It’s like if I would ask you solve for equilibrium quantity given that demand is Q=100-p and supply is Q=p+10. In a richer model that would had negotiations you could perhaps get a range even in 23 case but it depends on the type of model because sellers
1muflon1
CC BY-SA 4.0
2022-04-14T06:54:44.150Z
Could always start with strategy start with highest price possible and drop by 1 cent until market clears. In any case again in this simple model there are no explicit negotiations. Only information you have is supply and demand curve. That would be like asking for a simple mode where you solve for Q and P using the equations above why actual quantity should not be higher than equilibrium because some goods get lost in transit or stores might prefer to throw some food out than having bad optics of having half filled shelves. Well in real life sure there can be such situations but they are not
1muflon1
CC BY-SA 4.0
2022-04-14T06:58:30.687Z
Part of a simple model where you just equate supply and demand. You can build richer model where there is some probability good will break in transit and then you might find Q is larger than equilibrium quantity etc. however, if you are given exercise to solve you can’t make up additional assumptions for the mode you have. Given the Varian exercise, and **only** info given in the exercise how could the price be lower than 500 in case of 23 houses? Try to explain how price could be 250 let’s say using **only** info in set up.
1muflon1
CC BY-SA 4.0
2022-04-14T07:22:09.477Z
@Rick regarding the equilibrium, 1. That is not definition of equilibrium but description of what usually happens in equilibrium. 2. Trivial example, consider 101 prisoner dilemma where we have firm A and B both firms can either produce more than Q so that Q_s>Q_d or Q at which exactly Q_S=Q_d, but because customers like to see full  shelves if one company over produces and other doesn’t most customers go to the other company. If both firms produce at point Q_s=Q_d they both get 10 mil dollars profit. If one firm doesn’t overproduce but other does the over producing firm gets 15 mill
1muflon1
CC BY-SA 4.0
2022-04-14T07:29:36.483Z
The other firm that produces quantity to exactly match demand will only get 3 mil profit, since we assumed consumers prefer shop with full shelves. Next if they both overproduce they both get just 4 mil profit (since they have to produce excess goods that won’t sell). Clearly in the above example I listed the equilibrium strategy is to overproduce (if you ever encountered prisoners dilemma this is the same thing applied to firms). To overproduce here would be equilibrium, so it’s not true that every equilibrium will occur at point where Q_s=Q_d. That will occur often in micro hence Varian is
1muflon1
CC BY-SA 4.0
2022-04-14T07:32:29.110Z
Justified in calling it an equilibrium principle since principle in science is just some general theorem which has numerous special applications across wide field, but Q_s=Q_d is not a general law that will apply to every problem.
1muflon1
CC BY-SA 4.0
2022-04-16T00:49:14.937Z
I'm trying to maintain a framework of introductory econ books, just as you. There's no negotiation required in my reasoning, there's just demand and supply (people buying and selling). If the collection of suppliers perceive an excess of demand, the price rises (some interaction must exist, but this is still econ 101 stuff). But the price must start somewhere for that dynamics to happen. Since the suppliers just see demand and not reservation prices, when the price is for example 250, the suppliers would have no incentive to change the price, and it would get stuck there, since Q_d = Q_s
Rick
CC BY-SA 4.0
2022-04-16T00:50:43.833Z
So, when you say "Try to explain how price could be 250" for Q=24, I'd say: the same way you think it could happen P=250 when Q=25. It's exactly this answer: [What is the equilibrium price in this case?](https://economics.stackexchange.com/a/47343/15391).
Rick
CC BY-SA 4.0
2022-04-16T00:51:39.397Z
My proposition is that either someone accepts that the answer is a range in all of the 3 cases or none. Depending on your "world view" about how the suppliers will act and what kind of knowledge they have, either the price is fixed at the maximum price accepted or not. It seems that the quirks found in this problem are just a consequence of the discrete stair case.
Rick
CC BY-SA 4.0
2022-04-16T00:53:29.517Z
Although a lot can be said about equilibrium, there must exist some agreement for the word to be used objectively, and in the context of econ 101, the equilibrium price is simply the one that makes Q_s=Q_d. I understand that further uses of the concept can lead to other definitions and interesting philosophical discussions.
