Under first-degree price discrimination, the firm examines each individual’s de- mand separately, and charges each consumer the maximum price he or she is will- ing to pay for every unit. Charging demand price (i.e., the maximum price) for every unit of the product effectively transforms every bit of consumer surplus into economic profit for the price-discriminating firm. While first-degree price dis- crimination is indeed “perfect” in the sense that it captures all consumer surplus, achieving this degree of pricing perfection is hardly ever possible. To know the maximum possible price for every unit sold, a firm must possess a tremendous amount of extremely accurate information about the demands of each and every
consumer arbitrage When low-price buyers resell a product to buy- ers in a high-price mar- ket, which establishes a single, uniform price.
Now try Technical Problem 1.
first-degree price discrimination Every unit is sold for the maximum price each consumer is willing to pay, which allows the firm to capture the entire consumer surplus.
consumer. Buyers, of course, will try to hide or misrepresent their true willingness to pay for a product.
Examples of successful first-degree price discrimination are rather hard to find.
Perhaps the closest situation occurs at auction houses or on Internet auction sites.
While auction methods vary, the fundamental purpose of auctions is generally to identify the buyer who values an auction item most and extract the highest pay- ment possible from that buyer. To the extent that an auction is successful in these two tasks, consumer surplus is extracted from buyers and paid to sellers (and auc- tioneers). Examples of attempted perfect price discrimination can be found in most any market where price is negotiated on individual sales. Automobile salespeople, for example, try to size up each customer’s willingness to pay by finding out how much income a potential buyer makes, whether the buyer currently owns an old or broken-down car, and so on. Experienced sports ticket scalpers can quickly and accurately estimate a buyer’s willingness to pay for tickets. Scalpers look for in- dicators of affluence and strong team loyalty. A potential ticket buyer who arrives at a stadium decked out in the team’s jersey and ball cap, wearing a 24-karat-gold University of Miami class ring, with the team mascot tattooed on his forearm, and acting eager to get seated before kickoff is certainly going to pay much more for his ticket than a buyer who avoids such obvious signals of high willingness to pay (i.e., high demand price).
To illustrate first-degree price discrimination, let’s suppose the firm discussed in the previous section wishes to avoid the curse of uniform pricing by practicing perfect price discrimination. Figure 14.2 reproduces the demand and cost condi- tions for this firm. To keep matters simple, let’s further suppose that each con- sumer buys just one unit of product. At a price of $7 (point U), for example, 3,000 consumers each buy one unit of the good. The firm knows that it faces precisely demand curve D and wishes to charge the demand price—the maximum price a buyer is willing to pay—for every unit it sells. When it sells every unit at its demand price, the firm’s marginal revenue is no longer the curve labeled MR in Figure 14.1. Instead, marginal revenue under perfect price discrimination is the firm’s demand curve D, because every unit sold adds P dollars to total revenue.
Thus D = MR in Figure 14.2. Since the equivalence of demand and marginal revenue is crucial for understanding perfect price discrimination, we must care- fully examine this relation before we continue with our analysis.
Under perfect price discrimination, the 3,000th unit adds $7 (its demand price) to total revenue. However, under uniform pricing (see Figure 14.1), the 3,000th unit adds only $4 to total revenue, because increasing sales from 2,999 to 3,000 units requires the firm to cut price slightly below the demand price for the 2,999th unit. For this linear demand curve, the demand price for 2,999 units is $7.001 (= 10 2 0.001 × 2,999).2 From the firm’s point of view, the trouble with uniform pricing is now clear: selling the 3,000th unit requires cutting price by $0.001 (one- tenth of a penny) on every unit sold, not just the incremental unit. With a bit of
2You can confirm, based on Chapters 2 and 6, that the inverse demand equation for D in Figures 14.1 and 14.2 is P = 10 2 0.001Q.
arithmetic, you can verify that the price cut required to sell the 3,000th unit reduces that unit’s contribution to total revenue by approximately $3 (= 2,999 × $0.001).
Thus, marginal revenue from selling the 3,000th unit is only $4 (= $7 − $3), which is distinctly less than its price, $7. Perfect price discrimination avoids this loss of revenue by selling every unit of the product at a different price.
To maximize profit under first-degree price discrimination, the firm will haggle over price to sell additional units until it reaches a total of 6,000 units, which is the output level for which MR = MC. Any units sold beyond the 6,000th unit can be sold only at prices below their marginal cost of production. At point F, the perfect- price-discriminating firm charges 6,000 different prices—consumers each buy just one unit—making it possible for the firm to collect total revenue equal to the area of the shaded trapezoid 0gFa in Figure 14.2. Total revenue for the perfectly discrim- inating firm is $42,000 [= 6,000 × ($10 + $4)y2]. The total cost of producing 6,000 units is $24,000 (= 6,000 × $4), and the firm earns $18,000 (= $42,000 2 $24,000) of economic profit, which is the area of triangle acF in Figure 14.2.
First-degree price discrimination is clearly the goal of sellers who negotiate prices for each individual customer. However, perfect price discrimination is sel- dom actually achieved because, even if they can cheaply identify and separate lower- and higher-priced buyers, most firms do not know precisely the demand prices for every buyer of every unit sold. Second-degree price discrimination requires much less information about buyers’ preferences.
F I G U R E 14.2 First-Degree (Perfect) Price Discrimination:
Capturing All Consumer Surplus
0 1,000 2,000
Quantity
3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 1
2 3 4 5 6 7 8 9 10
Price and cost (dollars)
D = MR g
c a
U
F MC = AC
Total revenue = Area 0gFa
= $42,000