*J. L. Kellogg Graduate School of Management, Northwestern University, Evanston, IL 60208. E-mail: jems@nwu.edu. This article is a revision of a March 1999 working paper. I thank JimAnton, Gary Biglaiser, Ramon Casadesus-Masanell, Johannes Moenius, and Dennis Yao forhelpful suggestions. I thank Ofer Azar for valuable research assistance. I also thank seminarparticipants at West Point, the University of Arizona, Yale School of Management, Wharton, andthe University of Toronto conference on Industrial Organization..

Market Microstructure and Incentives to Invest

Daniel F. Spulber*

Northwestern University

Revised February 2001

Abstract

The paper examines the effects of market organization on incentives to invest and on the volume oftrade. Businesses purchase trillions of dollars worth of resources and manufactured inputs from otherbusinesses both directly and through dealers. Hundreds of new dealers have entered the market withthe advent of business-to-business electronic commerce. Buyers and sellers in business-to-businessmarkets undertake substantial complementary investments that respectively raise the value ofpurchased inputs or lower the cost of manufacturing inputs that are sold. Such complementaryinvestments are likely to be general rather than transaction specific. The paper examines three typesof market organization: a search market, a dealer market and competition between a search marketand a dealer market. In either the search market or the dealer market, there are incentives forinefficient under investment. The search market results in an excessive volume of trade and themonopoly dealer market leads to insufficient trade. Competition between the search market and thedealer market improves incentives to invest. Competition between dealers further enhancesefficiency of investment and the volume of trade. The analysis suggests that the entry of dealers intothe business-to-business market should stimulate investment by business.

1

I. Introduction

What are the effects of market organization on incentives for businesses to invest?

Businesses purchase trillions of dollars worth of inputs from other businesses either directly from

suppliers or indirectly through dealers. With the advent of business-to-business electronic commerce

hundreds of new intermediaries entered such industries as aerospace, agriculture, automotive parts,

chemicals, computers, construction, electronics, energy, financial services, food and beverages,

healthcare, industrial equipment, intellectual property, metals, MRO (maintenance, repair and

operations), office products and supplies, paper, pharmaceuticals, plastics, telecommunications

bandwidth, textiles, and transportation, see Lucking-Reiley and Spulber (2001). At least 600

independent trading exchanges entered the market by mid-2000 with projections of thousands more

potential entrants (Latham, 2000, p. 3). Although shakeouts are expected, entry appears to have

increased the number of intermediaries. Eriksen (2000, p. 7) reports that �To date, there are no

examples of vertical marketplaces disintermediating existing channels.�

Buyers and sellers in the business-to-business marketplace undertake significant

complementary investments. Buyers make investments that enhance the value of purchased inputs

and sellers make investments that reduce the cost of providing inputs. Buyers and sellers often make

these investments before knowing the identity of future trading partners and without being tied

contractually to specific trading partners, so that these investments are general rather than transaction

specific. The expectations of buyers and sellers regarding prices, transaction costs, the likelihood of

completing a transaction, and the characteristics of potential trading partners, will have important

effects on the marginal value of complementary investment. The expected returns to investment thus

depend on the institutions of exchange that buyers and sellers encounter, that is, on the

2

microstructure of business-to-business markets. Knowing the effects of market microstructure on

investment makes possible the design of more efficient markets. The purpose of this paper is to

examine the impact of different market microstructures on buyer and seller incentives to invest. The

results suggest that the entry of dealers should stimulate investment by businesses and enhance the

efficiency of trade.

The paper examines three alternative market microstructures: a search market, a dealer

market, and competition between a search market and a dealer market. These market organizations

affect investment efficiency because they impact the marginal return to investment. I show that

search markets lead to inefficient investment due to the uncertainty of the search process and since

buyers and sellers share the marginal gains from investment after a match is made. This effect is

similar to the traditional hold-up problem because a lack of contractual commitment in search

markets affects incentives even if investment is not transaction specific. Next, I show that a

monopoly dealer market can make matters worse. Even though the dealer commits to bid and ask

prices, investment inefficiency occurs because a dealer with market power chooses a monopoly price

spread that reduces the volume of trade.

When there is competition between a search market and a dealer market, I show that

incentives to invest are enhanced for several reasons. The market power of the dealer is mitigated

by the search market which reduces the dealer�s price spread. Moreover, the presence of the search

market gives some low-value buyers and high-cost sellers the possibility of trading within the price

spread, so that the search market improves investment efficiency in a manner resembling contract

contingencies. Finally, the presence of the dealer improves the efficiency of search by offering price

commitments for high-value buyers and low-cost sellers thus enhancing investment efficiency. In

3

addition, the price spread makes the lowest-value buyers and highest-cost sellers inactive, leading

to self-selection in which only intermediate value buyers and intermediate-cost sellers enter the

search market, thus improving the efficiency of the search market.

Markets with general investments provide ex ante incentives to invest, that is, anticipated

terms of trade with potential trading partners affect returns to investment. Companies often do not

know the identity of potential trading partners when making investments, which suggests that many

types of capital investment by buyers and sellers are not transaction specific. The analysis shows that

the establishment of centralized business-to-business dealers, in tandem with informal search

markets, improves economic efficiency relative to decentralized search markets alone. Competition

between multiple dealers narrows the price spread and crowds out the search market, leading to first-

best investment and to an efficient volume of trade. Therefore, increased competition between

intermediaries should lead to improvements in the efficiency of business-to-business markets and

consequently greater investment by companies that are customers and suppliers in those markets.

I begin by examining a decentralized search market with random matching. Buyers and

sellers meet and bargain over the terms of trade. I show that random matching is inefficient because

low-value buyers and high-cost sellers can complete trades successfully, possibly excluding high-

value buyers or low-cost sellers. This lowers the total gains from trade and results in a volume of

trade that is greater than the efficient level. The inefficiency of random matching reduces the returns

to investment, leading to under investment at the market equilibrium.

Next, I examine intermediated exchange by considering a market with a single intermediary

who deals with many buyers and sellers. The intermediary posts a bid price for sellers and an ask

price for buyers, who then choose whether or not to transact at the posted prices. Unlike random

4

matching, the price spread excludes low-value buyers and high-cost sellers. Buyers and sellers invest

before observing the intermediary's prices while the intermediary sets prices without observing

investments. I assume that investments and prices are determined at a Nash equilibrium, that is,

equilibrium investments and equilibrium prices represent strategic best responses. Because the

intermediary follows a Nash strategy in setting prices, prices are not directly tied to investment

levels, rather, they are a best response to equilibrium investment levels. Buyers and sellers are not

subject to opportunism from contract renegotiation because the intermediary has no incentive to

change prices in equilibrium. Since prices are not dependent on investment levels, pricing by the

intermediary encourages investment relative to bilateral negotiation between buyers and sellers.

However, the stimulus to capital investment from equilibrium prices is offset by the intermediary's

monopoly price spread, which reduces the marginal return to investment for buyers and sellers.

