Market Structure, Factor Endowment andIndustrial Upgrading�

Yong Wangy

February 10, 2012

Abstract

We develop a simple dynamic general equilibrium model to study theindustrial upgrading process, where the market structure may change en-dogenously depending on when the �rst mover chooses to start operatingthe new technology, which is more capital-intensive and initially privatelyaccessible and becomes publicly available one period after its initial oper-ation. We show that the endowment structure (capital-labor ratio in theaggregate economy) plays a very important role. It determines the mag-nitude of the monopoly rent, therefore a¤ects whether or not and whenthe new technology will be implemented. In particular, when the capitalendowment is su¢ ciently small or su¢ ciently large, the equilibrium alloca-tion always achieves Pareto e¢ ciency, no matter whether the endogenousmarket structure is monopoly or perfectly competitive. When the endow-ment structure falls into some intermediate range, ine¢ ciency arises: Oldtechnology (industry) survives for too long, the industrial upgrading isdelayed, and the aggregate output is depressed. We also show that theremay exist multiple dynamic equilibria, which can be Pareto-ranked. Inaddition, a limited improvement in the initial endowment structure maysometimes delay the adoption of capital-intensive technology. Welfare-enhancing industrial policies are discussed.

Key Words: Market Structure, Industrial Policies, Structural Trans-formation, Industrial Upgrading, Capital Accumulation

JEL Codes: L50, O14, O25, O41

�Preliminary. Pease do not circulate this draft without the author�s permission. Thispaper has been presented at HKUST and CCER. This project was conducted when theauthor visited the World Bank as a resident research fellow in 2010-2011 academic year. Thehospitality and �nancial support from the World Bank is gratefully acknowledged.

yAssistant Professor in Economics, Hong Kong University of Science and Technology.Email: yongwang@ust.hk

1

1 Introduction

Economic development is a process of technological innovation and structuraltransformation. New industries emerge with the adoption of new technologiesand old industries decline. To understand how industrial upgrading kicks startin developing economies, we must study the incentive and behavior of the �rstentrant (or �rst mover thereafter) to the new industry, which is the main taskof this paper.Industrial upgrading would su¤er delay, perhaps for inde�nitely long, when

the �rst-move advantage is dominated by the �rst-move disadvantage. Varietiesof economic forces may a¤ect the relative magnitude of the �rst-move advantageand disadvantage. For instance, there is a vast information economics literatureaddressing how the risk and uncertainty a¤ect investment decisions includinglearning behaviors and strategic delay.1 Another literature emphasizes the im-portance of early entrance when there exists the increasing return to scales ordynamic comparative advantage.2 There is also a vast literature examining therole of strategic complementary and coordination in industrial upgrading, themain implication of which is that industrial upgrading cannot take place unlessa su¢ cient large amount of investors are well coordinated to enter simultane-ously.3

In this paper, we focus on the situation where the �rst-move advantagemainly comes from the private information about the new technology (and otherrelevant information), which gives the �rst mover monopoly power before othercompetitors learn enough and enter. The �rst-move disadvantage mainly liesin the fact that the �rst mover exhibits positive information externality to thefollowers but only the �rst mover pays all the exploration cost including thecertainty equivalence for the risk it bears, and the followers can freely imitatethe successful practice.The key novel feature of this paper is that we will explicitly examine the role

of endowment structure (measured by the capital-labor ratio in the aggregateeconomy) in shaping the optimal decision of the technology adoption and indus-trial upgrading, where the market structure may also change endogenously withthe adoption of the new technology. To this end, we develop a dynamic generalequilibrium model to explain how the �rst mover�s behavior and the aggregateindustrial upgrading process are a¤ected by the relative factor prices, which inturn are determined by the endowment structure and the market structure in ageneral-equilibrium fashion.To �x ideas, imagine there are two technologies (industries). One is labor

intensive and publicly available (old technology) and the other is capital in-tensive, which is new and initially only privately known. The capital-intensivetechnology is superior if and only if the rental price of capital is su¢ ciently small

1Chamley (2004) is an excellent monograph on this topic.2See, for example, Krugman (1987).3See, for example, Murphy, Shleifer and Vishny (1989), Rodrik (1997), Krugman (1991),

Matsuyama (1991), Andres (2007). Ju, Lin and Wang (2011) study the impact of Marshallianexternality on industrial upgrading in a dynamic growth model with both capital and labor.

2

relative to the wage. Both the endowment structure and the market structure ofthe consumption goods would ultimately a¤ect the relative cost of capital andlabor, hence a¤ect the optimal choice between the two di¤erent technologies.We ask under what conditions the capital-intensive technology is adopted andhow it takes place in a dynamic economy with endogenous capital accumula-tion. We �rst develop a static model to illustrate how the exogenous endowmentstructure a¤ects the market equilibrium under di¤erent market structures, andthen we move to the dynamic analysis by incorporating the endogenous changesboth in the endowment structure and the market structure.In the static model, two di¤erent market structures are compared. The

�rst one is when the market is always perfectly competitive by assuming thatboth technologies are publicly and freely available. The second one is when thecapital-intensive technology is only freely accessible to one lucky �rm, whichmay operate with a monopoly power. Not surprisingly, in both cases the capital-intensive technology is adopted if and only if the capital endowment is largerthan some �nite cuto¤value. Moreover, this cuto¤value is shown to be invariantto the two di¤erent market structures. On the other hand, the labor-intensivetechnology will completely stop operating when the capital endowment is largerthan another �nite cuto¤ value, which does depend on the market structure.The most surprising and interesting result is perhaps that the monopoly canstill achieve the Pareto e¢ ciency when capital is su¢ ciently large. This isbecause the positive income e¤ect on the demand due to the extra monopolypro�t and the negative price e¤ect due to the monopoly markup pricing exactlycancel out each other via the general equilibrium feedback. This is di¤erentfrom the standard partial equilibrium result.Monopoly would cause economic ine¢ ciency only when the capital endow-

ment falls on certain intermediate range, in which circumstance both technolo-gies are operating but the monopolist of the capital-intensive technology pro-duces less than the socially optimal amount. Again, the reason is di¤erent fromthe standard argument in the partial equilibrium framework, but rather that, bydoing so, the monopolist can depress the relative rental price of capital to wageso that the monopoly rent is maximized. To put it di¤erently, the old (labor-intensive) technology is "overly used" from the social welfare point of view. Itis shown that, when capital endowment falls to a certain interval, the labor-intensive technology would be fully abandoned under the perfect competitionmarket structure, but this technology can still survive when the new technologyis monopolized.In the two-period dynamic model, we also compare the perfect competition

