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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{...


2

Let $x = D(p)$ be the demand for a good if the price is equals to $p$. The inverse demand curve (as you would draw it) is then given by $p = D^{-1}(x)$. It gives the price as a function of the quantity. If there is a rebate of $r$ and if $p$ is the price, then the consumer only pays $p^\ast = p - r$. Then the demand is given by: $$ x = D(p^\ast) = D(p - r). $...


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