I then combine the direct exchange and intermediated exchange models to examine

competition between the decentralized search market and the intermediary. I show that the

combination of the two markets improves incentives to invest for buyers and sellers. Competition

between direct and intermediated exchange reduces the intermediary's market power and narrows

the bid-ask spread. Moreover, competition allows buyers and sellers to self-select, with high

willingness-to-pay buyers and low-cost sellers trading with the intermediary, and buyers and sellers

with valuations within the spread entering the search market. The self-selection of buyers and sellers

reduces the economic impact of costly searching and matching. Very-high-cost sellers and very-low-

value buyers are inactive in equilibrium. This means that they do not enter the matching market,

which alleviates the inefficiency of random matching within that market. Moreover, because they

are dealing with the intermediary, high-value buyers and low-cost sellers do not face any risk of

5

exclusion from the market. The combination of the reduced market power of the intermediary and

the self-selection of buyers and sellers choosing between the two markets increases the marginal

return to investment relative to either the search market or the dealer market alone, thus increasing

equilibrium investment.

The model of a dealer posting bid and ask prices follows standard models of financial

intermediaries beginning with Garman (1976), see Spulber (1996a, 1999) for a more comprehensive

survey of market microstructure models. I extend Gehrig�s (1993) basic model of competition

between a dealer and a search market by considering a two-stage setting with investment by buyers

and sellers in the first stage and Nash bargaining in the second-stage search market. Gehrig (1993)

does not consider investment and assumes first-and-final offer bargaining under asymmetric

information. Rubinstein and Wolinsky (1987) allow intermediaries to compete with direct exchange

in a random matching model with bilateral bargaining but also without investment. Spulber (1996b)

examines competition between dealers when buyers and sellers search across dealers.

A number of related papers examine investment incentives in a competitive framework with

general investments, although they do not consider the effect of intermediaries on the market

equilibrium, see Acemoglu (1996, 1997), Acemoglu and Shimer (1999) and Felli and Roberts

(2000). The large search literature recognizes inefficiencies from random matching but does not

consider investment or intermediation, see the discussion in Osborne and Rubinstein (1990) and

Pissarides (2000, pp. 183-203). The analysis of intermediation presented hear sheds light on the

causes of search inefficiency.

The article is organized as follows. Section II presents the basic model of investment and

exchange and examines efficient investment with efficient matching. Section III examines the search

6

market by setting out a second-best efficiency criterion for when matching is random and shows that

under investment is inefficient relative to both the first-best and second-best criteria. Section IV

examines investment when there is a single dealer. Section V considers competition between a dealer

and the search market. Section VI addresses competition between dealers. Section VII considers

some empirical implications and provides additional discussion of the results and related literature,

and Section VIII concludes.

II. The Basic Framework

Consider a market with many heterogeneous buyers and sellers who make irreversible

investments. Buyer investments enhance their expected willingness to pay and seller investments

lower their expected production costs. Investments are general, that is, they do not depend on the

identity or characteristics of prospective trading partners. The sequence of events is as follows.

Buyers and sellers invest before entering the market, so all buyers have the same investment level

and all sellers have the same investment level. Then, buyers and sellers learn their own willingness

to pay and costs respectively. Finally, buyers and sellers make trading decisions and complete

transactions.

There is a continuum of buyers with uncertain willingness to pay v for a unit of a good

determined by v = x + V(b). The parameter x represents the buyer�s type and is uniformly distributed

with unit density on the unit interval. The buyer�s value is increasing in the investment b. The

function V(b) is positive, strictly concave, and twice continuously differentiable. At price p, the

7

1 The aggregate demand function is D(p, b) = 1 + V(b) � p for 0 � 1 + V(b) � p � 1, D(b, p) =0 for 1 + V(b) � p < 0, and D(p, b) = 1 for V(b) � p >0.

2 The aggregate supply function is S(w, k) = w � C(k) for 0 � w � C(k) � 1, S(w, k) = 0 for w �C(k) < 0, and S(w, k) = 1 for w � C(k) > 1.

aggregate demand function is D(p, b) = Pr{x: x + V(b) � p}.1

There is a continuum of sellers with uncertain cost c of supplying a unit of the good

determined by c = y + C(k). The parameter y represents the seller�s type and is uniformly distributed

with unit density on the unit interval. The seller�s cost is decreasing in the investment k. The

function C(k) is positive, strictly convex, and twice continuously differentiable. At price w, the

aggregate amount supplied by sellers is S(w, k) = Pr{y: y + C(k) � w}.2

To guarantee that the market demand function D(p, b) and the market supply function S(w,

k) cross, assume that 0 <δ < 1 for all b, k, where δ(b, k) � V(b) � C(k). The requirement that δ < 1

implies that market demand cannot be everywhere above market supply, thus ruling out the case in

which all random matches would result in trade. The requirement that 0 <δ implies that market

demand cannot be everywhere below market supply, so there exist some feasible matches. The

assumption holds for example if V(b) = 1 � 1/(b + 2) and C(k) = 1/(k + 3).

Buyers invest before observing their value parameter and sellers invest before observing their

cost parameter. Before they observe their own types, all buyers are identical to each other and all

sellers are identical to each other. Thus, we can restrict attention to symmetric investment equilibria.

Individual investment levels b and k equal total investment levels since the measure of buyers and

of sellers equals one.

The buyer and the seller investment levels, b and k, and their value and cost parameters, x and

y, remain private information prior to trade. After a match is made, the buyer and the seller learn

8

G F(b,k) � �1

x F(x � V(b)) dx � �

y F

0(y � C(k))dy � (1 � V(b) � C(k))2/4.

(3)

each other�s private information. Investment levels impact expected gains from trade by affecting

the likelihood of trade and the available net benefits to be allocated through negotiation.

First-best efficiency maximizes social welfare. First-best efficiency has two components:

Investments must be efficient and the market mechanism must be efficient as well. For the market

mechanism to be efficient, the marginal buyer's willingness to pay must equal the marginal seller's

cost, as in the basic supply and demand framework. For investment levels to be efficient, they must

maximize total expected gains from trade. Moreover, the market mechanism must be efficient given

investment efficiency and investment must maximize total gains from trade given efficient matching.

Efficient matching requires that there exist parameter values xF and yF such that low

willingness-to-pay buyers of type x < xF and high-cost sellers of type y > yF are inactive. Having

excluded these buyers and sellers, it is then efficient to match randomly any buyer in [xF, 1] with any

seller in [0, yF]. With efficient matching, the marginal buyer�s willingness to pay and the marginal

seller�s cost are equal,

xF + V(b) = yF + C(k). (1)

Also, the total amount demanded should equal the total amount supplied, 1 � xF = yF. Thus, using

equation (1), the first-best volume of trade equals

QF(b, k) = 1 � xF = yF = (1 + V(b) - C(k))/2. (2)

Total expected gains from trade with efficient matching equals GF(b, k), where

F

i r

st-best investment levels (bF, kF) maximize expected gains from trade net of investment costs, GF(b,

k) � b � k. Assume that there exist interior maximizers, although the maximizers need not be unique.

9

G S(b,k) � �1

1� (V�C) �1

0(x �y�V�C)dydx � �

1� (V �C)

0 �x� (V�C)

0(x�y�V�C)dydx

� (1 � 3δ � 3δ2� δ3)/6. (5)

III. Investment Incentives in a Search Market

This section considers investment incentives when the buyers and the sellers are in a search

market. After a match is made, the buyer and the seller learn each other�s type. If there are potential

gains from trade, the buyer and the seller bargain over the division of the surplus. Bargaining is

represented by the Nash bargaining solution, so that buyers and sellers evenly divide the gains from

trade. The analysis carries through with uneven divisions of the surplus. Similar results can be

obtained when the buyer and the seller divide the surplus under asymmetric information, see for

example Gehrig (1993) and Spulber (1999) for alternative versions of matching.