(�rst best) and the monopoly. In the �rst best case, we show that there couldexist six di¤erent dynamic patterns of industrial development, depending on theinitial capital endowment and the e¢ ciency in the capital good production. Inthe monopoly case, we examine whether the potential monopolist chooses toimplement the new technology immediately or delay the operation. The timingdecision a¤ects the market structure dynamically because, the new technology,once operated, will become publicly and freely available to all the �rms oneperiod later, hence the market structure will change from monopoly to perfect

3

competition. In other words, the information externality generated by the �rst-mover monopolist is realized with a one-period lag.We show that adoption of the new technology (industrial upgrading), if

adopted, will be delayed if and only if the initial capital endowment is suf-�ciently small for two reasons. First, when the initial capital endowment issu¢ ciently small, the current monopoly rent is small in the �rst period. Sec-ond, the equilibrium inter-temporal interest rate would be small so that thefuture monopoly pro�t is not discounted too much. Consequently, adoption (in-dustrial upgrading) will be delayed until the pro�t is su¢ ciently large as capitalaccumulates.Our paper is di¤erent from the standard literature of "creative destruction"

in several important ways.4 First, we emphasize the role of the endowmentstructure with both capital and labor, which endogenously determines whichtechnology is superior and when to upgrade the industries, while in the creativedestruction literature labor is typically assumed to be the only production factorand which technology is superior is presumed rather than endogenously a¤ectedby the endowment structure. Second, the natures of the �rst mover�s behaviorand the analytical focuses are di¤erent. The standard creative destruction lit-erature mainly studies the developed countries, where the �rst mover obtainsmonopoly power by conducting very costly R&D to invent brand-new productsand the analytical focus is on how individual �rms make optimal R&D decisionsthat determines the speed of the aggregate technological progress. By contrast,our paper focuses on industrial upgrading in developing countries, where the�rst mover mainly adopts and adapts the existing foreign technologies. Themonopoly power is de facto, coming from the fact that some �rms happen tobe luckier than their competitors by having earlier access to the foreign bet-ter technology and related information (perhaps after some costly exploration).Our analytical focus is on the economic consequence of such potential monopolypower instead of how a �rm optimally acquires the monopoly power. Third, thepolicy implications are di¤erent. The major policy implications of the creativedestruction literature center on how to achieve the socially optimal level ofR&D by subsidy or designing a better patent system. In this paper, the defacto monopoly power bestowed on the �rst mover typically lasts for a very shortperiod because the exploration activities such as collection of market informa-tion and technology imitation are much less costly and their practices are moreeasily imitated as they are not patentable or legally protected in other forms.5

Correspondingly, our policy implications are more about how to crack downthe de facto monopoly power by lowering the information barrier to encouragetechnology adoption (by subsidizing the training program or encouraging FDI,etc) and facilitating the competition (by deregulation, for example), or alter-natively, how to rectify the price signals in the factor markets to facilitate thetimely industrial upgrading.

4See , for example, Aghion and Howitt (1992), Grossman and Helpman (1991), etc.5Even if the foreign better technology is adopted in the form of a legal license from abroad,

the violation of the international property rights protection is rampant in many developingcountries.

4

The paper is structured as follows. Section 2 studies the static model, fol-lowed by the analysis of the dynamic model in Section 3. Based on these twosections, industrial policies are discussed in Section 4. The last section con-cludes.

2 Static Model

Consider a static autarky populated by a continuum of identical householdswith a measure equal to unity. Each household is endowed with K units ofcapital and L units of labor (time). De�ne the endowment structure as k � K

L .There is only one consumption good, which can be produced with two alter-native C-D technologies, called technology 1 and technology 2, respectively.Throughout the paper we also interchangeably call them industry 1 and in-dustry 2, respectively. The corresponding production functions are given byF [1] (K1; L1) = A1K

�11 L1��11 and F [2] (K2; L2) = A2K

�22 L1��22 , where Ai;Ki;

Li and �i are the total factor productivity, capital, labor, and capital share fortechnology i 2 f1; 2g. Without loss of generality, assume technology 2 is morecapital intensive: 0 < �1 < �2 < 1. Following the pertinent literature, whentechnology 2 is adopted, it is referred to as industry upgrading. A representativehousehold�s utility function is

u(c) =c1�� � 11� � ; where � � 1:

We �rst analyze the competitive equilibrium when both technologies are freelyand publicly available, and then we analyze the case in which technology 2 isaccessible only to a monopolist.

