Today marks the start of a new textbook. The textbook that I will be using now is Intermediate Microeconomics A Modern Approach by Hal R. Varian. This is a more advanced microeconomic textbook. The reason that I am using it is very similar to the last one, basically I have it because I used it in a class. It seems to be a good textbook. It is quite a bit longer than the last textbook and so will take me longer to go through. Some of the concepts that I have gone over previously will be gone over again, either just in passing or in more detail.
The first chapter of the textbook is talking about some basic market examples. I will be following along with this example because it works very well to explain some of these economic concepts. As well, this example serves to show a very basic economic model and how it can be useful.
The example that is used is of a town that has a university. In this town there are two types of apartments, ones that are close to the university and ones that are far away. The ones that are close are considered more desirable since they allow easier access to the university. These two types of apartments will be called inner and outer apartments to make things simpler.
The focus on the model will be the market for the inner apartments. There are several assumptions that we are making in this model.
- People who can’t find an inner apartment live in an outer apartment
- Outer apartments price is fixed at some level
- All apartments are identical except for location
The difference in the two prices in this model is a good example of exogenous variables and endogenous variables. The price of the outer apartments is an exogenous variable, which means that it is determined by forces outside of the model. The price of the inner apartments is an endogenous variable, which means that it is determined by forces within the model.
What will be determined with this model is:
- The price of inner apartments
- Who lives in the inner apartments and who lives in the outer apartments
The textbook at this point also discusses two economic principles that helps us try to explain human behaviour. The first of these is the optimization principle. This is pretty much just the maximization principle that we talked about earlier but states slightly differently. The optimization principle is that people try to choose the best patterns of consumption they can afford. The second principle that it discusses is what it calls the equilibrium principle. This is just the idea that prices adjust until the amount that is demanded of something is equal to the amount that is supplied.
The chapter has a brief description of the demand and supply curves and I really like how it is explained so I will talk about it here for a little bit. The chapter brings in the concept of the reservation price. A reservation price is the maximum price that someone would be willing to accept for a good and still buy it. In our example that would be the rent on an inner apartment.
For the moment let’s imagine that there are five people looking for apartments. The first person is willing to pay $500 for the apartment, the second person is willing to pay $490 and so on, until the last person will be willing to pay $460. These are the people’s reservation prices. The demand curve in this market then is made up of this. If the rent for an apartment is $500 then only one apartment will be rented. This means that the number of apartments that are rented will just be equal to the number of people whose reservation price is above the market price. When we plot this on a curve it looks like this.
It has steps because there are so few people in the market. When you introduce more and more people than we see the curved demand curve that we are used to.
After having looked at the demand curve briefly we can talk about the supply curve as well. For now we will be looking at the competitive market, which is where there are many independent landlords. We will be making a couple more assumptions here as well.
- Consumers will have perfect information about price
- There are no regulations or contracts
- We are operating in the short-run.
- Landlords have no costs
Under these conditions we can show that the equilibrium price of all the inner apartments will be the same. The easiest way to show this is to start with a situation where the prices are not all equal. In this situation there will be two prices, a high price and a low price. Under this situation what will happen is that people who are renting a place that has a high price will go to a landlord who has a low price and offer them more money than the low price but less money than the high price for a place. In this situation there will be a trade and both people will be made better off. This will continue to happen until the prices for all apartments are the same.
Since we have shown that prices will all be the same, it is time to look at why the third assumption is important. The reason that for now we will be looking at the short run is that in the short run the number of apartments will not change. This is pretty easy to imagine as it takes quite a while to build more apartments. As such the supply curve will just be a vertical line as such.
Using the basic information that we have so far, we have been able to come up with both a supply curve and a demand curve. In order to get our equilibrium now we will put them together.
In this graph now P* is equal to the price where the quantity demanded and the quantity supplied are equal. At this price, all consumers who are willing to pay more than P* find an apartment and the landlords are able to rent all of their apartments. Neither the consumers nor landlords have any reason to change their behaviour.
This has answered the first thing that we were looking for in our model which was to find the price. The second thing that we wanted to know was who rents which apartment. As was briefly mentioned before this is actually very simple. The people who get the inner apartments are the ones that are willing to pay the most for them. In this case everyone who is willing to pay above P*. The difference between P* and their reservation price is their consumer surplus. So apartments in the competitive will be assigned based on how much people are willing to pay.