If a buyer of type x and a seller of type y are matched, trade occurs if and only if gains from

trade are positive,

x + V(b) � y + C(k). (4)

The second-best outcome is defined as the investment levels that maximize the expected gains from

trade in a search market net of investment costs. With random matching, a high-value buyer of type

x in [x~, 1], where 0 < x~ = 1 - V(b) + C(k) < 1, is able to trade with any seller. A low-value buyer

of type x in [0, x~] is only able to trade with low-cost sellers of type y � x + V(b) - C(k). The total

expected gains from trade in a search market GS(b, k) are defined by

Second-best investment levels (bS, kS) maximize GS(b, k) - b - k. Assume that there exist interior

maximizers.

Random matching in a search market satisfies the ex post efficiency criterion that buyer value

10

exceeds seller cost, as in equation (4). Random matching is not ex ante efficient because trade should

be restricted to higher-value buyers and lower-cost sellers, with marginal buyers and sellers as

specified in equation (1). For any given investment levels b and k, the efficiency loss from random

matching relative to efficient matching equals

GF(b, k) � GS(b, k) = (1 � 3δ2 + 2δ3)/12 > 0. (6)

The difference is positive because the right hand side is decreasing in δ for δ > 0 and zero at δ = 1.

Random matching would be efficient if and only if the market demand curve were everywhere above

the market supply curve. The inefficiency of random matching results from the presence in the

market of high-cost sellers and low-value buyers who are to the right of the crossing point of the

supply and demand curves. For example, a buyer with a low willingness to pay, x = (1 � V(b) +

C(k))/3 < xF, who would not buy under efficient matching, might be matched with a low-cost seller

of type y = (1 + V(b) - C(k))/4 < yF , so that a high-value buyer could fail to find a match.

It may be surprising to observe that too many matches occur with random matching. With

random matching, the expected volume of trade equals QS(b, k) = [1 +2(V(b) � C(k)) � (V(b) �

C(k))2]/2. Thus, the second-best volume of trade is greater than the first-best volume of trade

evaluated at the same investment levels, QS(b, k) > QF(b, k). The possibility of successful matches

for buyers or sellers who are to the right of the crossing point of supply and demand raises the

expected number of matches. This shows that the inefficiency of random matching is due to the

presence of low-value buyers and high-cost sellers, leading to excessive trade.

I now compare first-best and second-best outcomes. The analysis applies standard monotone

comparative statics techniques, see Athey et. al (1996).

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Proposition 1. First-best investment levels with efficient matching are less than second-best

investment levels with random matching, (bF, kF) < (bS, kS). The first-best trading volume is less than

the second-best trading volume, QF < QS.

Proof of Proposition 1. Let J(δ) = minb, k b + k subject to δ = V(b) � C(k). Note that the minimizers

b and k are increasing in δ. The first-best and second-best problems reduce to one dimensional

problems, maxδ GF(δ) � J(δ) and maxδ GS(δ) � J(δ). Since GS(δ) � GF(δ) is strictly increasing in δ

from equation (6), standard monotone comparative statics analysis implies that every maximizer of

the first-best problem is smaller than every maximizer of the second best problem, δF < δS. The

indicators for the first and second best problems serve as parameters. By monotone comparative

statics, δF < δS implies that (bF, kF) < (bS, kS). Since δ < 1, QF(δ)= (1 + δ)/2 < [1 + 2δ � δ2]/2 = QS

(δ). Since QF (δ) is increasing in δ and δF < δS, it follows that QF = QF(δF)<QF(δS) <QS (δS) = QS.Q.E.D.

The proposition shows that because of the inefficiency of random matching, the second-best criterion

requires greater investment than does the first-best criterion. The result that first-best investment is

less than second-best investment is unexpected since the returns to investment would appear to be

greater with efficient matching. The reason that second-best investment levels are higher is that

greater investment increases the likelihood of trade. In a search market, buyers and sellers must

invest more to overcome the inefficiency of random matching. Random search with bilateral trade

satisfies only the ex post efficiency standard that buyer value exceeds seller cost. The resulting

trading inefficiency leads to an investment efficiency criterion that is too strict. Efficient markets

require less investment because there is no need for higher investment to overcome transaction

inefficiencies.

12

Consider now equilibria of the search market. Before observing their type, and before

entering the search market, the buyer and the seller choose investment levels to maximize their

expected gains from trade. The sequence of events is as follows.

Period 1a: At the beginning of the period, each buyer chooses investment b and each

seller chooses investment k.

Period 1b: At the end of the period, each buyer i observes their type xi and each seller j

observes their type yj, which remain private information before a match is

made.

Period 2: Buyers and sellers are matched randomly. After a match is made, the trading

partners observe each other�s type and decide whether or not to trade. If gains

from trade are positive, they bargain over the terms of trade. Otherwise, the

trading partners exit the market.

The buyers and the sellers play a Nash noncooperative game in investment levels. Let (bR, kR)

represent the Nash equilibrium investment levels with random matching in a search market.

After a successful match, the buyer and the seller engage in Nash bargaining and divide the

gains from trade equally, so that the expected gains from trade for a buyer or for a seller equal

(½)GS(b, k). Accordingly, buyers choose b to maximize (½)GS(b, kR) � b and sellers choose k to

maximize (½)GS(bR, k) � k. Assume that there exist interior maximizers.

Consideration of the Nash equilibrium shows that under investment occurs in a search market

relative to the first-best and second-best levels. In the search market equilibrium with random

matching, buyers and sellers invest before bargaining over the division of surplus. They correctly

anticipate that they will not capture the full marginal return to their investment. Accordingly, they

13

have an incentive to scale back their investment levels, thus reducing the value of a match relative

to the second-best optimum.

Proposition 2. Nash equilibrium investment levels in a search market with random matching are

less than first-best levels and second-best levels, (bR, kR) < (bF, kF)< (bS, kS). The Nash equilibrium

trading volume in the search market with random matching is less than the second-best trading

volume, QR < QS.

Proof of Proposition 2. Nash equilibrium investment levels in a search market must maximize

(½)GS(δ) � J(δ). Since GF(δ) � (½)GS(δ) is strictly increasing in δ, every maximizer of (½)GS(δ) �

J(δ) is smaller than every maximizer of the first-best problem so that δR < δF . By the definition of

δ, it follows that (bR, kR) < (bF, kF). The trading volume is less than the second-best trading volume

since QS(δ) = [1 + 2δ � δ 2]/2 is increasing in δ and δR < δS, so that QR = QS(δR) < QS(δS) = QS.Q.E.D.

The Nash equilibrium trading volume in a search market may be greater than or less than the first-

best trading volume. Although the trading volume in the search market is greater than the trading

volume with efficient matching for the same investment levels, the under investment at the Nash

equilibrium with search may reduce the trading volume below the first best level.

