- Explore the creation of a demand curve
- Explore the creation of a supply curve
- Visualize the intersection of the demand and supply curves
1. Introduction to the Classic Supply and Demand Model
When we think about markets and how buyers and sellers interact within them, there are a lot of elements to consider. In this module, we begin by examining the classic supply and demand model, which is primarily concerned with two questions as applied to a specific good being exchanged in a specific market: at what price will the good be bought and sold? And how much of the good will be sold?
In the way it is usually described, the analysis begins as follows: different buyers have different amounts that they are willing and able to pay for the good. We'll return to this in much more detail later, but for our purposes here, we'll call this amount for each buyer their "reservation price." We can visualize the buyers in a figure, where buyers with the highest reservation prices are shown on the left, while buyers with the lowest reservation prices are shown on the right. In other words, buyers that are willing and able to pay the highest price for the good are on the left, while those who are willing and able to pay lower prices are on the right.
Note that the end statement below tells the data generator that we're done specifying options for the buyers being added. In a later module, we'll fine-tune some other parameters, such as the amount of demand each buyer has. In those cases, there will be additional lines before the end statement.
Click on the "Generate Data" button below to generate a set of buyers with random reservation prices and then visualize them in a diagram. By changing the text in the box below, you can experiment modifying the number of buyers (set to 10 by default) and the possible range of their reservation prices (set to $1 to $10 by default). Once you make any changes, click on the "Generate Data" button to update the diagram.
Click "Generate Data" to view results
We can fit a line through these individual points to form a curve (click on the "Draw Demand Curve" button below to see it). We can think of this curve as a function, where the input to the function is price, and the output of the function is the (approximate) total number of buyers willing and able to purchase it.
Click "Draw Demand Curve" to view results
As shown above, there is an inverse relationship between the price of the good and number of buyers willing and able to purchase it, meaning that at a relatively lower price, more buyers will buy, and at a relatively higher price, fewer buyers will buy. There is a simple reason for this, which is based on a commonsense assumption: a buyer willing to pay a certain price for a good is also willing (and likely prefers) to pay less than that price for the same good. In turn, at a given price, not only will buyers who are willing and able to pay that price participate in the market, but so will buyers who would have been willing and able to pay even more than that price.
The demand curve is usually captured as a downward-sloping straight line with a positive intercept:
QD = a + bP
where
a > 0, b < 0
The value of a represents the quantity (in units) that would be demanded if the good had a price of zero. The value of b represents the decrease in demand (in units) for each one-dollar increase in the price. The value of b is closely related to the concept of elasticity, which is essentially a measure of how responsive demand is to price changes.
Note that supply and demand diagrams traditionally show price on the vertical axis and quantity on the horizontal axis, even though we think of price as being the independent variable (the one that drives quantities, rather than the other way around). imagine economics uses this convention for consistency with other teaching materials the learner might see.
There is a similar, though slightly different, narrative for sellers. Different sellers are able to produce (or acquire) the good for different costs, which we term their "marginal cost." In turn, different sellers are willing and able to sell the good for different minimum prices, under the assumption that they must make at least some amount of positive profit. We can visualize these sellers in a figure, where sellers with the lowest marginal costs are shown on the left, while sellers with the highest marginal costs are shown on the right.
Click on the "Generate Data" button below to generate a set of sellers with random marginal costs and then visualize them in a diagram. You can experiment by modifying the number of sellers and the possible range of their marginal costs by changing the text in the box below. Once you make any changes, click on "Generate Data" again to update the diagram.
Click "Generate Data" to view results
We can fit a line through these individual points to form a curve (click on the "Draw Supply Curve" button below to see it). We can think of this curve as a function, where the input to the function is price, and the output of the function is the (approximate) total number of sellers willing and able to sell at that price. Note that an important aspect of the classic supply and demand model is that sellers are "price-takers," which means that they are not able to adjust the price at which they offer their product. Instead, the market as a whole sets one single price, and individual sellers can choose to participate or not participate depending on their individual marginal cost.
Click "Draw Supply Curve" to view results
As shown above, there is a positive relationship between the price of the good and the number of sellers that are willing and able to sell it, meaning that at a relatively higher price, more sellers will sell, and at a relatively lower price, fewer sellers will sell. Analogous to the case of buyers, there is a simple reason for this: a seller willing to sell a good at a certain price is also willing (and likely prefers) to sell that same good for an even higher price. In turn, at any given price, not only will sellers who are willing and able to sell at that price participate in the market, but so will sellers who would have been willing and able to receive even less than that price.
The supply curve is usually captured as an upward-sloping straight line with a non-negative intercept:
QS = c + dP
where
c ≥ 0, d > 0
The value of c represents the quantity (in units) that would be supplied if the good had a price of zero. The value of d represents the increase in supply (in units) for each one-dollar increase in the price. The value of d is closely related to the concept of elasticity, which is essentially a measure of how responsive supply is to price changes.
We can combine the downward-sloping demand curve and the upward-sloping supply curve into a single figure, and there is a particular price and a particular quantity where these two curves meet. Click on the "Draw Intersection" button below to visualize this using the curves constructed above.
Click "Draw Intersection" to view results
In the classic supply and demand setup, we assume that the market clears, which means that the quantity of the good produced is exactly the same as the quantity of the good demanded. There is only one price where this occurs, which is what we call the "equilbirum price" and is represented by the location of the horizontal black line in the digram above. The quantity of the good that's exchanged at that price is reprsented by the vertical black line in the diagram above.
From the examples above, we can write the equation for the demand curve alongside the equation for the supply curve:
QD = a + bP
QS = c + dP
As described above, the market-clearing assumption in the classic model states that the quantity demand (the QD in the first equation) must be equal to the quantity supplied (the QS in the second equation). If we set the equations equal to one another, we have:
a + bP = c + dP
Given the linearity of the curves and the restrictions on the slopes, there is one price that will satisfy this equation, which we refer to as the equilibrium price. This price (under the market-clearing assumption) also implies a single quantity, which we refer to as the equilibrium quantity.
Note that this model doesn't have anything to say about how the market reaches this equilibrium price and quantity. This is simply where the market clears, which is an assumption embedded within the model.