# Demand as a function of supply and storage

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!

• The demand for what? Usually prices and income are important explanatory variables when I go shopping. Why should medical equipments matter? Jul 15 at 11:30
• I'm trying to model this situation where supply is proportional to the demand and supply is less than the inventory. The price of the supply and demand do not matter. It is great that in practical situation as you describe the prices of commodity matter, but I'm trying to model this without considering that. Jul 15 at 14:48
• Why does your case need an entirely different treatment? There is a good reason why demand and supply functions depend on the price. It makes sense theoretically and is backed up empirically. Rather than reinventing economics, I'd see how you can incorporate potentially additional drivers of demand, ie limitations to storage space, or cost of storage (if you can outsource it).
– BrsG
Jul 15 at 15:12
• I'm not trying to reinvent economics. Price of the medical supply is already handled by the government and is thus not considered by the hospital. Therefore, demand only depends on the supply and storage. Is there a way to help me around this? Jul 15 at 15:17

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.

• Instead of having price, can we have quantity? I understand your model, but I've not been provided with any price at all. Jul 16 at 9:06
• @IshaanSingh What is the thing which you want to adjust to make supply and demand be the same? Why does supply go down? Why does demand go up? What causes people to want more equipment and manufacturers to produce less equipment (or the converse)? Jul 16 at 9:56