IV. Investment Incentives in a Dealer Market

This section considers a market with a monopoly dealer and no search by buyers and sellers.

The dealer transacts with many buyers and sellers. The dealer posts an ask price p for buyers and a

bid price w for sellers. Buyers and sellers choose their investment levels before observing prices and

14

the dealer chooses prices without observing investment levels. The dealer , the buyers, and the sellers

play a Nash noncooperative game in prices and investment levels. The sequence of events is as

follows.

1a: At the beginning of the period, each buyer chooses investment b and each seller

chooses investment k. The dealer posts prices p,w.

1b: At the end of the period, each buyer i observes their type xi and each seller j observes

their type yj.

2: Buyers and sellers decide whether or not to transact with the dealer. Transactions are

completed.

Nash equilibrium investment levels are (bD, kD) and the dealer�s Nash equilibrium ask and bid prices

are (pD, wD).

The aggregate demand function is D(p, b) = Pr{x: x + V(b) � p}, so that the dealer�s inverse

demand is PD(Q, b) = 1 + V(b) - Q. For the aggregate supply function S(w, k) = Pr{y: y + C(k) � w},

the dealer�s inverse supply is W D(Q, k) = C(k) + Q. The dealer�s profit-maximizing prices balance

the amounts demanded and supplied. The dealer�s profit can be stated as a function of output,

Π(Q; bD, kD) = (PD(Q, bD) � W D(Q, kD))Q = (1 + V(bD) � C(kD) � 2Q)Q. (7)

The dealer�s profit-maximizing output is a unique best response to the Nash equilibrium investment

levels (bD, kD),

QD = (1/4)(1 + V(bD) - C(kD)). (8)

From equation (8) and the inverse demand and supply functions, the Nash equilibrium ask and bid

prices are

pD = (1/4)(3 + 3V(bD) + C(kD)), (9)

15

h S(b, k) � �w D

� C(k)

0(w D

� y � C(k)) dy. (12)

h B(b, k) � �1

p D� V(b)

(x � V(b) � p D) dx, (11)

wD = (1/4)(1 + V(bD) + 3C(kD)). (10)

The dealer�s equilibrium ask and bid prices straddle the Walrasian equilibrium price PW evaluated

at the equilibrium investment levels, wD < PW = (1 + V(bD) + C(kD))/2 < pD.

The buyer and the seller choose investment levels as best replies to the dealer�s Nash

equilibrium prices. The buyer and seller have expected benefits defined by

The buyer maximizes hB(b, kD) � b and the seller maximizes hS(bD, k) - k.

Intermediation reduces investment relative to direct exchange. Because the buyers and the

sellers play a Nash noncooperative game with the dealer, the buyers� and the sellers� investment is

a best response to the dealer�s equilibrium prices. The dealer�s prices are in turn a best response to

the buyers� and sellers� equilibrium investments. Accordingly, the buyers, the sellers and the dealer

have no incentive to revise their equilibrium choices. Because the buyers and the sellers take the

dealer�s equilibrium prices as given, they capture the full marginal returns to their investments

unlike in the search market. However, the under-investment problem is exacerbated when the search

market is replaced by a monopoly dealer.

There may be multiple Nash equilibria of the investment game. Since the buyers� and the

sellers� benefit functions are increasing in each other�s investment, equilibria with higher

investments are Pareto preferred to equilibria with lower investments. To simplify matters, I restrict

16

attention to the Pareto-preferred equilibrium of the investment game, see Milgrom and Roberts

(1994).

Proposition 3. Nash equilibrium investment levels in the dealer market are less than Nash

equilibrium investment levels in the search market with random matching, and therefore less than

the first-best levels and less than the second best levels, (bD, kD) < (bR, kR) < (bF, kF) < (bS, kS). The

volume of trade in the dealer market is less than the first-best volume of trade, QD < QF, less than

the volume of trade in the search market, and therefore less than the second-best volume of trade,

QD < QR < QS.

Proof of Proposition 3. From the investment problems of the buyers and the sellers, equations (11)

and (12), the Nash equilibrium investment levels must maximize GD(b, k) � b � k where GD(b, k) =

hB(b, k) + hS(b, k). The buyer and the seller investments in the search market (bR, kR) must maximize

(½)GS(b, k) � b � k. The function (½)GS(b, k) is monotonically increasing in b and k, and it is

supermodular since �2(½)GS/�b�k = (½)[1 � (V � C)](�C�)V� > 0. Note that �(½)GS(b, k)/�b

=(1/4)[1 + 2(V(b) � C(k)) � (V(b) � C(k))2]V�(b) and �GD(b, k)/�b =[1 + V(b) � pD]V�(b).

Substituting for pD from equation (9) into the first derivative of GD yields �GD(b, k)/�b =(1/4)[1 +

V(b) � C(k)]V�(b), so that �(½)GS(b, k)/�b > �GD(b, k)/�b. The same analysis applies for k. Also,

after substituting for pD from equation (9) into the first derivative and differentiating with respect

to k, it follows that �2GD(b, k)/�k�b = �C�(k)V�(b)/4 >0. By Topkis (1978), the maximum best-reply

function for the investment game in the search market is above the maximum best-reply function for

the investment game in the dealer market. By Theorem 4 of Milgrom and Roberts (1994), the buyer

and seller investment levels in the high-investment Nash equilibrium of the search market are greater

17

than their investment levels in the high-investment Nash equilibrium of the dealer market, so that

(bD, kD) < (bR, kR).

Recall that the volume of trade for the first-best problem is QF(δ) = (1 + δ)/2 where δ = V(b)

� C(k). The volume of trade in the dealer market is QD(δ) = (1 +δ)/4 from equation (8). Note that

QD(δ) <QF(δ). Since δ is increasing in b and k and QF(δ) and QD(δ) are increasing in δ, then (bD, kD)

< (bF, kF) implies that QD <QF. The volume of trade for the second-best problem is QS = [1 + 2 δ

� δ 2]/2, so QD (δ)< QS(δ). Since QD(δ) and QS(δ) are increasing in δ, then (bD, kD) < (bR, kR) implies

that QD <QR. Q.E.D.

The reason investment is lower in the dealer market than in the search market is that the dealer�s

price spread lowers the likelihood of trade, reducing the marginal return to investment, because only

the highest-willingness-to-pay buyers and lowest-cost sellers will transact with the dealer. This

monopoly effect dominates the benefits of the dealer market for buyers and sellers who receive the

full returns to their investment when trade occurs. The intermediated equilibrium resembles efficient

matching except that it also excludes buyers and sellers whose willingness to pay and cost levels fall

within the dealer�s price spread. A combination of direct exchange and intermediation would address

this inefficiency by allowing direct exchange between buyers and sellers whose valuations are within

the price spread.

V. Competition Between a Dealer and the Search Market

This section considers competition between a dealer and the search market. As before buyers

and sellers invest before observing their types. After observing their types, buyers and sellers decide

18

whether to enter the search market or to purchase from, respectively sell to, the dealer at the posted

prices. Buyers and sellers entering the search market are matched randomly. The sequence of events

is as follows.

1a: At the beginning of the period, each buyer chooses investment b, each seller chooses

investment k, and the dealer posts prices p,w.

1b: At the end of the period, each buyer i observes their type xi and each seller j observes

their type yj.

