The shipping strategies of internet retailers: Evidence from internet book retailing

Abstract

Managing the shipment of goods to consumers is one of the central aspects of retail competition on the internet. In this article, we analyze internet retailers’ shipping strategies using data from the internet book retailing industry. We find that, controlling for a variety of observable firm characteristics, firms with lower product prices offer lower shipping fees and higher quality shipping in terms of average delivery time, compared to firms with higher product prices. These patterns cannot be readily reconciled with a large class of models of competition under perfect consumer information. Theories based on imperfect consumer information can explain the findings better.

Appendices

Appendix A:   Equilibrium in the vertical product differentiation model

This appendix solves for the equilibrium of the vertical product differentiation model of Section 2.1. Given any fixed choice of shipping options in the first stage, the consumer type, $\alpha ^{*}$, who is indifferent between purchasing from the two firms, is given by $\alpha ^{*}=\frac{\Delta p+\Delta f}{\Delta q}$, where $\Delta x=x_{1}-x_{2}$ for $x=p,f,q$. All consumers with types in $[\alpha ^{*},1]$ buy from firm 1, and the rest from firm 2. The profit maximization problem for firm 1 in the second stage is then given by

$$\max_{p_{1}}(p_{1}-c_{1}+f_{1}-c(q_{1}))\left( 1-\frac{\Delta p+\Delta f}{\Delta q}\right), $$

which generates the first order condition for $p_{1}$

$$ \left( 1-\frac{\Delta p+\Delta f}{\Delta q}\right) -\frac{1}{\Delta q}(p_{1}-c_{1}+f_{1}-c(q_{1}))=0. $$

(A.1)

Similarly, for firm 2 we have

$$ \left( \frac{\Delta p+\Delta f}{\Delta q}\right) -\frac{1}{\Delta q}(p_{2}-c_{2}+f_{2}-c(q_{2}))=0. $$

(A.2)

From (A.1) and (A.2), we obtain

$$\displaylines{ p_{1} = \frac{2}{3}\Delta q+\frac{2}{3}c_{1}+\frac{2}{3}c(q_{1})+\frac{1}{3}c_{2}+\frac{1}{3}c(q_{2})-f_{1}, \cr p_{2} = \frac{1}{3}\Delta q+\frac{1}{3}c_{1}+\frac{1}{3}c(q_{1})+\frac{2}{3}c_{2}+\frac{2}{3}c(q_{2})-f_{2},\cr \Delta p = \frac{1}{3}\left( \Delta q+\Delta c+\Delta c(q)\right) -\Delta f, }$$

(A.3)

where $\Delta c(q)=c(q_{1})-c(q_{2}).$ From (A.3 ), the total price, $P_{i},$ a consumer pays if he buys from firm i is

$$P_{i}=p_{i}+f_{i}=(1-\frac{i}{3})\Delta q+\frac{2}{3}(c_{i}+c(q_{i}))+\frac{1}{3}(c_{j}+c(q_{j})), $$

(A.4)

for $j\neq i.$ Now consider the first stage, where firms choose their qualities and associated fees. Firm 1 solves

$$ \max_{(q_{1},f_{1})}(p_{1}-c_{1}+f_{1}-c(q_{1}))\left( 1-\frac{\Delta p+\Delta f}{\Delta q}\right), $$

which, after substituting for p ₁ and Δ p using (A.3), is equivalent to

$$ \max_{q_{1}}\left( \frac{[2\Delta q-\Delta c-\Delta c(q)]^{2}}{\Delta q}\right). $$

(A.5)

Note that shipping fee $f_{1}$ does not appear in the objective function, making it impossible to identify $f_{1}$, or equivalently, $p_{1}$. A similar conclusion applies to the first-stage maximization problem of firm 2. To complete the solution, we need to determine the choice of quality by each firm. This problem is analyzed by Motta (1993) for firms with equal marginal costs and the results apply here with little modification. Either firm can become the high quality firm, depending on the parameters.