2.1 Perfect Competition

The second welfare theorem holds, so the competitive equilibrium can be char-acterized by solving the following central planner problem:

G (K;L) = maxfKn;Lng2n=1

A1K�11 L1��11 +A2K

�22 L1��22

s:t:

K1 +K2 = K;

L1 + L2 = L;

Kn � 0; Ln � 0; n = 1; 2:

The resource allocation problem is a standard nonlinear programming problemwith a strictly concave objective function. As a result, there exists a uniquesolution characterized by the Kuhn-Tucker condition.If the solution is interior, then it satis�es two �rst-order conditions that

equate the marginal productivity of labor and capital across the two di¤erent

5

technologies. Let kn � Kn

Lndenote the capital-labor ratio in sector n. We obtain

k�1 =

"��1�2

��2 �1� �11� �2

�1��2 �A1A2

�# 1�2��1

; (1)

k�2 =

"��1�2

��1 �1� �11� �2

�1��1 �A1A2

�# 1�2��1

: (2)

Since k�1k�2=��1�2

��1��21��1

�< 1, the capital per worker is higher in industry 2

than industry 1 when the two industries coexist.Using the following factor market clearing conditions

k�1L1 + k�2L2 = K;

L1 + L2 = L;

together with (1) and (2), we get

L�1 =k�2L�Kk�2 � k�1

; L�2 =K � k�1Lk�2 � k�1

; (3)

K�1 = k�1L

�1; K

�2 = k�2L

�2: (4)

To satisfy the interior physical constraint L1 > 0 and L2 > 0, we must have

k�1 <K

L< k�2 :

If instead KL � k�1 or

KL � k�2 , then the solution is a corner one. To put it more

formally, we have the following proposition.

Proposition 1 Let k�1 and k�2 be de�ned as in (1) and (2). In the perfectcompetitive equilibrium,(a) If KL � k�1 , only technology 1 operates with the aggregate production functionG (K;L) = A1K

�1L1��1 .(b) If k�1 < K

L < k�2 ; then both technologies operate with resource allocatedaccording to (3) and (4). The implied aggregate production function is

G (K;L) = aK + bL,

where a � A1�1 (k�1)�1�1 and b � (1� �1)A1 (k

�1)�1 . (c) If KL � k�2 , only tech-

nology 2 operates and the aggregate production function G (K;L) = A2K�2L1��2 .

From the Proposition, the aggregate production function G (K;L) is con-stant return to scale, continuously di¤erentiable, concave and strictly increasingin both arguments. Intuitively, this proposition can be illustrated by Figure 1.

6

11

αkA

22

αkA

bak +

y

0 k~ *2k*

1k k

M

N

Q

Figure 1. Static Competitive Equilibirum

It plots the output per worker y as a function of the capital-labor ratio k. Thetwo di¤erent technologies are represented by the two di¤erent concave curves,which cross each other at the origin and point Q, where the corresponding

capital-labor ratio is denoted by ek � �A1

A2

� 1�2��1 . Clearly, technology 1 is

better than technology 2 if and only if k � ek. The two curves have one uniquecotangent straight line y = ak + b and the x-coordinates of the two tangentpoints M and N exactly correspond to k�1 and k

�2 given by (1) and (2). The

aggregate production function per labor (G(K;L)L ) is the convex envelope of thetwo technology curves. In particular, when k�1 < k < k�2 , both technologies areused simultaneously and the aggregate production function per labor is linear(denoted by segment MN), in which case the equilibrium rental price of capitalis just the slope a and the wage rate is just the intercept b. When k � k�1 , onlytechnology 1 is operating so G(K;L)

L = A1 (k)�1 . When k � k�2 , only technology

2 is operating, so G(K;L)L = A2 (k)

�2 .It is worth emphasizing that capital is not subject to the decreasing return

to scale when k�1 < k < k�2 , even though there is no productivity change ineither of the two speci�c technologies (i.e., A1 and A2 are �xed) or any non-convexity such as Marshallian externality. It is the resource reallocation duringthe technology upgrading that sustains the capital return.

7

2.2 Monopoly in Technology 2

Now suppose technology 2 is a new technology and only one potential entranthas access to it. Suppose this potential entrant is randomly chosen from thewhole population. Technology 1 is still publicly and freely accessible. The own-ership, hence the dividend, of each �rm is equally divided by all the households.The question is whether the potential entrant will operate the second technol-ogy, given the endowment K and L. Here this potential entrant can be alsointerpreted as the "e¤ective" coalition of all the people or �rms that have accessto technology 2.Denote the wage rate by W and the gross rental rate of capital by R. Cost

minimization implies that the unit costs under these two technologies are given,respectively, by

�1(W;R) =R�1W 1��1

A1 (�1)�1 (1� �1)1��1

and

�2(W;R) =R�2W 1��2

A2 (�2)�2 (1� �2)1��2

: (5)

Normalize A1 = 1 and let A2 = A. Thus �2(W;R) < �1(W;R) if and only if

R

W< �

"A��2

2 (1� �2)(1��2)

��1

1 (1� �1)(1��1)

# 1�2��1

: (6)

The factor markets are assumed to be perfectly competitive. Given the factorprices, cost minimization (no matter whether a �rm has monopoly power ornot) always implies that to produce Q units of output with technology 2 willrequire the following amount of the production factors:

L�2(Q;W;R) =Q

A�

�21��2

��2 �WR

��2 ; K�2 (Q;W;R) =

Q

A�

�21��2

��2�1 �WR

��2�1 :(7)

Similarly, to produce Q units of output with technology 1, it requires

L�1(Q;W;R) =Q�

�11��1

��1 �WR

��1 ; K�1 (Q;W;R) =

Q��11��1

��1�1 �WR

��1�1 :Observe that

k1(Q;W;R) � K�1 (Q;W;R)

L�1(Q;W;R)=

�11� �1

W

R; (8)

k2(Q;W;R) � K�2 (Q;W;R)

L�2(Q;W;R)=

�21� �2

W

R: (9)

If technology 2 is operated in the equilibrium, then it must be that RW � .