2: Buyers and sellers decide whether to transact with the dealer, to enter the search

market, or to be inactive. Transactions are completed.

The Nash equilibrium with competition between a dealer and a direct-exchange market is denoted

by (p*, w*, b*, k*). I begin by considering the second-stage market subgame, taking the investment

levels (b*, k*) as given.

VA. The Market Equilibrium

The analysis of the market game is based on Gehrig (1993) who examines competition

between a dealer and a search market, but does not consider investment. The dealer rations the long

side of the market and buyers and sellers who cannot trade with the dealer enter the search market,

and the dealer�s purchases and sales balance. In contrast to Gehrig (1993), I assume that once a buyer

and a seller are matched they learn each others� type and that the gains from trade are allocated by

Nash bargaining.

The market equilibrium is defined by four critical values: X0, X1, Y0 and Y1. In equilibrium,

low-value buyers with types in the interval [0, X0) are inactive and high-cost sellers with types in

19

3 See Gehrig (1993) and Spulber (1999) for further discussion.

U(x,b �,k �,ψ) � �y � x � V(b �) � C(k �)(1/2)(x � V(b �) � y � C(k �))dψ(y). (13)

(Y1, 1] are inactive. To see why, observe that if a buyer X0 is inactive, all buyers with a lower value

x must be inactive as well. Otherwise the buyer of type X0 could follow the strategy of the buyer of

type x and secure at least the same payoff.

Active buyers and sellers are defined as follows. Buyers with type in [X0, X1) enter into the

search market and high-value buyers with type in [X1, 1] buy from the dealer. Sellers with type in

(Y0, Y1] enter into the search market and low-cost sellers with type [0, Y0] sell to the dealer. Let ψ(y)

be the equilibrium distribution of sellers in the search market, so that ψ(Y0) = 0 and ψ(Y1) = 1. Let

φ(x) be the equilibrium distribution of buyers in the search market, so that φ(X0) = 0 and φ(X1) = 1.

The equilibrium distributions can be shown to be uniform.

To see why the equilibrium is defined by these intervals, consider the buyers� decision

problem since that of the sellers is similar. The buyer�s expected value from entering the search

market is

Suppose that the buyer of type X1 prefers to enter the search market rather than to trade with the

dealer, U(X1) > X1 + V(b*) � p. Then, any buyer with a lower type x also prefers to enter the search

market, since U(x) � x � V(b*) � p* is strictly decreasing in x. the properties of the equilibrium hold

even if the buyer (or seller) expects to be rationed in the search markets, although such rationing

does not occur in equilibrium.3

In equilibrium, both the dealer market and the search market balance. Thus, the critical values

20

U(x,b,k,Y0,Y1)��x � V(b) � C(k)

Y0

(1/2)(x � V(b) � y � C(k))dψ(y)�(x � V(b) � Y0 � C(k))2

4(Y1 �Y0). (16)

R(y,b,k,X0,X1) � �X1

y � C(k) � V(b)(1/2)(x � V(b) � y � C(k))dφ(x) �

(X1�V(b)�y�C(k))2

4(X1 � X0). (18)

of buyer value and seller cost are such that the marginal buyer�s value and the marginal seller�s cost

are equal,

X0 + V(b) = Y0 + C(k), (14)

X1 + V(b) = Y1 + C(k). (15)

These relationships hold because a seller with cost c = y + C(k) greater than X1 + V(b) will find no

trading partners in the matching market, so the highest cost seller that is active has cost Y1 + C(k)

= X1 + V(b). Similarly, a buyer with value v = x + V(b) less than Y0 + C(k) will find no trading

partners in the search market, so that the lowest value buyer that is active has value X0 + V(b) = Y0

+ C(k).

To examine the dealer�s problem, it is useful to derive aggregate demand and supply. The

buyer of type x who enters the direct-exchange market has expected benefits equal to

The buyer of type x purchases from the dealer if and only if the net benefits equal or exceed those

expected from search. The dealer faces the market demand D(p; b*, k*) = Pr{x: x + V(b*) � p � U(x,

b*, k*,Y0, Y1)}, so that

D(p; b*, k*) = 1 + V(b*) � p � U(X1, b*, k*,Y0, Y1). (17)

The seller of type y sells to the dealer if and only if the net benefits from doing so equal or

exceed those expected from direct exchange,

21

The seller of type y sells to the dealer if and only if the net benefits equal or exceed those expected

from search. The dealer faces the market supply S(w; b*, k*) = Pr{y: w - y - C(k*) � R( y, b*, k*, X0,

X1)}, so that

S(w; b*, k*) = w � C(k*) � R(Y0, b*, k*, X0, X1). (19)

The dealer�s profit function is Π(q) = [P(q) � W(q)]q, where P(q) is inverse demand and

W(q) is inverse supply from equations (17) and (19), suppressing b and k. By the following

proposition, the dealer�s prices are the unique best response to equilibrium investments (b*, k*). The

dealer�s bid-ask spread is positive and there is an active search market in equilibrium.

Proposition 4. With competition between a dealer and the search market, the equilibrium bid�ask

spread straddles the Walrasian price evaluated at the equilibrium investment levels, that is,

w* < PW = (1 + V(b*) + C(k*))/2 < p*.

Proof of Proposition 4. The quantity demanded by buyers is 1 � X1, and the quantity offered by

sellers is Y0. The dealer chooses prices that equate the amount demanded and supplied, so that q =

1 � X1 = Y0. From equations (14) and (15), note that X0 = q � V(b) + C(k) and Y1 = 1 � q+ V(b) �

C(k). Then, from equations (16) - (19), the inverse demand and supply functions are

P(q) = (1/4)(3 + 3V(b*) + C(k*) � 2q), (20)

W(q) = (1/4)(1 + V(b*) + 3C(k*) � 2q). (21)

The dealer�s profit can then be written as follows,

Π(q) = (½)(1 + V(b*) � C(k*) � 2q)q. (22)

Setting marginal profit equal to zero, the dealer�s first order condition can be solved for the dealer�s

equilibrium output:

22

q* = (1/4)(1 + V(b*) � C(k*)). (23)

The second order sufficient condition for a unique interior maximum is satisfied, so the dealer�s

output q* is the unique solution to the dealer�s profit-maximization problem for any investments (b*,

k*). The dealer�s Nash equilibrium prices (p*,w*) are obtained by substituting the dealer�s profit-

maximizing output into the inverse demand and supply functions. From equations (20), (21) and

(23),

p* = (1/8)(5 + 5V(b*) + 3C(k*)), (24)

w* = (1/8)(3 + 3V(b*) + 5C(k*)). (25)

So, p* � PW = w* �PW = (1/8)(1 + V(b*) � C(k*)) >0. Q.E.D.

The search market is active and the volume of trade on the search market is positive and equals

X1* � X0

* = Y1* � Y0

* = (½)(1 + V(b*) � C(k*)).

The total volume of trade equals the sum of the dealer�s volume and the search market volume,

Q* = q* + X1* � X0

* = (3/4)(1 + V(b*) � C(k*)).

The volume of trade with competition between a dealer and a search market exceeds the second-best

and first-best volumes of trade when evaluated at the same investment levels, Q*(δ) > QS(δ) =QF(δ).