Rick
CC BY-SA 4.0
2022-04-16T01:05:01.400Z
@Rick 1. But for any price below 500 there will be excess demand. With a flat horizontal demand curve the demand for price above demand curve is 0 and below demand curve is $\infty$. 2. Look here the solution concept is just to equate demand and supply. Suppliers in this model don’t choose prices at random. This is not stochastic model there is no randomness in it. 3. This is also static model there is no dynamics there. 4. If the price would be 250 suppliers **would have incentive to change the price** suppliers could earn more by charging higher price. 5. But demand does not intersect supply
1muflon1
CC BY-SA 4.0
2022-04-16T01:10:03.033Z
Over range everywhere only at $q=25$. Here the solution concept is to simply find where demand and supply curve overlap. There is no strategic interaction or negotiation or dynamics or some stochastic processes - none. You can imagine that in a background to make a rationalization for a model or to tell yourself a story about what the model describes, but there is no stochastic and dynamic behavior in it. 6. Yes, but that’s my point. Objectively in economics equilibrium is not defined as a point where Q_s=Q_d that is an example of equilibrium. Eg, a duck is a bird but is every bird a duck?
1muflon1
CC BY-SA 4.0
2022-04-16T01:13:39.160Z
The 2 main definitions of equilibrium used widely are either a situation where no agent has any incentive to deviate from their current actions. Or second one is a situation where everyone has correct expectations. If Q_s=Q_d usually no agent will have incentive to deviate so that is an example of equilibrium. But there are equilibria in complex strategic interactions when Q_s is not equal Q_s
1muflon1
CC BY-SA 4.0
2022-04-16T02:04:09.110Z
"If the price would be 250 suppliers would have incentive to change the price suppliers could earn more by charging higher price". I think I found my mistake, I didn't see the excess demand! Since the demand is flat, there is always an excess of demand when the supply is less than 25 (the demand is always fixed in 25 until the price reaches 200) and an incentive to raise the price. If P=501 the suppliers see no demand, so the price gets stuck in 500, a situation where Q_d=25 and Q_s=24.
Rick
CC BY-SA 4.0
2022-04-16T02:04:23.117Z
In this situation agents have no reason to change their behaviors and I have to get used to the idea that Q_s=Q_d is much less general than I thought, so that when the supply is just Q_s=1, the "equilibrium price" is still 500 (it cannot be higher because this lowers the demand to 0 and it won't be lower because the suppliers receive a signal of excess demand) and there's no problem with that. Are we in agreement now?
Rick
CC BY-SA 4.0
2022-04-13T01:21:31.827Z
2022-04-13T01:21:31.827Z
1muflon1
<p>My questions refer to the first exercise in chapter one of Varian - Intermediate Microeconomics (9th edition). The exercise deals with an apartment rental market, an example explored in the first chapter. In the short run the supply curve is considered perfectly inelastic.
<a href="https://i.sstatic.net/RM7kc.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/RM7kc.jpg" alt="enter image description here" /></a></p>
<p>These are the demand and supply curves I constructed for the item I'm interested:
<a href="https://i.sstatic.net/44Gug.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/44Gug.png" alt="enter image description here" /></a></p>
<p>1 - If there are 24 apartments to rent, why isn't it the case that the equilibrium price is also in a range, like the 25 and 26 cases (Varian's answer is just 500)? If there are 24 apartments, there will also be just 24 renters when the price is in ]200, 500] and not only in 500, thus making the number of apartments supplied equal to the number of renters. Is this reasoning correct?</p>
<p>2 - What if the supply is even lower than 24? In the extreme case, with just one apartment being supplied, how can the value of 500 be called an equilibrium price (or the range ]200, 500] if I was correct) if there are a total of 25 people willing to pay the maximum value of 500, but only one person getting the apartment and 24 left out?</p>
<hr>
<p>Ps: This problem was already approached in other 2 posts (<a href="https://economics.stackexchange.com/questions/40427/what-is-the-equilibrium-price-in-this-case">What is the equilibrium price in this case?</a> / <a href="https://economics.stackexchange.com/questions/23798/why-is-the-equilibrium-price-not-anything-between-0-and-200">Why is the equilibrium price not anything between 0 and 200?</a>), but related to the 25 and 26 cases.</p>