Now that we have our model, we are able to play around with different situations and see how they affect the behaviour of the equilibrium price. In order to do this what we will do is look at two different equilibrium situations and see what the difference is. We will not worry for now about how the market moves from one equilibrium to another, what we are doing is known as comparative statics.
First we will look at what will happen when supply in the market increases.
We can see that it is pretty obvious that the price of the apartments will fall. The opposite is also true though, if supply were to decrease than prices would rise. This is a very basic and obvious change. We can also look at more complicated changes that could happen as well. The textbook uses the example of what might happen if some of the apartments were converted into condominiums. The first obvious thing that will happen is the supply of apartments will fall. However this is not necessarily the only change that will take place in the market. There is the question of who is going to buy the condos. In our model it is conceivable that the people who will buy the condos are those that are willing to pay the most for apartments, in other words people who were living in inner apartments already. If all of the people who buy condos used to live in inner apartments then there will be no change in price as both supply and demand for apartments will fall equally.
This shows that it is important not just to look at how the supply side changes but also at how the demand side changes. The reality is that most likely there will be some people who used to live in apartments that will buy condos and some people who didn’t live in apartments who buy condos. This means that prices will most likely rise for rent, but by less than people might think.
We can also look at another interesting example given in the textbook, that of a unit tax on the apartments. So now each landlord needs to pay $50 a year for each apartment. What would this do to the price of the apartments? The usual assumption that people make is that some of the tax will be paid by the landlord and some will be passed along to the consumer. However if we look at our model, keeping the assumption of the short run, we will find out that is not actually true.
It is actually fairly easy to see that prices will not actually change, the landlord will absorb the entire tax. If we look at our model, the supply curve is not changing, there are still the same number of apartments as before. The demand curve is also not changing. If neither the demand curve, nor the supply curve shift, then there will be no change in price.
From a logical point of view it is pretty easy to see this as well. Before the tax each landlord was charging the maximum price that they could to keep all of their apartments rented. After the tax, this is still the case. If the landlords try to raise the price in order to transfer some of the cost of the tax what will happen is the consumers at the margin will drop out of the market and move to outer apartments. This means that not all of the apartments will be rented and the landlords will lose money. This for now is assuming that supply is fixed and the landlords are unable to do anything else with them, it is also functioning off of the assumption that the landlords do not have any costs with the apartments. In the long run where supply can change, this will not hold true.
Now that we have done a bit of analysis of the competitive market we can look at other ways of allocating apartments and how that will change the price and who gets which apartment. Following the textbook we will look at three other ways in which we could allocate the apartments, the discriminating monopoly, the ordinary monopoly and rent control.
A monopoly could either be a single dominant landlord or it could be a number of individual landlords getting together and coordinating their actions to act as one. For this example let’s say that instead of a normal renting procedure, the landlord decides to auction off the apartments. This means that each person will be paying a different price for an apartment. This is called a discriminating monopolist. Right now for simplicity we will assume that the landlord has perfect information. That is, that he knows the reservation price for each person.
In this situation what the landlord will do then is rent out each apartment to each person at his or her reservation price. What is interesting about this is that the exact same people who got the apartments in the competitive market will get the apartments in this situation. The last person to rent an apartment in this situation will in fact be paying P*, the market equilibrium price. So people will pay more money for their apartments but the same number and same people will all rent the apartments as before.
Now let’s look at a situation with an ordinary monopoly, this means that everyone will be charged the same price. Now the landlord faces a dilemma. He can set a low price and rent out all of his apartments or he can set a higher price and rent out less apartments but he may make more money. If we use D(p) to represent the demand function, which is the number of apartments that will be demanded based on the price. Then if the monopolist sets a price P, he will rent D(P) apartments and receives a revenue of P * D(P) or PD(P). The revenue can be thought of graphically as a box, where the height of the box is P and the width of the box is D(P). The area of the box is thus the revenue. If the monopolist has no costs, than he will want to maximize revenue and so choose the biggest box that he can. As can be seen, this will not always be at the equilibrium price.
