Consumer and producer surplus in the classic model
- Explore the concepts of consumer surplus and producer surplus using the dynamic supply and demand model
3. Consumer and Producer Surplus in the Dynamic Model
In the introductory dynamic module, we explored how a simulated version of the supply and demand model can lead to predictions that are sometimes different than those of the classic model. Here, let's consider the dynamic model within the context of consumer and producer surplus.
To start, let's create a market with some buyers and sellers and then simulate their interactions for a number of rounds. As before, feel free to edit the number of buyers and sellers and their reservation prices and marginal costs, respectively. When you're ready, click on the "Generate Data" button to get the data ready, and then click "Run" to see the simulation in action.
Click "Generate Data" to view results
Note that in addition to the supply and demand graph we saw previously, there is also a diagram showing the matches between the buyers and sellers. Specifically, each seller (in orange on the left) that makes a sale in a round is connected to the buyer (in blue on the right) who purchases from them in that round. Each grey circle sits on a line connecting a seller and a buyer, where its position represents the exchange price between that seller and that buyer in that round. The higher the circle, the higher the exchange price.
The concepts of consumer surplus and producer surplus are the same here as they were in the classic model, with two big differences: (1) the surpluses can change because there is no concept of equilibrium in the dynamic model and (2) we can see the surpluses of the individual buyers and sellers because each one is represented individually in the model (i.e., buyers are not aggregated into a demand curve, and sellers are not aggregated into a supply curve).
When an exchange occurs between a seller and a buyer, the higher the exchange price, the greater the surplus for the seller and the lower the surplus for the buyer. For example, if a seller has a marginal cost of $1 and exchanges with a buyer who has a reservation price of $10, then there is essentially $9 ($10 - $1 = $9) of surplus to split between them. If the exchange price is, say, $3, then the seller captures $2 of that surplus and the buyer captures $7 of that surplus. If the exchange price were higher, say, $6, then the seller would capture $5 of the surplus while the buyer would capture $4 of the surplus.
We can see this in the matches diagram by considering the grey circles. More specifically, when looking at any grey line and its associated circle, the higher up the circle (i.e., the higher the exchange price) the greater the surplus for the associated seller and the smaller the surplus for the associated buyer. As described in the introductory dynamic module, in the first round, sellers set their prices to exactly their respective marginal costs. In turn, their individual surpluses in the first round are always zero, even if they make a sale. If they raise their prices over multiple rounds, then their individual surpluses will increase, while the surpluses of their buyers will decrease.
An example with two buyers and two sellers
Let's explore this with a concrete example. Below are some commands that add two buyers and two sellers to a market. One buyer has reservation price of 9 (call this buyer A), and the other has reservation price of 10 (call this buyer B). One of the sellers has marginal cost of 1 (call this seller A), and the other has marginal cost of 5 (call this seller B). Given that the marginal costs of sellers A and B (1 and 5, respectively) are below the reservation prices of buyers A and B (9 and 10, respectively), each seller will be matched with one of the buyers in every round, though the matches may switch back and forth (e.g., buyer A may be matched with seller A in round one, may be matched with seller B in round two, and then be matched with seller A again in round three, etc.).
As described previously, sellers in the dynamic model move their individual sales prices upwards towards the highest exchange price they can see. In this case, seller A will incrementally increase its sales price towards seller B's sales price, while seller B will leave its sales price equal to its marginal cost, as it will always have the highest price in the market. In turn, seller A's surplus will increase over time, while seller B's surplus will remain at zero.
At first, whichever buyer purchases from seller A will capture a lot of surplus because seller A's price will be low. Over time, seller A will increase its price, and the surplus will be divided more evenly between seller A and whichever buyer purchases from it. Whichever buyer purchases from seller B in a round will capture the surplus above seller B's marginal cost (because its price will remain constant at 5).
Click on the "Generate Data" button to get the data ready, and then click "Run" to see the simulation in action. Once the simulation has finished running, click on "Reset and Run Initial Setup" if you want to see it again.
Click "Generate Data" to view results
In addition to the matches diagram, there is now a diagram showing the consumer (buyer) surplus and producer (seller) surplus. As the simulation runs, we can see that seller A's surplus increases, while seller B's surplus is a constant zero. At the beginning, whichever buyer buys from seller A will have the much larger surplus, but over time, buyers A and B will have similar surpluses as seller A moves its sales price closer to seller B's.
An example with twenty buyers and twenty sellers
Finally, let's consider an example with many more buyers and sellers. As before, click on the "Generate Data" button to get the data ready, and then click "Run" to see the simulation in action. If you want to replay the simulation from the beginning, click on "Reset and Run Initial Setup" once it has stopped.
Click "Generate Data" to view results
There are a few things to notice here. The first is that, as in the simple example above, the sellers' surpluses start at zero and gradually increase as the exchange prices increase. On the flip side of this, the buyers' surpluses start out being larger and then gradually decrease as the exchange prices increase. In fact, some buyers with lower reservation prices participate in the market only at the beginning when prices are generally lower, and then later exit the market because they are not able to, or are unwilling to, pay higher prices.
The main takeaways here are that consumer surplus and producer surplus can change over time and that there may be significant differences in how surpluses are distributed among buyers and sellers. Although the dynamics here serve to illustrate these points, the exact patterns are not as important. In later modules, we'll look at different scenarios that can provide greater insight into real-world situations.