VB. Incentives for Investment

Having characterized the market game in the second period, I now derive the first period

Nash equilibrium investment strategies of the buyers and sellers. A buyer chooses investment b as

a best response to the Nash equilibrium prices p* and w*, and the equilibrium investment of the

sellers k*. A seller chooses investment k as a best response to the Nash equilibrium prices p* and w*,

23

g B(b, k �) � �1

X1

(x � V(b) � p �)dx � �X1

X0

U(x,b,k �,Y0,Y1)dx, (26)

g S(b �,k) � �Y0

0(w �

� y � C(k))dy � �Y1

Y0

R(y,b �,k,X0,X1)dy. (27)

and the equilibrium investment of the buyers, b*. The buyer and the seller expected benefits combine

the expected returns from direct and intermediated exchange,

The buyers choose investment b to maximize the expected net benefit, gB(b, k*) � b and the sellers

choose investment k to maximize the expected net benefit, gS(b* , k) � k.

Competition between the dealer and the search market increases the returns to investment.

The high-value buyer and the low-cost seller avoid the uncertainties of search and bargaining and

benefit from the certainty of trade with the dealer at posted prices. Intermediate-value buyers and

sellers who do not transact with the dealer still realize a return on their investment by entering the

search market. Thus, the presence of a search market adds contingencies that allow the

intermediated-value buyer and intermediate-cost seller the option of search.

Proposition 5. Nash equilibrium investment levels with competition between a dealer and a search

market are greater than Nash equilibrium investment levels with search alone and greater than the

Nash equilibrium investment levels in a market with a dealer alone, (bD, kD) < (bR, kR) < (b*, k*). The

equilibrium volume of trade with competition between a dealer and a search market is greater than

the equilibrium volume of trade in a market with search alone or in a market with a dealer alone, QD

24

< QR < Q*.

Proof of Proposition 5. In the individual buyer�s problem, X1 solves X1 + V(b) � p* =U(X1 ,b, k*,Y1,

Y0) and X0 solves U(X0, b, k*,Y1, Y0) = 0. From the definition of U, �U(x, b, k*,Y1, Y0)/�b = V�(b)(x

+ V(b) � Y0 � C(k*) �Y0)/2(Y1 �Y0). Applying the envelope theorem, and using equation (16) and the

values of X1, X0, the buyer�s value is monotonically increasing in b,

�gB(b, k*)/�b = (1 + V(b) � p*)V�(b) > 0.

In the individual seller�s problem, Y0 solves w* � Y0 � C(k) = R(Y0, b*, k, X0, X1) and Y1 solves R(Y1,

b*, k, X0, X1) = 0. As before, the seller�s value is monotonically increasing in k,

�gS(b*, k)/�b = �(w* � C(k))C�(k) > 0.

The comparison in the Proposition involves the equilibrium investment levels. Accordingly, it is

necessary to substitute for p* and w* as obtained in the proof of Proposition 4, to obtain �gB(b, k*)/�b

=(3/8)(1 + V(b) � C(k*))V�(b) and �gS(b*, k)/�b =(3/8)(1 + V(b*) � C(k))(�C�(k)). The value

functions are supermodular in b and k, �2gB(b, k)/�k�b =�2gS(b, k)/�k�b = �(3/8)V�(b)C�(k).

Compare the equilibrium with the search market with random matching. Recall that the buyer

and the seller investments in the search market (bR, kR) must maximize (½)GS(b, k) � b � k. As

already noted, the function (½)GS(b, k) is monotone increasing in b and k, and it is supermodular

since �2(½)GS(b, k)/�b�k = (½)(1 � δ)(�C�(k))V� (b)> 0. Since �(½)GS(b, k)/�b =(1/4)(1 + 2δ �

δ2)V�(b) and �gB(b, k)/�b = (3/8)(1 + δ)V�(b), it follows that �gB(b, k)/�b > �(½)GS(b, k)/�b. The same

analysis applies for k. So, by Topkis (1978) and Theorem 4 of Milgrom and Roberts (1994), (b*, k*)

> (bR, kR).

Recall that the volume of trade with a dealer and a search market is Q*(δ) = (3/4)(1 + δ) and

the volume of trade in the search market with no dealer is QS(δ) = [1 + 2δ � (δ )2]/2, so QS (δ)< Q*(δ).

25

Since QS(δ) and Q*(δ) are increasing in δ, then (bR, kR) <(b*, k*) implies that QR =QS(δR) <Q*(δR) <

Q*(δ* ) = Q* . Q.E.D.

Competition between the dealer and the search market enhances incentives for investment.

The introduction of search enhances incentives to invest because buyers and sellers with valuations

within the spread trade with each other, thus raising the expected returns to investment relative to

an equilibrium in which those buyers and sellers would not trade. The presence of the search market

allows buyers and sellers within the spread to have some chance of completing an exchange. Thus,

in comparison with the market with only an dealer, the mixed market allows buyers and sellers to

realize the returns to their investment by trading with the dealer and by entering the search market.

The combination of intermediated and search has another advantage in that it enhances the

efficiency of the matching process in the search market. The dealer�s price spread diverts high-value

buyers and low-cost sellers from the search market and guarantees that they will be able to complete

a transaction without being displaced by matches with lower gains from trade. The combination of

intermediated and direct exchange has an additional and more subtle effect on matching, The low-

value buyers and high-cost sellers, whose values are outside the spread, are inactive since they would

not find a suitable match in the search market. See the circled portions of the demand and supply

curves in Figure 1. Because these traders do not enter the search market, the inefficiency of that

market is mitigated, even if it is not fully eliminated. The enhanced performance of the search market

further increases the returns to investment.

Competition between a dealer and a search market reduces the dealer�s market power and

thus narrows the bid-ask spread. This raises the gains from trading with the dealer for buyers and

26

sellers. The narrower spread also increases incentives to invest. Moreover, the narrower spread

reduces the number of buyers and sellers entering the search market thus reducing market uncertainty

and search inefficiencies.

Proposition 6. The Nash equilibrium with competition between the dealer and the search market

results in a lower ask price and a higher bid price than the Nash equilibrium prices in a dealer market

without a search market, wD< w* < p* < pD.

Proof of Proposition 6. Recall that �gB(b, k)/�b = [1 + V(b) � p]V�(b) > 0, so that gB(b, k) � b is

supermodular in b and �p. The seller�s value is monotonically increasing in k, �gS(b, k)/�b = �[w

� C(k)]C�(k) > 0 so that gS(b, k) � k is supermodular in k and w. In the market with a dealer but no

search, note that hB(b, k) � b is supermodular in b and �p and hS(b, k) � k is supermodular in k and

w. Note further that for any given p and w, �gB(b, k)/�b = �hB(b, k)/�b and �gS(b, k)/�k = �hS(b, k)/�k.

Since (b*, k*) > (bD, kD) in equilibrium it must be the case that p* < pD and w* > wD. Q.E.D.

The presence of a dealer alleviates the problems with investment incentives that arise under

direct exchange. However, under investment is still present.

Proposition 7. Nash equilibrium investment levels with competition between a dealer and a search

market are less than the first-best efficient investment levels and the second-best efficient levels, (b*,

k*) < (bF, kF)< (bS, kS).

