Are there any economic models in which demand is a function of supply?



Answer:
Sure, an economic model that shows the effective level of trendy goods.

Essentially, there was no demand for "Tickle Me Elmo" before he was introduced.

After he was introduced, there was demand based on supply and then after the initial shot, the standard market forces took hold.
In aggregate theory there is Say's law which states that "supply creates its own demand". This is based upon classical theory prior to John Maynard Keynes. The baker doesn't bake bread because he likes to eat bread! Thru the production process incomes are earned which allows him to consume or demand other goods, etc. Is this what you are talking about?
there is something called "network externalities" - a situation when the good is worth more when many people are consuming it. Like game consoles - if many XBoxes are sold already, there will be many games for them, making an XBox more valuable.

Or like cell phone networks - it is not really worth it unless the network covers entire nation.

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