The equilibrium price of the output, denoted by P , must be no larger than

8

�1(W;R) because of the free entry of competitive �rms accessible to technology1. What is the necessary and su¢ cient condition under which only technology 2is operating (that is, the monopolist of technology 2 serves the whole economy)?The monopolist tries to maximize the pro�t:

� = maxP��1(W;R)

[P � �2(W;R)]Y

P;

where Y is the total consumption expenditure of the economy. For the moment,suppose the monopolist takes Y and factor pricesW and R as exogenously given.Then the unit elasticity implies that the monopolist would choose the highestpossible price P � = �1(W;R). Thus

� = [1� �2(W;R)

�1(W;R)]Y: (10)

The total expenditure is equal to the total household wealth, which is the sumof pro�ts, labor income and capital income:

Y = �+WL+RK: (11)

Combining (10) and (11), we obtain

Y =�1(W;R)

�2(W;R)(WL+RK) :

In this general equilibrium, the market clearing conditions for the consumptiongood, capital and labor jointly imply

AK�2L1��2 =Y

P;

or equivalently,

AK�2L1��2 =WL+RK

�2(W;R): (12)

The right-hand side is the total production cost divided by unit cost, so itis equal to the total output given by the left-hand side. (12) and (5) jointlydetermine the equilibrium rental wage ratio:

R

W=

�2(1� �2) k

: (13)

Thus the monopolist�s operation condition (6) is precisely equivalent to

k > k�2 ; (14)

where k�2 is given by (2). Interestingly, recall that in the competitive equilibriumonly technology 2 is operated if and only if k > k�2 (see Proposition 1). So thecuto¤ values for the capital labor ratio are identical for the perfect competition

9

and monopoly. Moreover, when k > k�2 , the monopoly also achieves the Paretooptimality. This is because the negative e¤ect of the price markup on theconsumption demand is exactly cancelled out by the positive income e¤ect ofthe extra pro�t earning on the demand through the general equilibrium channel.Nonetheless, the equilibrium prices for the output are di¤erent for these twodi¤erent market structures. Moreover, the monopoly pro�t is strictly positive,

given by �W =

��kk�2

��2��1�1�

(1��2) L when measured by the wage rate, while thepro�t is certainly zero in the perfectly competitive equilibrium.If the ownership of the monopolist �rm is no longer equally distributed

among all the households, then the equilibrium is no longer egalitarian in termsof consumption distribution across di¤erent households, but the equilibrium isstill Pareto optimal because the income distribution does not a¤ect the totalwealth of the economy or the aggregate demand for the consumption goods.The competitive equilibrium is, by contrast, always egalitarian independent ofthe ownership distribution of �rm 2 because the dividend is always zero.

One key assumption in the above analysis is that the monopolist takes Y andfactor prices W and R as exogenously given. However, the monopolist producesall the output in this closed economy , so it can actually a¤ect the factor pricesby choosing di¤erent output levels. Hence we will assume from now on that themonopolist is sophisticated enough to take all the general equilibrium e¤ect intoaccount.For, simplicity, �rst consider the necessary and su¢ cient condition under

which both technologies are operating (the monopolist of technology 2 onlyserves a fraction of total demand in the whole economy). The monopolist max-imizes the pro�t by choosing the optimal price P and quantity Q:

� = maxP��1(W;R);Q�0

[P � �2(W;R)]Q (15)

Combining (7), (8) and factor markets clearing conditions yields

K�1

L�1=

K � Q

A�

�21��2

��2�1(WR )�2�1L� Q

A�

�21��2

��2(WR )�2=

�11� �1

W

R;

which can be rewritten as

Q = Q(R

W) �

A�

�21��2

��2(1� �1) (1� �2)

�2 � �1

"�R

W

�1��2K � �1

1� �1L

�R

W

���2#:

(16)Thus Q0( RW ) > 0; implying a monotonic general-equilibrium relationship be-tween the monopolist output Q and the rental wage ratio R

W . [[[[wrong: This isbecause when the rental wage ratio becomes smaller, the monopolist technologybecomes more cost e¤ective than the labor-intensive technology, so the substi-tution e¤ect induces the monopolist to produce more, which means that the

10

competitive �rms (with technology 1) will produce less due to the resource con-straint (general equilibrium e¤ect). Since the monopolist will charge a markupprice and produce less than the social optimal amount for any given demand,the increase in the output produced by the monopolist cannot compensate thedecrease in the output produced by the competitive �rms, so the net change inthe total output goes down.]]]]The total output is

Qtotal = Q+Q1c; (17)

where Y1c denotes the total output produced by the competitive �rms withtechnology 1, so

Q1c =

�R

W

���1 � �21� �2

��R

W

�K

L

�(1� �2)��11 (1� �1)1��1

(�2 � �1)L

SO

Q =A�

�21��2

��2(1� �1) (1� �2)

�2 � �1

��R

W

�K

L� �11� �1

�L

�R

W

���2Therefore

Qtotal = bY (K;L; RW) �

8<: ��11 (1� �1)1��1h

�21��2 �

�RW

�KL

i �RW

���1+A

��21��2

��2(1� �1)

h�RW

�KL �

�11��1

i �RW

���29=; (1� �2)(�2 � �1)

L

(18)Now the monopolist solves (15) subject to (16). So the pro�t (measured by

wage) is given by

�

W=

A�

�21��2

��2(1� �1) (1� �2)

�2 � �1

��R

W

�K � �1

1� �1L

�� (19)" �

RW

��1��2(�1)

�1 (1� �1)1��1� 1

A (�2)�2 (1� �2)1��2

#:

Normalizing W = 1, (15) is equivalent to

maxR�

"R�1��2

(�1)�1 (1� �1)1��1

� 1

A (�2)�2 (1� �2)1��2

# �RK � �1

1� �1L

�;

which yields the following �rst-order condition

(1 + �1 � �2)R�1��2(�1)

�1 k+(�2 � �1)R�1��2�1

(1� �1)�1��11 � (1� �1)1��1

A (�2)�2 (1� �2)1��2

k = 0:

(20)

11

It can be veri�ed that the second order condition also holds, so there existsa unique solution R to (20), denoted as R = �(k), where function �(k) iscontinuously di¤erentiable and strictly decreasing.This condition also implies that R� < , k > k�1 , Q > 0: That is,

the monopolist technology will operate if and only if the capital is su¢ cientlyabundant (k > k�1). Again, this cuto¤ value is the same as in the perfectcompetitive equilibrium characterized previously.

