I was trying to go over the math to see if it checks out, and I think it does under some assumptions.
1. we need the marginal demand distribution to be a probability distribution:
a. The marginal demand for any price is non-negative
b. we need the entire integral to equal 1. This might sound rather limiting, but as long as the integral is finite we can just normalize it (for this we need to allow resizing units - someone can demand 0.43 units)
2. If we want the demand curve to be the CDF of the marginal demand distribution, it needs to be monotonic (decreasing)
3. Everything should be (almost) continuous
Under these assumptions i think any demand curve is a CDF of the marginal demand distribution (and vice versa)
Definitely beyond what you where describing here, but some interesting thoughts on how such a function would look/behave in the following situations:
1. Demand for a good that is imperfectly subsitutatable, especially during the internet age. Research has shown that people have become less price sensitive due to the internet (one-click reordering).
2. A good whose benefit is dependent on usage. Social media is a good that research experiments have shown to have negative value and thus should have no demand. However, if your friend is using social media, then not being on social media has even larger negative value on the non-user of social media. So everyone ends up using it, which ultimately makes everyone worse off.
Just some supply/demand thoughts I've had and your post triggered these thoughts again :)
Yeah, those cases seem difficult to represent. You might be able to use a third dimension for 'friend's choice/usage' or price in a substitutable market, but it seems complicated.
Super cool idea!
I was trying to go over the math to see if it checks out, and I think it does under some assumptions.
1. we need the marginal demand distribution to be a probability distribution:
a. The marginal demand for any price is non-negative
b. we need the entire integral to equal 1. This might sound rather limiting, but as long as the integral is finite we can just normalize it (for this we need to allow resizing units - someone can demand 0.43 units)
2. If we want the demand curve to be the CDF of the marginal demand distribution, it needs to be monotonic (decreasing)
3. Everything should be (almost) continuous
Under these assumptions i think any demand curve is a CDF of the marginal demand distribution (and vice versa)
Do a Pareto curve next
Cool visualization of this!
Definitely beyond what you where describing here, but some interesting thoughts on how such a function would look/behave in the following situations:
1. Demand for a good that is imperfectly subsitutatable, especially during the internet age. Research has shown that people have become less price sensitive due to the internet (one-click reordering).
2. A good whose benefit is dependent on usage. Social media is a good that research experiments have shown to have negative value and thus should have no demand. However, if your friend is using social media, then not being on social media has even larger negative value on the non-user of social media. So everyone ends up using it, which ultimately makes everyone worse off.
Just some supply/demand thoughts I've had and your post triggered these thoughts again :)
Yeah, those cases seem difficult to represent. You might be able to use a third dimension for 'friend's choice/usage' or price in a substitutable market, but it seems complicated.
Great post. I hadn’t thought about it this way, but the intuition is clear.