<microeconomics><supply-and-demand><equilibrium-price>
Why is this equilibrium price unique? (Varian exercise)
Rick
# Why is this equilibrium price unique? (Varian exercise)

(Asked by: username_0 on 2022-04-13)

My questions refer to the first exercise in chapter one of Varian - Intermediate Microeconomics (9th edition). The exercise deals with an apartment rental market, an example explored in the first chapter. In the short run the supply curve is considered perfectly inelastic.
[![enter image description here](https://i.sstatic.net/RM7kc.jpg)](https://i.sstatic.net/RM7kc.jpg)

These are the demand and supply curves I constructed for the item I'm interested:
[![enter image description here](https://i.sstatic.net/44Gug.png)](https://i.sstatic.net/44Gug.png)

1 - If there are 24 apartments to rent, why isn't it the case that the equilibrium price is also in a range, like the 25 and 26 cases (Varian's answer is just 500)? If there are 24 apartments, there will also be just 24 renters when the price is in ]200, 500] and not only in 500, thus making the number of apartments supplied equal to the number of renters. Is this reasoning correct?

2 - What if the supply is even lower than 24? In the extreme case, with just one apartment being supplied, how can the value of 500 be called an equilibrium price (or the range ]200, 500] if I was correct) if there are a total of 25 people willing to pay the maximum value of 500, but only one person getting the apartment and 24 left out?

---

Ps: This problem was already approached in other 2 posts ([What is the equilibrium price in this case?](https://economics.stackexchange.com/questions/40427/what-is-the-equilibrium-price-in-this-case) / [Why is the equilibrium price not anything between 0 and 200?](https://economics.stackexchange.com/questions/23798/why-is-the-equilibrium-price-not-anything-between-0-and-200)), but related to the 25 and 26 cases.

**Tags:** microeconomics, supply-and-demand, equilibrium-price

---

## 1 answers

### Answer by username_1 on 2022-04-13. Score: 1 | Accepted answer

> If there are 24 apartments to rent, why isn't it the case that the equilibrium price is also in a range, like the 25 and 26 cases (Varian's answer is just 500)?

The equilibrium price is given by intersection of demand and supply curve. With supply being 24 there is only one intersection of supply and demand at the point where P=500. If you want some economic intuition you can ask yourself, why would suppliers charge less than P=500 on this market? For charity?

Here we assume people are self interested and rational. If suppliers see that all houses sell for 500 why would they offer lower price? Unless you assume some sort of charitableness or masochistic preferences it makes absolutely no sense for suppliers to offer lower price than 500. That price will be acceptable to all buyers and sellers get as much as they can from their goods.

When the number of houses is 25 or 26 the price will be bid lower (or in 24 case there will be range) because if it would stay 500 some houses would be left unsold.

> What if the supply is even lower than 24? In the extreme case, with just one apartment being supplied, how can the value of 500 be called an equilibrium price (or the range ]200, 500] if I was correct) if there are a total of 25 people willing to pay the maximum value of 500, but only one person getting the apartment and 24 left out?

There are at least 4 distinct notions/concepts of equilibrium in economics (see my past answer [here](https://economics.stackexchange.com/a/50699/15517) for details). In this case you call it equilibrium either because there are no endogenous tendencies to change (notion 1 in my old answer), or that no agents have any incentive to deviate from their behavior (notion 4 in my old answer).

