Critical Mass Problems: Difference between revisions
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*The remainder of students may tend to participate more when others participate and less when others do not. | *The remainder of students may tend to participate more when others participate and less when others do not. | ||
Below are two fairly more robust critical mass models. | |||
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==The Used Car Market== | ==The Used Car Market== | ||
Revision as of 21:51, 28 April 2009
A critical mass is considered to be the amount necessary to create a system that will sustain itself in perpetuity. Whenever one element is added to or substracted from this mass, the system begins to limitlessly deteriorate. These kinds of situations are ever present in society and the sciences.
For instance, think about an average seminar of students:
- Certain students will always participate
- Conversely, certain students will never participate
- The remainder of students may tend to participate more when others participate and less when others do not.
Below are two fairly more robust critical mass models.
The Used Car Market
It is well known that as soon as a new car is bought and driven off the lot, its value drops significantly. Walrasian economics cannot explain this phenomena.
The Model:
Cars can be divided into two categories and two subcategories:
- First, a car is new or used
- Second, a car is good or bad (a "lemon" or not)
The purchaser of a new car soon finds out whether or not his car is a lemon but, importantly, he is the only one who knows this.
Someone in the market for a used car knows that the market is comprised of both lemons and non-lemons. Knowing this, the used car purchaser seeks to bid no more than a weighted average of the price they'd pay for a lemon and the price they'd pay for a non-lemon using their best estimate of the populations for each.
Let: qL=the estimated population of lemons pL=price willing to pay for a lemon pNL'=price willing to pay for non-lemon
Then,
Bid=q*pL+(1-q)*pNL
The important part to note is that the bid price will be lower than pNL but higher than pL. Owners of non-lemons will have less incentive to sell their cars while owners of lemons will have more.