Demand as a function of supply and storage

Question

I'm trying to model a situation where demand is a function of the supply of medical equipments. The equipment costs are already covered, hence price is not taken into consideration. The supply however should be less than the storage. All of the models that are currently over the internet are based on demand and supply equations which are price dependent. Can someone help me formulate an equation in which demand is dependent on the supply and supply is dependent on the demand. However, the supply must be less than the storage of a hospital.

Thanks!

Answer 1

I think your question is a bit strange. If you have demand and supply and you want them to be equal at equilibrium (supply = demand), there should be some third variable that makes the equilibrium possible. Usually this is the price.

Let $d$ be demand $s$ be supply and $i$ be the inventory. Reading your question, you have in mind something like: $$ \begin{align*} &d = f(s),\\ &s = \min\{g(d), i\} \end{align*} $$ If you want to set $d = s$ at equilibrium, you have a problem as substituting $d = s$ gives $d = f(d)$ and $d = \min\{g(d), i\}$ which in general has no solution.

Intuitively you have 3 equations (supply equation, demand equation & equilibrium equation) and 2 unknowns (demand and supply), so your system is overdetermined.