> **Comments:**
> **username_1**: @Rick 1. but here there are no information asymmetries between buyers and sellers, in this simple model supply and demand are common knowledge 2. You asked why the situation above can be called equilibrium. From economic perspective this is justified because equilibrium is not simply defined as situation where quantity demanded equals quantity supplied. You can always invent new terminology if you want, heck you can even call demand equilibrium instead of demand that’s up to you but i personally don’t see reason why we should make up new terminologies when the current ones work fine  
> **username_0**: 1 - If you assume that, is it correct to say that you disagree with the answers of both links I sent (for the cases where the supply curve is fixed in 25 and 26)? You don't think that there is a range in any case, because the seller would always know the maximum price accepted by the buyers. 2 - The author makes right in the beginning some caveats about the notion of equilibrium, but says that this is accepted "The equilibrium principle: Prices adjust until the amount that people demand of something is equal to the amount that is supplied."  
> **username_1**: @Rick no there is range on 24 because sellers can see demand not reservation prices. Look this is simple model do not over think it, there is no negotiation in place, none, suppliers and customers just look at where demand intersects supply and instantly arrive at price. There are no iterations no guessing as to what correct price is. It’s like if I would ask you solve for equilibrium quantity given that demand is Q=100-p and supply is Q=p+10. In a richer model that would had negotiations you could perhaps get a range even in 23 case but it depends on the type of model because sellers  
> **username_1**: Could always start with strategy start with highest price possible and drop by 1 cent until market clears. In any case again in this simple model there are no explicit negotiations. Only information you have is supply and demand curve. That would be like asking for a simple mode where you solve for Q and P using the equations above why actual quantity should not be higher than equilibrium because some goods get lost in transit or stores might prefer to throw some food out than having bad optics of having half filled shelves. Well in real life sure there can be such situations but they are not  
> **username_1**: Part of a simple model where you just equate supply and demand. You can build richer model where there is some probability good will break in transit and then you might find Q is larger than equilibrium quantity etc. however, if you are given exercise to solve you can’t make up additional assumptions for the mode you have. Given the Varian exercise, and **only** info given in the exercise how could the price be lower than 500 in case of 23 houses? Try to explain how price could be 250 let’s say using **only** info in set up.  
> **username_1**: @Rick regarding the equilibrium, 1. That is not definition of equilibrium but description of what usually happens in equilibrium. 2. Trivial example, consider 101 prisoner dilemma where we have firm A and B both firms can either produce more than Q so that Q_s>Q_d or Q at which exactly Q_S=Q_d, but because customers like to see full  shelves if one company over produces and other doesn’t most customers go to the other company. If both firms produce at point Q_s=Q_d they both get 10 mil dollars profit. If one firm doesn’t overproduce but other does the over producing firm gets 15 mill  
> **username_1**: The other firm that produces quantity to exactly match demand will only get 3 mil profit, since we assumed consumers prefer shop with full shelves. Next if they both overproduce they both get just 4 mil profit (since they have to produce excess goods that won’t sell). Clearly in the above example I listed the equilibrium strategy is to overproduce (if you ever encountered prisoners dilemma this is the same thing applied to firms). To overproduce here would be equilibrium, so it’s not true that every equilibrium will occur at point where Q_s=Q_d. That will occur often in micro hence Varian is  
> **username_1**: Justified in calling it an equilibrium principle since principle in science is just some general theorem which has numerous special applications across wide field, but Q_s=Q_d is not a general law that will apply to every problem.  
> **username_0**: I'm trying to maintain a framework of introductory econ books, just as you. There's no negotiation required in my reasoning, there's just demand and supply (people buying and selling). If the collection of suppliers perceive an excess of demand, the price rises (some interaction must exist, but this is still econ 101 stuff). But the price must start somewhere for that dynamics to happen. Since the suppliers just see demand and not reservation prices, when the price is for example 250, the suppliers would have no incentive to change the price, and it would get stuck there, since Q_d = Q_s  
> **username_0**: So, when you say "Try to explain how price could be 250" for Q=24, I'd say: the same way you think it could happen P=250 when Q=25. It's exactly this answer: [What is the equilibrium price in this case?](https://economics.stackexchange.com/a/47343/15391).  
> **username_0**: My proposition is that either someone accepts that the answer is a range in all of the 3 cases or none. Depending on your "world view" about how the suppliers will act and what kind of knowledge they have, either the price is fixed at the maximum price accepted or not. It seems that the quirks found in this problem are just a consequence of the discrete stair case.  
> **username_0**: Although a lot can be said about equilibrium, there must exist some agreement for the word to be used objectively, and in the context of econ 101, the equilibrium price is simply the one that makes Q_s=Q_d. I understand that further uses of the concept can lead to other definitions and interesting philosophical discussions.  
> **username_1**: @Rick 1. But for any price below 500 there will be excess demand. With a flat horizontal demand curve the demand for price above demand curve is 0 and below demand curve is $\infty$. 2. Look here the solution concept is just to equate demand and supply. Suppliers in this model don’t choose prices at random. This is not stochastic model there is no randomness in it. 3. This is also static model there is no dynamics there. 4. If the price would be 250 suppliers **would have incentive to change the price** suppliers could earn more by charging higher price. 5. But demand does not intersect supply  
> **username_1**: Over range everywhere only at $q=25$. Here the solution concept is to simply find where demand and supply curve overlap. There is no strategic interaction or negotiation or dynamics or some stochastic processes - none. You can imagine that in a background to make a rationalization for a model or to tell yourself a story about what the model describes, but there is no stochastic and dynamic behavior in it. 6. Yes, but that’s my point. Objectively in economics equilibrium is not defined as a point where Q_s=Q_d that is an example of equilibrium. Eg, a duck is a bird but is every bird a duck?  
> **username_1**: The 2 main definitions of equilibrium used widely are either a situation where no agent has any incentive to deviate from their current actions. Or second one is a situation where everyone has correct expectations. If Q_s=Q_d usually no agent will have incentive to deviate so that is an example of equilibrium. But there are equilibria in complex strategic interactions when Q_s is not equal Q_s  
> **username_0**: "If the price would be 250 suppliers would have incentive to change the price suppliers could earn more by charging higher price". I think I found my mistake, I didn't see the excess demand! Since the demand is flat, there is always an excess of demand when the supply is less than 25 (the demand is always fixed in 25 until the price reaches 200) and an incentive to raise the price. If P=501 the suppliers see no demand, so the price gets stuck in 500, a situation where Q_d=25 and Q_s=24.  
> **username_0**: In this situation agents have no reason to change their behaviors and I have to get used to the idea that Q_s=Q_d is much less general than I thought, so that when the supply is just Q_s=1, the "equilibrium price" is still 500 (it cannot be higher because this lowers the demand to 0 and it won't be lower because the suppliers receive a signal of excess demand) and there's no problem with that. Are we in agreement now?  

---