Proof of Proposition 7. The function GF is monotone increasing in b and k, and it is supermodular

since �2GF/�b�k = �C�V�/2 > 0. From the proof of Proposition 5, the buyer�s value gB(b, k) is

monotonically increasing in b and supermodular in b, k. The seller�s value gS(b, k) is monotonically

27

increasing in k and supermodular in b, k. Further, �gB(b, k)/�b = (3/8)(1 + δ)V�(b) < (½)(1 + δ)V�(b)

= �GF(b, k)/�b and similarly �gS(b, k)/�k <�GF(b, k)/�k. So, by Topkis (1978) and Theorem 4 of

Milgrom and Roberts (1994), (b*, k*) < (bF, kF).Q.E.D.

Under investment persists with competition between intermediated and direct exchange.

When making investment choices, buyers and sellers take into account the possibility that they will

wind up in the matching market and strategically underinvest. Moreover, the bid-ask price spread

set by the dealer also reduces the marginal returns to investment.

For any given investment levels the volume of trade with competition between a dealer and

a search market is greater than the second-best and the first-best efficient volume of trade, Q*(δ)>

QS(δ)> QF(δ). This occurs because of the excessive amount of trade in the search market. Even

though the size of the search market is smaller due to the presence of a dealer, the total of trade with

the dealer and trade in the search market is larger than the efficient levels. It is not possible to

evaluate the efficiency of the equilibrium volume of trade with competition between a dealer and a

search market. Since under investment is observed, and since the volume of trade is increasing in

equilibrium investment levels, the equilibrium volume of trade may be greater or less than the

efficient levels.

VI. Competition Between Dealers

Competition between dealers eliminates the price spread thus rendering the search market

inactive. Competition results in the Walrasian equilibrium price so that matching of buyers and

sellers is efficient. By Bertrand competition arguments, Gehrig (1993) shows that the Walrasian

28

equilibrium is a Perfect Bayesian Equilibrium for the competitive game with two dealers, although

it is not necessarily unique. With competition between two or more dealers, the market price equals

the Walrasian price evaluated at the equilibrium investment levels, p** = w** = P** = (½)(1 + V(b**)

+ C(k**)) and the volume of trade equals the Walrasian equilibrium output.

Buyers and sellers choose investments at a Nash equilibrium taking market equilibrium prices

as given. Let (p**, w**, b**, k**) represent the Nash equilibrium prices and investments.

Proposition 8. With competition between dealers, there is a Nash equilibrium at which dealers

choose bid and ask prices equal to the Walrasian price and buyer and seller investment levels are

efficient, (b**, k**) = (bF, kF).

The proposition shows that markets provide incentives for efficient investment by buyers and sellers.

Suppose that dealers have constant marginal cost t per transaction, so that the equilibrium price

spread with competing dealers equals p � w = t. Then, a search market would still exist because of

the price spread, assuming that direct exchange was costless. As the unit cost t approaches zero, the

search market is displaced and the volume of trade and investment levels approach the efficient

outcome.

VII. Discussion

VIIA. Empirical Implications

Market microstructure has significant implications for investment efficiency, as the preceding

results suggest. To determine the importance of such transactions, it is worthwhile examining the

29

4 This figure and subsequent data and information referred to in this section are from UnitedStates Census Bureau (2000). Establishments means business locations, a firm can operatemultiple establishments.

nature of interbusiness transactions. Many sectors of the economy involve interbusiness trade,

including manufacturing, agriculture, mining, construction, transportation, and public utilities.

Wholesale trade, which equals over $4 trillion in annual sales, provides a useful window on

interbusiness markets.4 Wholesale trade comprises �(a) goods for resale (i.e. goods sold to other

wholesalers or retailers), (b) capital or durable nonconsumer goods, and (c) raw and intermediate

materials and suppliers used in production.�

According to the U.S. Census Bureau (2000), wholesalers normally do not advertise directly

to the general public. Moreover, wholesale warehouses and offices generally do not have

merchandise displays: �neither the design nor the location of the premises is intended to solicit walk-

in traffic.� In addition, the Census Bureau observes that initial contacts with wholesale transactions

customers are generally by telephone, in person marketing, or by specialized advertising that may

include Internet communication. The Census Bureau finds that follow-up orders �typically exhibit

strong ties between sellers and buyers� and that �transactions are often conducted between

wholesalers and clients that have long-standing business relationships.�

These observations suggest that initial contacts between wholesalers and their customers have

features of a search market. The use of targeted direct marketing might indicate that search is

relatively costly in these markets. The subsequent formation of long-term relationships with

wholesalers allows buyers and sellers to avoid the costs of further search. Long-term relationships

can offer other advantages such as learning about the characteristics of trading partners that can aid

in planning and reduce costs of negotiation. Companies that rely on long-term relationships

30

potentially forego benefits that might be offered by dealing with alternative trading partners.

Two thirds of wholesale transactions (approximately $2.8 trillion) are sales made by two

types of intermediaries: (1) wholesale merchants (including also distributors, jobbers, drop shippers,

import/export merchants, grain elevators and farm product assemblers), and (2) agents (including

also brokers, commission merchants, import/export agents and brokers, auction companies, and

manufacturers� agents). There are about 424,164 establishments operated by wholesale merchants

and agents. The largest category is wholesale distributors and jobbers comprising over $1.8 trillion

in sales and 338,872 establishments.

The remaining third of wholesale transactions are sales made by manufacturers to ($1.259

trillion annually) that are conducted through manufacturers� sales branches and offices. There are

approximately 29,306 such establishments. Although these sales are made by manufacturers, many

of the purchases from manufacturers are made by dealers: wholesalers, retailers and other

manufacturers who assemble parts and components.

Thus, sales by dealers and other kinds of intermediaries constitute well over two-thirds of

wholesale transactions. This is consistent with our assumption that the investments are general rather

than transaction specific. The analysis presented in this article suggests that dealers improve

allocative efficiency when they compete with search markets or when they compete between

themselves. Moreover, the analysis suggests that competitive intermediation enhances dynamic

efficiency by increasing the investment efficiency of suppliers and customers in interbusiness

markets. These findings are consistent with the observed widespread use of intermediaries in

interbusiness transactions.

The role of intermediaries as mechanisms for reducing search costs and enhancing investment

31

efficiency suggests additional empirical implications. Since carrying out investment takes more time

than the time involved in switching to new suppliers or distributors, it should be possible to observe

the effects of such switching on investment. As a test of the hypothesis that dealers enhance market

efficiency and stimulate investment by their customers and suppliers, firms that switch to using

dealers (whether as customers or suppliers) should experience an increase in investment as compared

to firms that are already served by dealers or firms who rely on search markets. The entry of

additional dealers due to the growth of electronic commerce provides many additional instances of

buyers and sellers switching from search markets to dealers.