In addition, according to (20), k > 0 and R > 0 would require that

R > (1 + �1 � �2)1

�2��1 , which, together with (20), implies that R is astrictly decreasing function of k: Obviously, �(k�2) < �(k�1) = . Let � 2((1 + �1 � �2)

1�2��1 ; 1), then R = � if and only if

k =A�1��11 ��22 (1� �2)1��2 (�2 � �1) (� )�1��2�1

(1� �1)2��1�1� (1 + �1 � �2) ��1��2

� ; (21)

which implies that k0(�) < 0 or equivalently, �0(k) < 0. Thus (19) is reduced to

�(�) =�1L

�2 � �1

���1��2 � 1

�2�1� (1 + �1 � �2) ��1��2

� :Thus � is a strictly increasing function of k since �0(�) < 0 and �0(k) < 0:Since the monopolist serves only a fraction of the whole market, we have

Q(R

W) < AK�2L1��2 ; (22)

which is equivalent to RW < �2

(1��2)k due to (16). Recall W is normalized tounity, so (22) holds if and only if

k =A�1��11 ��22 (1� �2)1��2 (�2 � �1)R�1��2�1

(1� �1)2��1�1� (1 + �1 � �2)

�R

��1��2� <�2

(1� �2)R;

from which we obtain k < k�; where we de�ne

k� � k�2

��2 (1� �1)

�1�2 � �21 + �2 � �22

� 1�2��1

: (23)

Observe that k� > k�2 .When k = k�, only technology 2 is operating and the corresponding interest

rate

R =

"(1� �1)2��1 �

�1

1

A��2�12 (1� �2)(1��2) [�1�2 � �21 + �2 � �22]

# 1�1��2

:

12

The pro�t at this threshold value is

� =L (�2 � �1)2

[1� �2] [�1�2 � �21 + �2 � �22]:

When k � k�, only technology 2 is operating and the market structure ismonopoly, but there are potential entrants with technology 1. Since both tech-nologies satisfy the Inada condition, both production factors must be fully usedwith positive equilibrium factor prices, which implies that the equilibrium ag-gregate output must be equal to AK�2L1��2 . However, the monopolist couldchoose to sell less than the total output if she wants. The total production costis still WL+RK. So her optimization problem (after normalizing W = 1) is

� = maxR;P��1(1;R);Q�AK�2L1��2

P �Q� [L+RK]: (24)

Here we still impose the constraint P � �1(1; R) because otherwise the potential

entrant would have stolen the whole market from the �rm that has private accessto technology 2.6 The monopolist also understands that the total sales revenueP �Q must be equal to the aggregate wealth of all the households given by (11)with W = 1. Given that the monopolist can fully control the quantity to sell,she has no incentive to charge a price lower than �1(1; R), thus the optimalprice P = �1(1; R). After substituting the optimal price into (24), we obtainthe following �rst-order condition with respect to R :

R =�1

1� �1

�K

Q

� 1�1�1

: (25)

The second-order condition is satis�ed for the maximization problem. Substi-tuting (25) back to (24) we obtain

�(K;L) = maxQ�AK�2L1��2

Q

(�1)�1 (1� �1)1��1

(�1

1� �1

�K

Q

� 1�1�1

)�1�(L+

�11� �1

�K

Q

� 1�1�1

K

)= max

Q�AK�2L1��2Q

11��1K

�1�1�1 � L

=�A

11��1 k

�2��11��1 � 1

�L; (26)

where the third equality obtains by setting Q� = AK�2L1��2 . So it is optimalfor the monopolist to sell all the output. Thus (25) becomes

R =�1

1� �1

�K

AK�2L1��2

� 1�1�1

=�1

1� �1A

11��1 k

1��2�1�1 : (27)

6One may think that once all the factors are used for production by the monopolist,potential entrants would be no longer able to a¤ect the pricing decision of the monopolistbecause all the factors have been used up at that stage. However, in this static model werule out this possibility by assuming that the pricing decisions by all the �rms including themonopolist must be announced with full commitment at the same time as (or before) thewage and rental rate of capital are posted.

13

For comparison, in the perfect competition case with the same inputs, therental price is equal to the marginal product of the capital:

R

W=

�2Ak�2�1

(1� �2)Ak�2=

�2k�1

(1� �2);

so when k = k�, the rental price of capital is smaller under the monopoly thanin the perfect competition case.

Thus

�(k�L;L) =

"�2 (1� �1)1� �2

�(�1)

�1 (1� �1)�1�2 � �21 + �2 � �22

� 11��1

� 1#L:

We can show that

�(k�L;L) >L (�2 � �1)2

[1� �2] [�1�2 � �21 + �2 � �22]:

This means that the pro�t function �(K;L) is not continuous at the pointwhen K = k�L. It jumps up at that point. The reason is that the rental price ofcapital is depressed under the monopoly. However, the monopolist still achievessocial e¢ ciency since the aggregate output and aggregate consumption are thesame as in the perfect competition. When k < k�1 , which is given by (1), onlytechnology 1 is operating in the equilibrium and R

W must be strictly larger than :When k 2 (k�1 ; k�), both technologies are operating. Let Qmi and Qci de-

note the output produced with technology i (i = 1; 2) when technology 2 ismonopolized and publicly available (so perfect competition for technology 2),respectively.

Lemma 2 When k 2 (k�1 ; k�), we must have Qm1 > Qc1 , Qm2 < Qc2; Q

m1 +Q

m2 <

Qc1 +Qc2.

