Introduction to the dynamic supply and demand model
- Understand some of the key assumptions in the dynamic model
- Test what happens when the assumption that buyers can see all sellers is changed
- Test what happens when the assumption that sellers can see all other sellers is changed
2. Modifying Assumptions in the Dynamic Model
There are several key assumptions embedded within the dynamic model in the previous section that cause the model to yield average prices and total quantities analogous to the equilibrium outcomes that would have been predicted by the classic supply and demand model. These reasons include:
- that buyers and sellers know their own reservation prices and marginal costs, respectively, and will not buy above or sell below those limits, respectively;
- that buyers can see the offer prices of all sellers and will only buy from a particular seller if that seller has the lowest price they can see;
- that all sellers know the sales prices of all of their competitors and will raise their own sales price towards the highest price they can see (unless they fail to make any sales at their current price);
- and that there is no limit to the number of tentative matches within a round, in the sense that tentative matches will continue to be made until all unmatched sellers have marginal costs that are above the reservation prices of all unmatched buyers.
In this section, we'll explore what happens if we change the second and third of these assumptions, namely the perfect visibility of both buyers and sellers.
In the Interactivity section of the Imagine Economics introductory module, we describe how we can think about economic modeling assumptions in layers, where the outermost assumptions are those that allow particular models to function, while deeper assumptions may span multiple models and (at some times) may even remain unexamined.
In the section about the assumptions underlying the classic model, we discussed how the classic model has a number of deeper assumptions beyond those we often focus on (such as the requirement that the market clears). Many of these deeper assumptions are also present here, such as: taking buyers and sellers to be different people; assuming that individual buyers and sellers are the entities that have decision-making power; and assuming that buyers and sellers make their decisions independently and without regard for non-market factors, such as social norms or influences.
However, we can think of the dynamic model presented here as "internalizing" some of the outer layers of assumptions that are taken as given in the classic model. Most critically, these changes include removing the equilibrium assumption and replacing it with an evolving system where sellers set their own prices. In addition, the information that buyers and sellers have access to when making decision is (partially) integrated into the model. By including these details directly within the model, it allows us to change them and test them in a way that we cannot within the structure of the classic version.
These are just a few of the assumptions that can potentially be explored with the dynamic version of the model.
Testing the assumption that buyers can see all sellers
One of the most important assumptions is that buyers are able to see the prices of all sellers, which allows them to find the very best deal possible. This is a component of what is called perfect information, which is a key aspect of the classic model and essentially means that buyers have everything they need to make a completely informed purchasing decisions. In the dynamic model, an assumption that buyers have perfect information—combined with a willingness to actually look across all sellers and choose the one with the lowest price—leads to downward pressure that keeps the average price from going above the equilibrium price as predicted by the classic model.
Let's explore what happens if we modify this assumption. Below we create a market with a set of buyers that have random reservation prices and a set of sellers that have random marginal costs. Initially, we specify that buyers should have visibility of 10%, which means that when they're searching for the best price in each round, they are only able to see 10% of sellers' offer prices (the specific sellers that each buyer sees is assigned randomly). We simulate a set of rounds in this configuration. For comparison purposes, we then raise buyers' visibility to 100%, which means that they can see all offer prices. We simulate another set of rounds after this intervention.
Click on the "Generate Data" button to get the data ready. Once the diagram appears, click on the "Run" button to see what happens in the initial configuration. When the simulation stops, click on the "Run" button again to apply the changes to the buyers' visibility and see what happens.
Click "Generate Data" to view results
In the initial configuration, we see that the average price tends to be higher than the equilibrium price predicted by the classic model, while the total quantity tends to be lower than the equilibrium quantity predicted by the classic model. The price chart below the supply and demand graph provides a way to see how this happens.
Specifically, the price chart shows all of the exchange prices in each round. In the initial configuration—when buyers' visibility of the market is greatly reduced—higher-priced sellers that usually would be unable to participate in the market are instead able to make some sales. More specifically, these higher-priced sellers would usually be unable to compete with lower-priced sellers because buyers could find better deals, but because of buyers' reduced visibility, some of these higher-priced sellers represent the best deal that some buyers can find, which allows those sellers to enter the market. In turn, other sellers see that they could potentially be successful raising their own prices, and over multiple rounds, this causes the average price in the market to increase. After the intervention (when buyers' full visibility is restored), we see that prices tend to converge to a single average price, which matches what we would expect in the traditional model.
There are at least three key takeaways here. One is that the assumption of buyer perfect information in the classic model is a critical one, as adjusting just this one factor causes the average price and the total quantity to deviate from the equilibrium prediction. Second, changing this assumption tends to introduce price dispersion (where exchange prices have more of a range) and also makes the market more volatile, where participants tend to change more frequently and the average price is less stable. Finally, and more generally, reducing buyer visibility is one form of decreasing buyers' power in the market, and when buyers' power is decreased, they are less able to exert downward pressure on prices. In turn, we tend to see average prices rise (and total quantity decrease).
Testing the assumption that sellers can see all competitors
Note that sellers, unlike buyers, actually have information about sellers beyond those they can directly see. The reason is that, as described in the previous section, each seller sets their price based on the highest-priced seller they can see, and although that seller may not have the highest price overall, that seller may be able to see the seller that does have the highest price (or perhaps it sees yet another seller that has the highest price, and so on). For the purposes of illustration, this example sets seller visibility to be very low to make it more likely that these types of chains are short. However, the key factor is not the visibility percentage per se, but how connected the sellers are to one another in this underlying visibility network.
Let's explore the assumption of perfect information on the seller side. In the dynamic model we're working with here, one of the key pieces of information sellers have is the list of prices of all the other sellers in the market.
Let's explore what happens if we modify this assumption. Below we create a market with a set of buyers that have random reservation prices and a set of sellers that have random marginal costs. We specify that sellers should have visibility of 10%, which means that when they're setting their price in each round, they are only able to see 10% of the other sellers' sales prices. The specific visibility for each seller is assigned randomly, meaning that all sellers are limited in what they can see, though they each will see a different set of sellers (see the box for more information). We then simulate a set of rounds with this configuration.
Click "Generate Data" to view results
We see that when the intervention to the sellers' visibility is applied, the average price tends to decrease, while the total quantity tends to stay the same. As before, the price chart below the supply and demand graph provides a way to see how this happens.
Specifically, before the intervention, we see that prices tend to converge to a single average price, which matches what we would expect in the classic model. After the intervention—when sellers' visibility of the market is greatly reduced— higher-priced sellers that were previously unable to participate in the market are able to "jump in." More specifically, these higher-priced sellers were previously unable to compete with lower-priced sellers because buyers knew they could find better deals, but after the intervention, some of these higher-priced sellers represent the best deal that some buyers can find, which allows those sellers to enter the market. In turn, other sellers see that they could potentially be successful raising their own prices, and over multiple rounds, this causes the average price in the market to increase.