Appendix B:  Proof of Proposition 2

We follow the basic arguments in Salop and Stiglitz (1977). Assume for now that $\sigma$ and $\omega$ are not too large so that high price firms do not charge monopoly base prices and shipping fees. We consider later the cases of large $\sigma$ and large $\omega$. In the proposed equilibrium, the base price and fee charged by a high price firm must be such that a naive consumer is indifferent between becoming informed and purchasing randomly. From (7), (8) and (9), we obtain²²

$$ p^{H}-p^{L}\leq \sigma , $$

(B.1)

$$ p^{H}+\mu f^{H}\leq p^{L}+\mu f^{L}-\mu \Delta u+\sigma +\omega . $$

(B.2)

First, we characterize the low-base-price firms’ equilibrium behavior. Because each skilled consumer has access to a list of base prices in the market, such a consumer has no incentive to search any further if he first visits the firm with the lowest base price, because in expected terms no other firm can bring higher surplus. Furthermore, all firms with low price must charge $P^{L}=$ $p^{L}+f^{L}=p^{* }+c^{H},$ where $p^ {*}=2\sqrt{Fc}$ is the competitive base price equal to the minimum average cost of sale, and $p^{L}\geq 0$ and $f^{L}\geq 0.$ ²³ If $P^{L}$ was greater than $p^{* }+c^{H},$ a firm could lower its base price $p^{L}$ slightly and could attract all skilled consumers and increase its profits, because skilled consumers first visit the firm with the lowest base price. Now, consider deviations by a firm from $P^{L}$. Deviating to a price higher than $P^{L}$ results in a loss of all skilled customers, and induces naive consumers to become informed via (7), which implies that the deviating firm also loses its naive customers. Charging a price below $P^{L}$ would be pricing below minimum average cost, resulting in a loss.

The partition of the total price $P^{L}$ must be such that $p^{L}=0,$ and $f^{L}=p^{*}+c^{H}$. Suppose that $p^{L}$ was above zero. Then, any firm charging this base price could lower its price slightly and attract all skilled consumers, because these consumers initially visit the firm with the lowest base price. If $p^{L}=0,$ no firm deviates to raise its price slightly either, because then the firm would attract no skilled consumers, and naive consumers would prefer to become informed because the benefits to search would increase. Because we assumed that base prices below zero are not feasible, we must then have $p^{L}=0$ and $f^{L}=P^{L}=p^{*}+c^{H}.$

No low price firm wants to unilaterally deviate from high quality and offer low quality instead. A firm that deviates and offers a low quality incurs a shipping cost of $c^{L}$ and can offer a consumer a surplus of at most $u^{L}-c^{L}.$ Because $u^{L}-c^{L}<u^{H}-c^{H},$ no skilled consumer prefers to purchase from this firm.

Next, consider the high price firms’ equilibrium behavior. From (8), any base price $p^{H}>$ $p^{L}+\sigma$ cannot be part of the proposed equilibrium, because at that price a naive consumer prefers to become informed. Therefore, $p^{H}\leq p^{L}+\sigma$. If $p^{L}<p^{H}<p^{L}+\sigma ,$ then a firm charging $p^{H}$ could deviate to $p^{L}+\sigma$ without inducing its naive customers to become informed. It follows that $p^{H}=p^{L}+\sigma$. It is not profitable for a firm with price $p^{H}$ to deviate locally. If a firm raises its price, it loses all its customers, as they prefer to become informed, as implied by (8). If a firm lowers its price, then the expected price in the market falls, but the minimum price, $p^{L}$, does not change. Benefits from becoming informed on the left hand side of (8) then decrease. The purchasing behavior of naive consumers does not change. The behavior of skilled consumers does not change, either. Thus, the deviation is not profitable, as it only lowers profits. This implies $p^{H}=\sigma ,$ since $p^{L}=0.$ Therefore, from (B.2), we have $f^{H}\leq f^{L}-\Delta u+\frac{\omega }{\mu }.$ It is easy to see that this must hold with equality, $f^{H}=f^{L}-\Delta u+\frac{\omega }{\mu },$ because, as in the case of base price, deviation from this fee in either direction results in a loss of profit.

Finally, consider the possibility of a high price firm deviating from low quality and offering high quality. If the deviant continues to charge $p^{H}$ and $f^{H},$ the benefits to becoming informed on the left hand side of (9) go down, because $u^{H}>u^{L}$. Naive consumers continue to visit stores randomly, meaning that the deviant does not acquire any additional customers. But then the deviant makes less profit than other high price firms because its cost of shipping has increased from $c^{L}$ to $c^{H}.$ If it increases its price to compensate for this cost, (8) then implies that naive consumers want to become informed, and the deviant attracts no consumers. A similar argument applies to the possibility of increasing the shipping fee to compensate for the higher cost. Therefore, a high price firm does not want to deviate from low quality shipping and alter its price.