In fact usually in a monopoly it is best to restrict the output and charge a higher price. So in the case of the ordinary monopoly, the price will be higher and fewer apartments will be rented as compared to the competitive market.
Finally let’s look at the case of rent control. This is where the government decides on a maximum amount of rent that can be charge for an apartment. In this situation we would have an excess of demand. Which means more people want apartments than are available. This begs the question, who will end up with an apartment? As it stands our model is unable to answer this question. There are really too many factors right now that would determine this to add to our model. So people who get the apartments will depend on how much time a person spends looking around, who knows current tenants, relationship with the landlord, and many other factors.
To make things simpler let’s just make the assumption that some of the people who had inner apartments before will have them now and some people who had outer apartments before will now have inner apartments and vice versa. The same number of apartments will be rented as in the competitive market just different people will have them. At least that is the situation in the short run.
We have now discussed four different ways to allocate the apartments, competitive market, discriminating monopolist, ordinary monopolist and through rent control. So which of these is the best way to allocate the apartments? It can be difficult to define best but here we will look at the economic positions of the people involved.
The landlords definitely end up in the best position if they are able to act as discriminating monopolists. This would maximize their revenue. Similarly the rent controlled situation is probably the worst for them.
The situation with the tenants is a little more complicated. Under the discriminating monopolist they will definitely be paying more money than under any of the other systems. However under the ordinary monopolist less people will get inner apartments than under the other systems. Finally under rent control some tenants will be better off, those who have inner apartments that otherwise would have had outer apartments. However the tenants who now have outer apartments but would have had inner apartments under the other systems are now made worse off. This shows that it is very difficult to determine which the best way is. One way that economists try to do this is to use the idea of Pareto efficiency.
If we are able to make some people better off without making anyone else worse off, we have a Pareto improvement. If we have a situation when we are unable to make any Pareto improvements, we say that the situation is Pareto efficient.
One way to think of Pareto efficiency in terms of our model is to look at the following situation. Suppose that who gets which apartment is decided by lottery. We then allow tenants to sublet their apartments to other people. If there are two people, person A that is assigned an inner apartment that he has a reservation price of $200 for, and there is person B that is assigned an outer apartment but has a reservation price of $300 for an inner apartment, then there is room for a Pareto improvement.
If person A trades apartments with person B, and person B pays person A some amount of money, both people are made better off, and no one is made worse off. In our model, what is important is that the people who have the highest reservation prices are the ones that get the inner apartments. This is because if people with low reservation prices get them, than there can be voluntary trade that makes both parties better off. Before we talked about efficiency as being when all gains from trade are maximize. We can see now that when all voluntary trades have been carried out, the situation will be Pareto efficient.
We can now use the idea of Pareto efficiency to look at our four ways of allocating the apartments. If we start with the competitive market we can see that since all voluntary trade is carried out, the situation is Pareto efficient.
If we look at the discriminating monopolist we can actually see that this is also Pareto efficient. The exact same people as in the competitive market get the apartments, and no one can be made better without making someone else worse off.
If we look at the ordinary monopolist we will see that this is not a Pareto efficient outcome. The reason for this is that all the apartments are not rented. As such the landlord could make more profit by renting a vacant apartment to another person at any positive price. Now the monopolist would only be able to do this if the other tenants were alright with people paying different prices. However as soon as that is the case we have a discriminating monopoly and not an ordinary monopoly. As such the ordinary monopoly is not Pareto efficient.
Finally we can look at rent control. We can immediately see that this is not Pareto efficient. If we look back to our example of person A and person B we can see why. Under rent control some people will have high reservation prices but be unable to get inner apartments. If we allowed voluntary trade then people would be able to trade and make at least one person better off, without making any one else worse off.
Everything that we have been talking about so far has been in the short run. However we do have to take a quick look at the long run as well because this is what will determine the supply. In the long run, supply of apartments will depend on how profitable it is for landlords to rent apartments as such, each situation will change the supply in the long run.
For today we have covered the simple model of apartments. The important idea of Pareto efficiency was introduced as well. Today was my first time introducing diagrams and I will try to go back over time and add more diagrams to my other posts.
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