# Why is this equilibrium price unique? (Varian exercise)

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. These are the demand and supply curves I constructed for the item I'm interested: 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? / Why is the equilibrium price not anything between 0 and 200?), but related to the 25 and 26 cases.

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 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).

• Leaving the graph aside for a moment, what I call equilibrium price here is the price where the number of supplied goods is the same as the number of demanded goods. The answer to your first question is in the not accepted answer of the first link I posted (from user HFM): it's not charity, but it's lack of information. " If suppliers see that all houses sell for 500 why would they offer lower price", that's the point, they don't see it ... they start choosing for example 400, and see that the there's no excess demand .. so this is in equilibrium for them.
– Rick
Apr 13 at 1:42
• @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
Apr 13 at 7:52
• 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
Apr 14 at 1:27
• @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
Apr 14 at 6:50
• 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
Apr 14 at 6:54