In equilibrium, low price firms sell to skilled consumers and lucky naive consumers who sample a low price firm. High price firms sell only to naive consumers. Therefore, the quantities sold by a low and a high price firm, respectively, are

$$ x^{L}=\frac{N\phi }{\mu n}+\frac{N(1-\phi )}{n}, $$

(B.3)

$$ x^{H}=\frac{N(1-\phi )}{n}.\label{outs1}\hphantom{000 000} $$

(B.4)

Free entry ensures zero profit for each firm in the market. For firms with low base price, the total price must equal the minimum average cost, and for firms with high base price, total price must equal the average cost:

$$ p^{L}+f^{L}=p^{* }+c^{H}=\frac{F}{x^{L}}+cx^{L}+c^{H}, $$

(B.5)

$$ p^{H}+f^{H}=p^{*}+c^{H}+\sigma -\Delta u+\frac{\omega }{\mu }=\frac{F}{x^{H}}+cx^{H}+c^{L}. $$

(B.6)

Given the expressions for $x^{L}$ and $x^{H}$ in (B.3) and (B.4), the equations in (B.5) and (B.6) jointly determine the number of firms, n, and the fraction of low price firms, $\mu$. This finishes the characterization of the proposed equilibrium.

If $\sigma$ is very large or both $\sigma$ and $\omega$ are very large, $p^{H}$ is the monopoly price $s$, and high price firms can afford to offer high quality and charge a monopoly fee of $f^{H}=u^{H}$. In this case, we still have $p^{H}>p^{L}$ and $f^{H}>f^{L}.$ If only $\omega$ is very large, $p^{H}=p^{L}+\sigma ,$ and $f^{H}=u^{H},$ and the ranking of base prices and shipping fees are still the same.

Finally, consider the conditions for the proposed equilibrium to exist and to be unique. As in Salop and Stiglitz (1977), we need the fraction, $\phi ,$ of skilled consumers not be too large and/or the declining portion of the average cost curve not be very steep. If the market consists of primarily skilled consumers (large $\phi$) to start with, there is a small market for firms with high base price, as they sell only to unlucky naive consumers. If the average cost curve is very steep, there will not be enough naive consumers to support even just one high-price firm. The required condition is then $(1-\phi )>x^{H}/x^{L}$. Additionally, we need global deviations by a high price firm below $p^{H}$ not be profitable, as opposed to local price deviations considered above. As shown in Salop and Stiglitz (1977), such deviations do not occur if there is a large number of consumers in the market.²⁴ A similar argument applies in our case. The equilibrium in Proposition 2 is unique if the number of consumers $N\rightarrow \infty$, which also follows from the arguments in Salop and Stiglitz (1977). We believe that the assumption of large number of consumers fits well to the on-line book retailing.

Appendix C:   Simultaneous discovery of base price and shipping fee

Consider now the case where becoming informed is equivalent to learning all base prices, shipping qualities and shipping fees, perhaps through a good search engine. Then, under the proposed equilibrium, (6) is now equivalent to

$$ p_{(1)}+f_{(1)}\leq p_{(2)}+f_{(2)}, $$

which implies that base price and shipping fee for low price firms are identified up to the total price $P^{L}=p^{*}+c^{H}.$ Also, (7), (8) and (9) now imply

$$ P^{H}\leq P^{L}+\frac{\sigma }{1-\mu }-\Delta u, $$

(C.1)

$$ p^{H}\leq P^{L}+\sigma -(1-\mu )\Delta u-E[f], $$

(C.2)

$$ P^{H}\leq P^{L}+\sigma +\omega -\Delta u. $$

(C.3)

Then, (C.2) allows identification of the high base price, $p^{H}$. It is easy to verify that

$$\displaylines{ p^{H} = P^{L}+\sigma -(1-\mu )\Delta u-E[f],\cr f^{H} = P^{L}+\min \left\{\sigma +\omega ,\frac{\sigma }{1-\mu }\right\}-\Delta u-p^{H},\cr P^{H} = P^{L}+\min \left\{\sigma +\omega ,\frac{\sigma }{1-\mu }\right\}-\Delta u. }$$

