Value-based pricing (or price discrimination)

I have been reading Competitive Solutions by Preston McAfee and just got through the chapter on pricing. I learnt a number of useful things, one of them being the idea of value-based pricing.

It is, by now, part of the received wisdom that the best strategy for a startup entering an industry is to define a niche or narrowly-defined market segment (of size roughly equal to next year’s expected revenues), to focus its marketing and product development efforts on that niche, and to aim for market leadership (defined as 40% of market share or more) within that segment. This should sound familar to all Chasmologists.

As a consequence of focusing on an underserved niche and of having a highly differentiated product with no obvious substitutes, the startup (if successful) may find itself being in the position of a monopoly within that segment. How should it set its prices? (More generally, how should any monopoly set prices?) This, of course, depends on a number of other considerations including: what is the relative importance (in terms of company valuation) of gaining revenues versus profits?, etc. Ignoring such questions, let us assume that the only goal is to maximize profits. Given this, how should the price be set?

Pricing is often determined by “cost-plus” arguments (tack on a 40% margin, etc.) or based on competitive proxies (“how much does Cisco charge for an analogous product in the enterprise space?”). Neither is a smart strategy for a monopoly (what if you end up charging $3K on a cost-plus basis when the market is willing to pay $5K per unit? Or what if your market is SMBs in India?: the reasoning of “MSFT charges $100 per Office license, so my pricing should be $x” is equally a bad idea). Well, it turns out that there is a simple pricing formula (see ‘Competitive Solutions’) for the profit-maximizing price: the “Monopoly Pricing Rule”.The rule is

P= MC*E/(E-1)

(Click below to continue reading)

Here E is the elasticity of demand – if a 1% decrease in price results in a 2% increase in quantity demanded, the elasticity is 2. MC is the marginal cost of producing an extra unit of the good. The Monopoly Pricing Rule provides the profit-maximizing price. It is an easy exercise for the reader to derive this formula (I had some fun this morning deriving it. In deriving the formula, it’s useful to note that (i) elasticity is defined for 1% increase/decrease in price - larger changes will need to be appropriately compounded, (ii) (a^x)'= (a^x) ln(a), (iii) ln(1+x)~x). It is also easy to generalize to the cases where the firm wishes to maximize not profits, but revenue, etc. (The revenue-maximizing price is P=MC/E, which is a markdown).

The big assumptions in deriving this rule are (1) no price competition (discussed above) and (2) that there is a single elasticity of demand. The latter assumption can probably be relaxed at the expense of complicating the formula.

The marginal cost is available to the firm. The elasticity of demand is a little harder to determine, but can presumably be obtained through customer interviews, polls, examination of demand for complementary/competitive products sold into the same market segment, etc.

When marginal costs are zero (approximately true for software companies), the profit-maximizing prices make the elasticity of demand equal to 1, i.e., with no marginal cost, the profit-maximizing price is the point on the demand curve so that the elasticity is one.

If you have the good fortune of being a monopoly in two different market segments, you should price discriminate and price differently for each class of customers (with their distinct elasticities of demand), using the Monopoly Pricing Rule, assuming that there is no risk of arbitrage across segments. So, for instance, if your customers include carriers as well as small ISPs, you should price lower for your ISP customers (they have a higher elasticity of demand).