J Brauer | © Stone Garden Economics
One of my favorite economic formulas is Mr. Lerner’s price-markup formula. Close to the heart of business people, it describes a condition that identifies how much the price of a good or service may be marked up over cost.
As my intermediate-level students of microeconomics learn, the Lerner index (L) formula is written as L = (p-MC)/p = – 1/e.
The “p” stands for the market price obtained and the “MC” stands for the cost of providing the product to the market. For example, if the price of a gallon of gasoline is US$3.50, and the tax-inclusive cost of provision is $3.40, then L equals ($3.50-$3.40)/$3.50, or a price markup of about 2.9 percent over cost. (More precisely, the markup is 0.02857 or 2.857 percent).
If due to competition, a firm cannot get away with raising price much over cost, then its markup over cost is small. If, in contrast, a firm has relatively much market power because of lack of competition, then it will get away with a higher markup over cost.
The nifty thing about Mr. Lerner’s formula, however, is not its markup portion but the “-1/e” part. The “e” stands for customers’ price sensitivity, or price elasticity in econ speak, hence the “e”. The more price sensitive are customers, the less they purchase, volume-wise, under rising prices and the more they purchase under falling prices. The precise degree of price sensitivity is given by “e.” In the gasoline example, if the markup part of the formula equals 2.857 percent, then one can work out that “e” equals -0.35. (To check, plug this into the formula: -1/-0.35 = +2.857).
The economic interpretation of e=-0.35 is that a one-percent change in price is associated with only a 0.35-percent change in the quantity demanded. So, if gas prices rise by one percent from $3.50 to $3.535, then the overall quantity of gasoline purchased declines by only about one-third of one percent. Because gas purchases by volume change by a disproportionally small amount (by less than one percent) in reaction to the one-percent price increase, economists refer to this market as “inelastic.” This means that this market is not particularly sensitive to price changes and economists label such goods “necessities.”
All this makes eminent sense: After all, one needs gasoline to drive one’s car. But what is true for the market as a whole, is not necessarily true for each firm that competes in the market. If one gas station raises its price from $3.500 to $3.535, motorists will readily fill up at the competitor station across the street. For this reason, nearby gas stations charge very similar prices, just above cost, and isolated interstate highway stations are able to charge higher prices.
But back to the point about Mr. Lerner’s “nifty” formula. What is nifty is that if we know the current market price and if we know how price sensitive customers are (by observing customers’ buying behavior over time or from customer surveys for example), we can work backward and obtain a sense of what the firms’ cost are likely to be! To wit: If e = -0.35, then -1/-0.35 = +2.857. Apply this into (p-MC)/p, and one can work out that MC, the cost, equals $3.40. Thus one can compute what firms often regard as a closely guarded secret, their cost!
Price sensitivity is a reflection of what customers are willing and able to pay; it is a reflection of the demand side of the market. While firms cannot do much about what people are able to pay, they spend a great deal of effort to influence what folks are willing to pay! If Exxon can convince customers that it has “put the tiger in the tank,” as Exxon’s famous marketing slogan once had it, then people may well be willing to pay a premium on the (albeit mistaken) belief that Exxon gasoline is somehow superior to all other gasolines on the market. Paying a premium means being less sensitive, being less fussy, about paying Exxon’s price. Thus, “e” becomes a smaller number. For example, suppose “e” is only -0.30 for Exxon gas, rather than -0.35. Working backwards, apply -1/-0.30 = +3.333, or 0.03333 percent. Plug this into (p-MC)/p, with cost at $3.40, and one can work out that Exxon can get away with charging $3.517 per gallon. Instead of a markup of 10 cents per gallon, it gets 11.7 cents.
Mr. Lerner came up with this formula in 1934. He made a number of other important contributions to economics, one of which is the Marshall-Lerner condition, the mathematics of which explains why contrary to what we teach in introductory economics, the devaluation of a country’s currency value on the foreign-exchange markets may not necessarily bring about an improvement in its trade balance. Ordinarily, we expect that devaluation makes a country’s products cheaper to purchase: Foreigners should snap up our products. Our exports rise. Similarly, a lower-valued currency makes it more expensive for us to buy other countries’ products, thus lowering our import bill. The combined effect is that higher exports and lower imports should improve the foreign trade position of the country that has devalued its currency. But at the intermediate-level of microeconomics, or in a class on international trade and finance or in a class on development economics, we learn that exports and imports depend not only on the foreign-exchange rate by itself but also on their price sensitivities. If these turn out to be “just so,” then the introductory economics result of an improving trade balance under currency devaluation may in fact not hold.
Mr. Lerner’s work is worth reading about!
J Brauer is Professor of Economics, James M. Hull College of Business, Augusta State University, Augusta, Georgia, USA.