Product standards provide another approach to testing the effects of market microstructure

on investment. An increase in the number of industry product standards facilitates transactions with

dealers. More product standards does not necessarily mean less product variety, but rather indicates

industry agreements on the definition of product features. Accordingly, a greater degree of

standardization should lead to greater trade with dealers. The analysis in this article therefore

suggests that an increase in standardization in a particular industry should lead to increased long-run

investment relative to other industries. There might be short-run increases in investment needed to

adapt to the standard, but controlling for this might allow identification of the long-run effects of

market efficiency gains on investment by suppliers and customers. The growth of business-to-

business electronic commerce provides a stimulus to standardization, particularly due to the

establishment of exchanges and industry buying and selling consortia. These efforts at coordination

and standardization should allow identification of the effects of greater intermediation on investment

since different industries will have different rates of adoption of electronic commerce.

32

VIIB. Markets with General Investments

The inefficiency of general investment observed here is due to ex ante incentives created by

market inefficiencies. When there is a search market, inefficient matching and dividing the surplus

leads to under investment. There is a growing literature on ex ante investment in a competitive

framework. MacLeod and Malcomson (1993) allow contracting parties to switch trading partners

after they have made investments, although the outside option is specified exogenously. Acemoglu

and Shimer (1999) and Holmstrom (1999) also consider general investments and examine conditions

for efficiency. In Felli and Roberts (2000), workers make complementary investments before being

matched. In their model, workers make competitive wage bids so that matches are efficient, that is,

the worker of the k-th highest quality is matched with the firm of the k-th highest quality. When both

workers and firms invest, there are coordination failure inefficiencies in the form of multiple

equilibria, some of which are inefficient.

Acemoglu (1996) examines the interaction between ex ante investments and costly search

in a labor market. Workers make human capital investments before finding out what firm will

employ them and firms invest before hiring, with workers being identical ex post. Acemoglu (1996)

interprets the under investment that results from random matching as �social increasing returns in

human capital accumulation.� Acemoglu (1997) also looks at labor market imperfections that lead

to underinvestment in training. Based on my analysis, I would expect that the entry of labor market

intermediaries would improve human capital accumulation. Internet-based job search sites, for

example, alleviate some search inefficiencies and improve the job matching process, possibly

enhancing the incentives of both workers and firms to make complementary investments.

The results presented here in a two-stage setting should extend to a dynamic analysis. The

33

inefficiencies of search tend to persist in a multistage setting, so that market inefficiencies should

continue to reduce incentives to invest. One would expect the beneficial effects of intermediaries on

market efficiency to carry over to a dynamic setting, so that the presence of dealers should enhance

investment over time. The results should also extend to a different information setting. The present

model assumed that buyers and sellers invested before learning their types so that investment levels

were the same across buyers and across sellers. If buyers and sellers invest after learning their types,

investment levels will be heterogeneous. Thus, buyers and sellers will still have heterogeneous types

after investing and the inefficiencies of the search market will continue to exist with heterogeneous

investments. Accordingly, the presence of intermediaries would continue to enhance efficiency with

heterogeneous investments.

VIIC. Incomplete Contracts

The hold-up problem is said to occur when buyers and sellers that share the surplus from

exchange do not obtain the full returns to their investment. The economics literature on contracts has

tended to focus on transaction-specific investment within bilateral relationships, see for example

Williamson (1975, 1985), Klein, Crawford and Alchian (1978), Grout (1984), Hart and Moore

(1988), Rogerson (1992), Nöldeke and Schmidt (1995), and Che and Hausch (1999). In the contracts

framework, investment incentives are ex post, that is, they depend on expectations about how the

contract will allocate the gains from trade between the contracting parties. When contracts are

incomplete or nonbinding, renegotiation leads to contract hold-up which creates incentives for under

investment relative to the outcome that maximizes joint gains from trade for the buyer and seller.

Although the present analysis concerns general investment with many buyers and sellers, it yields

34

some insights on bilateral contract models with specific investment.

The inefficiency of search has interesting implications for models based on bilateral

exchange. By law of large numbers arguments, random matching of buyers and sellers in a search

market is formally equivalent to a single buyer and a single seller who have independent random

draws of types. Bilateral contract models, such as Hart and Moore (1988), generally feature bilateral

trade between a single buyer and a single seller who enter into a contract and then make investments

before learning their own types. After learning their own types, the buyer and the seller then decide

whether or not to renegotiate the contract and whether or not to trade. In that literature, the standard

ex post efficiency criterion is used: trade occurs if and only if v � c. However, as noted previously,

with many diverse buyers and sellers, such an efficiency notion is second best. Efficiency would

require that buyers and sellers be matched such that total gains from trade are maximized as in the

standard supply and demand framework in which gains from trade are exhausted at the margin and

high cost suppliers and low value buyers are excluded from the matching process.

Thus, the investment efficiency benchmark in the contracts literature corresponds to second

best efficiency in the present framework. As shown by Proposition 1, the second-best efficient

investment levels are greater than the first-best efficiency levels. Therefore, the investment efficiency

criterion in the contracts literature that is used to show under investment due to hold-up requires

investment above first-best levels. Note further that the investment levels obtained in the contracts

literature in which buyers and sellers with transaction-specific investments cannot make binding

contractual commitments corresponds formally to investment levels obtained here in the case where

buyers and sellers are matched randomly in the search market. Accordingly, under investment in the

bilateral contracts framework corresponds to under investment relative to the second-best criterion

35

when buyers and sellers are matched in the search market.

The present analysis also has implications for the theory of the firm. The hold-up problem

in the contracts literature is due to splitting the surplus in ex post bargaining, see Klein, Crawford,

and Alchian (1978), Williamson (1975, 1985), and Grossman and Hart (1986). The contracts

literature suggests that firms should vertically integrate when investment is transaction specific, to

avoid contractual hold-up between primary input suppliers and companies buying those primary

inputs. In the bilateral contracts setting, the boundaries of the firm would then be determined by

contractual inefficiencies and the specificity of investment. In contrast, my analysis shows that by

posting prices, intermediaries alleviate problems due to splitting the surplus. More generally,

intermediaries reduce the problems associated with ex post bargaining by offering binding

contractual commitments, see Spulber (1999). If intermediaries have incentives to honor contracts

because they deal with many buyers and sellers, they can make commitments that cannot be made

by individual buyers and sellers. Thus, the solution to under investment is not necessarily vertical

integration but rather the entry of intermediaries that enhance market efficiency and reduce or

eliminate contract hold up.

VIII. Conclusion

The foregoing analysis shows that markets with competing dealers provide incentives for

efficient investment and are therefore superior to decentralized direct exchange. The entry of

competing intermediaries in business-to-business markets is likely to enhance complementary

investments by firms in a wide range of industries. The benefits from increased investment and the

improved efficiency of trade create market returns to the entry of intermediaries. Rather than engage

36

in costly search and bilateral bargaining, buyers and sellers turn to intermediaries to handle exchange

at posted prices.

With decentralized exchange in a search market, underinvestment has several sources. The

inefficiency of search creates uncertainty about the likelihood of finding a suitable trading partner.

Moreover, random matching lowers the expected gains from trade in successful matches. Finally,

bargaining with the trading partner means that buyers and sellers divide the gains from trade so that

companies do not obtain the full marginal return to their irreversible investment, which is similar

to the contract hold-up problem. By posting prices, intermediaries alleviate these three effects:

reducing uncertainty about finding a trading partner, reducing uncertainty about the gains from trade,

and reducing the hold-up problem since buyers and sellers that trade with the dealer keep the returns

to their investment. Market microstructure matters for the investment efficiency.

37

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