Proof. Let ek1 and ek2 denote the equilibrium capital-labor ratios for the twotechnologies in the monopoly. Then by the factor market clearing conditions weobtain the total output for each technology:

Qm1 = �(ek1;ek2) � ek2L�Kek2 � ek1

!�ek1��1 ; Qm2 = (ek1;ek2) � A

K � ek1Lek2 � ek1

!�ek2��2 ;(28)

where ek1 and ek2 are given by (8) and (9), respectively and RW is endogenously

determined by (20). In the competitive equilibrium, we have

Qc1 = �(k�1 ; k

�2); Q

c2 = (k

�1 ; k

�2);

where k�1 and k�2 are given by (1) and (2). Since (8)-(9) always hold, independent

of the market structure in the goods market, RW < implies ek1 > k�1 and

14

ek2 > k�2 . Moreover, ek2 > k > ek1. Consequently. Qm1 > Qc1 and Qm2 <Qc2. This is because function �(�; �) strictly increases in both arguments whilefunction (�; �) strictly decreases in both arguments. The monopoly obviouslydistorts the resource allocation compared with the competitive equilibrium, soQm1 +Q

m2 < Qc1 +Q

c2.

Furthermore, we have

Proposition 3 When k � k�1 , technology 2 is not operating and the marketachieves the competitive equilibrium with technology 1; When k 2 (k�1 ; k�), bothtechnologies are operating, the equilibrium R

W (WLOG, W � 1) is uniquely de-termined by (20), the total pro�t is given by (19), and the total outputs by tech-nologies 1 and 2 are given by (28) ; When k � k�, only technology 2 is operating

with RW determined by (13) and the pro�t being �

W =�A

11��1 k

�2��11��1 � 1

�L, the

total output is AK�2L1��2 , same as the competitive equilibrium output.

When compared with the social optimal equilibrium (perfect competition),the new technology (technology 2) is adopted under monopoly at the samethreshold value for capital endowment, but the total output is smaller thanthe �rst best when k 2 (k�1 ; k�), and the old technology 1 is "overused" in thesense that industry 1 should have been abandoned when k 2 (k�2 ; k�) but it stilloperates in the monopoly.

2.3 A Detour: Costly Acquisition of Technology 2

Now suppose technology 2 is still privately accessible to one �rm but it wouldrequire a �xed cost to operate it for the �rst time. After one period, the tech-nology can be freely imitated by all the other �rms.One Formulation:Denote the entry cost by � (in the units of capital). Technology 2 will be

adopted if and only if�(K;L) � R�:

Consider the simplest case when k is su¢ ciently large so that only technology2 is operating.

�

W=

��K��Lk�2

��2��1� 1�

(1� �2)L � R

W�;

where RW = �2L

(1��2)(K��) , so��K��Lk�2

��2��1� 1�

(1� �2)L � �2L

(1� �2) (K � �)��K � �Lk�2

��2��1� 1 � �2

(K � �)�

15

There exists a unique K�(L; �) such that the above inequality holds if and onlyif K � K�(L; �), where K�

1 (L; �) > 0 and K�2 (L; �) > 0.

Alternative Formulation: Denote the �xed cost by � (in the units ofconsumption goods, paid by credit). Technology 2 will be adopted if and onlyif

�(K;L) � P�: (29)

When k 2 (k�1 ; k�); the above inequality becomes

�(�) =�1L

�2 � �1

���1��2 � 1

�2�1� (1 + �1 � �2) ��1��2

� � (� )�1 �

��11 (1� �1)1��1(30)

so there must exist a unique �� 2 ((1 + �1 � �2)1

�2��1 ; 1) such that (30) holds

if and only if � 2 ((1 + �1 � �2)1

�2��1 ; ��], or equivalently,

k � A�1��11 ��22 (1� �2)1��2 (�2 � �1) (�� )�1��2�1

(1� �1)2��1�1� (1 + �1 � �2) ���1��2

� :

When k � k�, inequality (29) becomes���2

(1��2) RW k�2

��2��1� 1�

(1� �2)L �

�RW

��1�

��11 (1� �1)1��1;

which determines an upper bound for RW and hence a lower bound for k. More-

over, this lower bound for k decreases with L� and A.

3 Dynamic Models

Now we extend our analysis to a dynamic environment to study the dynamicpattern of technology adoption with possible changes in the market structure.The key insights can be illustrated with a simple two-period model. Again, we�rst characterize the socially e¢ cient equilibrium, where both technologies arepublicly and freely available. The derived perfect competitive dynamic equilib-rium serves as an analytical benchmark. Then we explore what happens whenthe capital-intensive technology is initially privately accessible to only one �rm(or an e¤ective coalition of some �rms). We compare these two scenarios anddiscuss the possible welfare-improving role that government can play.

3.1 Perfect Competition

Consider a two-period perfect competition dynamic model.7 A representativehousehold is endowed with K0 capital and L labor. Let Et and Ctdenote,

7Ju, Lin and Wang (2010) analytically characterize the equilibirum in an in�nite-horizondynamic growth model with in�nite industries, which di¤er in their capital intensities. Wang(2011) study how international trade and dynamic trade policies a¤ect the industrial upgradingwhen there are in�nite industries in each country.

16

respectively, the capital used for production and consumption at period t 2f1; 2g. Capital good itself cannot be consumed but it can be produced withAK technology with the investment-speci�c technological progress parameter�. Without loss of generality, assume all the capital used for production fullydepreciates. Consumption goods are perishable and thus are not saved in theequilibrium. Therefore, the arti�cial social planner solves the following problem.

maxC1��1 � 11� � + �

C1��2 � 11� �

subject to

E2 = �(K0 � E1);C1 � G (E1; L) ;

C2 � G (E2; L) ;

E1 � 0; E2 � 0; C1 � 0; C2 � 0;K0 and L are given.

