18.7 The “Inverse Demand” Curve Facing a Firm

OK, now that we’re reviewed elasticity, we can see how it applies to the revenue function of a firm.

We will assume that the firm sets a single price $p$, at which it sells all of its units. In particular, this means that we’re not thinking about a firm like an airline or movie theater that might sell the same product (a seat) to different customers for a different price. (That’s called “price discrimination,” and we’ll get to it in Econ 51.)

Furthermore, we will assume that the price the firm can charge may depend on the quantity of output it wants to sell: that is, if it produces $q$ units, the most it can charge is given by some function $p(q)$. Note that this is related to the notion of a “demand function,” but a demand function describes consumers’ behavior as a response to price: that is, $D(p)$ gives the quantity demanded by consumers when the price is $p$. Because we’re thinking of this from the firm’s perspective, we reverse the logic: we think of the price $p$ the firm could charge as a function of the number of units it wants to sell, $q$. For this reason we call it an “inverse demand function,” or, when plotted, an “inverse demand curve:”

[ See interactive graph online at https://www.econgraphs.org/graphs/market_power/profit_max/inverse_demand ]

In general, we might imagine that a firm faces a downward-sloping inverse demand curve: that is, if it wants to sell more units, it needs to lower its price. However, there’s an important special case to consider: the case of a “competitive” or “price taking” firm.

[ See interactive graph online at https://www.econgraphs.org/graphs/firm/supply/inverse_demand_competitive ]