Thus, $P^{H}>P^{L}$ as long as $\min \{\sigma +\omega ,\frac{\sigma }{1-\mu }\}>\Delta u.$ The last inequality holds, for instance, if $\sigma >\omega ,$ because $\omega >\Delta u.$ Since $P^{L}\geq p_{i}^{L}$ for all choices of $p_{i}^{L}\in \lbrack 0,p^{*}+c^{H}]$ by a low base price firm $i$, we have $p^{H}>$ $p_{i}^{L},$ as long as $\sigma -(1-\mu )\Delta u-E[f]>0.$ Thus, controlling for quality difference, we have $p^{H}>$ $p^{L},$ as long as $\sigma$ is large enough. Also, $f^{H}=\min \{\omega ,\frac{\mu \sigma }{(1-\mu )}\}-\mu \Delta u+E[f]$ and $E[f]=(1-\mu )f^{H}+\frac{1}{n}\sum_{i=1}^{n\mu }f_{i}^{L},$ where $f_{i}^{L}\in \lbrack 0,p^{*}+c^{H}]$ is the shipping fee for the $i$-th firm low-base-price firm, and the summation is taken over firms with low base price (assuming integer number of firms). Therefore, $f^{H}=\min \{\frac{\omega }{\mu },\frac{\sigma }{(1-\mu )}\}-\Delta u+\frac{1}{n\mu }\sum\nolimits_{i=1}^{n\mu }f_{i}^{L}.$ Since $\frac{1}{n\mu }\sum\nolimits_{i=1}^{n\mu }f_{i}^{L}\leq p^{*}+c^{H},$ $f^{H}$ exceeds any $f_{i}^{L}$ if $\min \{\frac{\omega }{\mu },\frac{\sigma }{(1-\mu )}\}+p^{*}+c^{H}>\Delta u.$ Since $\omega >\Delta u,$ this last condition holds for large enough $\sigma .$

Appendix D:  Data

Our data were collected in two different points in time. The first wave was collected in a single week during October of 2003, and includes 133 books sold by 21 sellers. Many books are common across sellers. The second wave was collected in a single week during January of 2004, and includes 129 books sold by 21 sellers. We avoided the holiday seasons in November and December, because most internet sellers engage in unusual promotions in pricing and shipping during these periods. We kept the duration of data collection as short as possible (one week) to ensure sure that no substantial changes took place in seller composition, shipping fees, and prices.

D.1.  Books

To focus on as many common books as possible across sellers, we only selected relatively more popular books sold online. We chose two categories: bestsellers and technical books. Having two different categories of books is also important in demonstrating that the results apply to different categories in a similar way. The data for 133 books collected in October 2003 consist of 60 New York Times bestsellers and 73 Amazon.com technical bestsellers. The data for 129 books collected in January 2004 consist of 60 New York Times bestsellers and 69 Amazon.com technical bestsellers. Since these books are sold by many sellers, we obtain sufficient variation in prices and shipping fees across sellers.

D.2.  Sellers

The data cover U.S.-based sellers that together account for a very large share of the all book sales in the U.S., including all major sellers and many smaller ones. 37 of the sellers provide regularly reported shipping options based on the quantity of books shipped, and we included all of them in the analysis of shipping fee-quality schedule. We excluded all sellers that based their shipping fee schedule on weight of books sold, rather than the quantity of books, to make the structure of shipping policies as uniform as possible across sellers. We also paid special attention to include a variety of sellers: general book sellers, specialized ones, and those that sell products other than books. This way our sample represents a broad set of sellers competing in the book market, not just those that are specialized in books. For the analysis of base and total prices, we focus on 21 sellers (out of 37 initially selected) for which price information on several books was available through the web-crawler www.fetchbook.info. For the remaining sellers, the crawler did not provide price quotes for a sufficient number of books. Thus, our sample of 21 retailers represent a segment of the market where retailers’ book selections mostly overlap.

D.3.  Variables

Variables in our data include book prices and seller characteristics (see Table 1), such as average delivery time, number of shipping options, age, scope, etc. We gathered price quotes using the web-crawler www.fetchbook.info. Unlike a search engine or a shopbot, this crawler does not charge any fee to retailers for their prices to be quoted. The wide coverage by this web-crawler alleviates concerns about certain sellers being left out from the price list, which results in a selection problem. The crawler claims to search across 126 on-line book retailers, but most books we searched for were available at a much smaller number of retailers. We double-checked the accuracy of book prices posted by the crawler by directly visiting retailers’ websites and found, for a large sample of books, a 100% match in prices. Shipping options and many other seller specific variables were collected directly from each retailer's website. The proxy for firm size, the number of websites that have a link to a particular seller's website (SIZE), as well as the seller's number of years of operation on the internet (AGE), was obtained from the information on websites provided by www.alexa.com. The only book-seller specific variable, availability (AVAIL), is the seller's reported expected time for a book to be shipment ready.