To make the analysis more interesting and empirically more relevant, we as-sume �� > 1 so that the capital production is su¢ ciently productive to supportcapital accumulation and technology upgrading. Depending on the di¤erentcombination of technologies over di¤erent periods, we have six possible equilib-rium patterns of technology adoption. Next, we characterize the necessary andsu¢ cient conditions for all these patterns one by one.Pattern 1: Only Technology 1 in both periods Establish the La-

grangian:

L =�E�11 L1��1

�1�� � 11� � + �

�E�12 L1��1

�1�� � 11� � + � [�(K0 � E1)� E2] ;

which yields the following two �rst-order conditions relative to E1 and E2,respectively:

�1�E�11 L1��1

���E�1�11 L1��1 = ��;

��1�E�12 L1��1

���E�1�12 L1��1 = �:

We obtain

E1 =K0

1 + ��1 (��)1

��1+1+�1�; E2 = K0

(��)1

��1+1+�1�

1 + ��1 (��)1

��1+1+�1�:

1

��1 + 1 + �1�Since �� > 1and � 2 [0; 1], to ensure E1 � k�1L and E2 � k�1L, we must have

17

K0

L� �1k

�1 ; (31)

where k�1 is given by (8) and �1 is de�ned as

�1 �1 + ��1 (��)

1��1+1+�1�

(��)1

��1+1+�1�:

In other words, technology 1 alone is adopted in both periods if and only if (31)holds.Pattern 2: Technology 2 in both periods Following the same method,

we have:

E1 =K0

1 + ��1 (��)1

��2+1+�2�; E2 = K0

(��)1

��2+1+�2�

1 + ��1 (��)1

��2+1+�2�;

To ensure E1 and E2 larger than k�2L, we require

K0

L� �6k

�1 ; (32)

where k�2 is given by (9) and �6 is de�ned as

�6 ��2 (1� �1)�1 (1� �2)

�1 + ��1 (��)

1��2+1+�2�

�:

In other words, technology 2 alone is adopted in both periods if and only if (32)holds.Pattern 3: Technologies 1 and 2 in both periods We can derive from

the �rst order conditions that

E1 =

h1� (��)

1�

i(1� �1)k�1L+ �1�K0

[(��)1� + �]�1

;

E2 = �(�1 (��)

1� K0 �

h1� (��)

1�

i(1� �1) (k�1)L

[(��)1� + �]�1

):

To ensure k�1L < E1; E2 < k�2L, we must have

�3k�1 <

K0

L< �4k

�1 ;

where

�3 �(��)

1� + ��1 � (1� �1)

�1�; �4 �

"1

�+(��)

� 1� � (1� �2)�2

#�2 (1� �1)�1 (1� �2)

:

18

The non-emptiness of K0 further requires �3 < �4, or

(��) <

�(1� �1)(1� �2)

��: (33)

That is, � has to be su¢ ciently small.

Pattern 4: Technology 1 in period 1, Technologies 1 and 2 inperiod 2 The Euler equation is�

A1 (k�1)�1 � A2 (k

�2)�2 �A1 (k�1)

�1

k�2 � k�1k�1

�L+

A2 (k�2)�2 �A1 (k�1)

�1

k�2 � k�1�(K0 � E1)

=

��� [A2 (k

�2)�2 �A1 (k�1)

�1 ]

�1L(1��1)(1��) (k�2 � k�1)

� 1�

E��1��1+1

�1 :

To ensure E1 � k�1L, we need

K0

L� �3k

�1 : (34)

On the other hand,

�A1 (k

�1)�1 � A2 (k

�2)�2 �A1 (k�1)

�1

k�2 � k�1k�1

�L+

A2 (k�2)�2 �A1 (k�1)

�1

k�2 � k�1E2

=

��� [A2 (k

�2)�2 �A1 (k�1)

�1 ]

�1L(1��1)(1��) (k�2 � k�1)

� 1��K0 �

E2�

���1��1+1�

;

To ensure k�1L < E2 < k�2L, we get

�1k�1 <

K0

L< �2k

�1 ; (35)

where

�2 � [��]1

���1+�1�1

�1� �11� �2

� ���1��1+1

+�2 (1� �1)�1 (1� �2) �

:

The non-emptiness for the set of K0 requires �1 < �2, or equivalently,

[��]1

���1+�1�1 <[��]

1� � 1�1�

+ 1;

which must hold because �� > 1. Also we require

�1 < �3;

or equivalently,

�1� < (��)1

��1+1+�1�h(��)

1� + ��1 � 1

i;

19

which automatically holds. In summary, the equilibrium demonstrates this in-dustrial pattern if and only if (34) and (35) hold.Pattern 5: Technology 1 in period 1, Technology 2 in period 2

The Euler equation is

���2 [�(K0 � E1)]�2�1���2�AL1��2

�1��= �1E

�1�1��1�1 L(1��1)(1��):

so E1 � k�1L implies

���2 [�(K0 � k�1L)]�2�1���2 �AL1��2�1�� � �1 (k

�1L)

�1�1��1� L(1��1)(1��);

which is equivalent toK0

L� �5k

�1 ;

where

�5 ���1�2

��1 "��(1��)�2

�1� �11� �2

�(1��2)((1��))# 11��2+��2

+ 1:

On the other hand

���2E�2�1���22

�AL1��2

�1��= �1

�K0 �

E2�

��1�1��1�L(1��1)(1��)

so E2 � k�2L implies

���2 (k�2L)

�2�1���2�AL1��2

�1�� � �1

�K0 �

Lk�2�

��1�1��1�L(1��1)(1��);

which is reduced toK0

L� �2k

�1 :

In summary, we must have

�2k�1 �

K0

L� �5k

�1 ;

the non-emptiness of which requires �2 � �5, or equivalently�(��)

�1�1� �11� �2

��� 1��1��1+1

� �2 (1� �1)�1 (1� �2) �

(�(��)

�1�1� �11� �2

���� 11��2+��2

� 1)+1;

(36)which holds if and only if (33) does not hold. In other words, Pattern 3 andPattern 5 are incompatible with each other.Pattern 6: Technologies 1 and 2 in period 1, Technology 2 in period

2:

20

���2�AE�22 L1��2

���AE�2�12 L1��2

=

24 �A1 (k�1)�1 � A2(k�2 )�2�A1(k

�1 )�1

k�2�k�1k�1

�L

+A2(k

�2 )�2�A1(k

�1 )�1

k�2�k�1E1

35�� A2 (k�2)�2 �A1 (k�1)�1k�2 � k�1

:

From k�1L < E1 < k�2L, we obtain

�6k�1 >

K0

L> �5k

�1 : (37)

To ensure �6 > �5, we require

�2 (1� �1)�1 (1� �2)

�1 + ��1 (��)

1��2+1+�2�

�>�2�1

"��(1��)�2

�1� �11� �2

�(1��2)((1��))# 11��2+��2

+1;

which must be true because �2(1��1)�1(1��2) > 1 and

(1� �1)(1� �2)

��1 (��)1

��2+1+�2� >

"��(1��)�2

�1� �11� �2

�(1��2)(1��)# 11��2+��2

:

On the other hand E2 � k�2L requires

K0

L� �4k

�1 : (38)

To ensure �6 > �4, we require

(��)1

��2+1+��2 >

"(��)

� 1� � 1

�2

#� + 1;

which automatically holds because �� > 1. In summary, the equilibrium hasthis pattern if and only if (37) and (38) hold.To summarize, we have the following proposition:

Proposition 4 Suppose �� > 1 and � 2 [0; 1]. When �� ��1��11��2

��is sat-

is�ed, the dynamic equilibrium follows Pattern 1 when K0

L 2 (0; �1], Pattern 4when K0

L 2 (�1; �2), Pattern 5 when K0

L 2 [�2; �5], Pattern 6 when K0

L 2 (�5; �6),and Pattern 2 when K0

L 2 [�6;1). When �� <�1��11��2

��, then the dynamic

equilibrium follows Pattern 1 when K0

L 2 (0; �1], Pattern 4 when K0

L 2 (�1; �3],Pattern 3 when K0

L 2 (�3; �4), Pattern 6 when K0

L 2 [�4; �6), and Pattern 2when K0

L 2 [�6;1).

21

This proposition states that the dynamic pattern depends on the initialcapital labor ratio and the technological parameter �. More speci�cally, when(33) is violated (that is, � is su¢ ciently large), then the equilibrium dynamicpattern of technology adoption is given by Figure 2.

2θ

1Pattern 4Pattern

1θ

5Pattern

5θ

6Pattern 2Pattern

6θ LK0

Figure 2: Dynamic Pattern of Technology Adoption when �� ��1��11��2

��When (33) is satis�ed (that is, � is su¢ ciently small, but still strictly largerthan 1

� ), then

3θ

1Pattern 4Pattern

1θ

3Pattern

4θ

6Pattern 2Pattern

6θ LK0

Figure 3: Dynamic Pattern of Technology Adoption when �� <�1��11��2

��3.2 Monopoly with Technology 2

Now consider a dynamic environment identical to the previous one except thattechnology 2 is privately accessible to only one �rm, which decides when toimplement this new technology. We call this �rm "�rm M" thereafter. If tech-nology 2 is implemented in period 1, then we assume that the technology be-comes publicly known in period 2 because people can successfully imitate thisnew technology after it is operated. If the implementation of technology 2 isdelayed until period 2, then the monopoly rent can be reaped only in period2. Since the second welfare theorem is not directly applicable, we need to solvethe decentralized optimal decisions of households and �rms. A representativehousehold solves

maxC1��1 � 11� � + �

C1��2 � 11� �

subject to

P1C1 +P2C2eR � (W1L+R1E1 +�1) +

(W2L+R2E2 +�2)eR ; (39)

E2 = �(K0 � E1);E1 � 0; E2 � 0; C1 � 0; C2 � 0;

K0 is given.

22

From the household optimization, we obtain

�

�C2C1

���=

P2

P1 eR; (40)

which, together with (39), implies

C1 =(W1L+R1E1 +�1) +

(W2L+R2E2+�2)eRP1 + �P1

hP2

�P1 eRi1� 1

�

; (41)

C2 = C1

�P2

�P1 eR�� 1

�

: (42)

To ensure E1E2 > 0, we must have the interest rate

eR = �R2R1

: (43)

Substituting (43) back to (40), we obtain

��

�C2C1

���=P2=R2P1=R1

: (44)

All the �rms with public technology maximize the total pro�t by taking thefactor prices as given. Firm M also maximizes its present discounted value oftotal pro�t. Firm M understands that it can change the relative factor prices bychanging the output when technology 2 is operated for the �rst time. Firm Mhas three options. Option 1 is to start operating technology 2 in period 1; option2 is to start operating technology 2 in period 2; option 3 is never to operatetechnology 2. It is obvious that the pro�t from option 3 is zero for this �rm. Inthis closed economy, the goods market, labor market and capital market mustbe all cleared at each period. Next we will characterize the consequences of the�rst two options for Firm M.Option 1: Immediate Operation of Technology 2In period 1, technology 2 is either operated together with technology 1 (Pos-

sibility A) or solely operated (Possibility B). Therefore, the market structure iseither a mixture of competition and monopoly or a pure monopoly in the �rstperiod, but in the second period the market structure is perfect competitive nomatter what technologies will be used. Thus �2 = 0 and �1 > 0. In addition,there are three possible cases for the technology operations for period 2: onlytechnology 1, only technology 2, and both technologies.Suppose �rm M uses up all the capital in period 1, then the output in period

2 is zero, which implies that P2 will be positive in�nity (assuming � 2 (0; 1])driving up the rental price for capital high enough in period 1 such that it isnot optimal for �rm M to use so much capital. Thus, there are two possibilities.Possibility A for Option 1. Both technologies are operated in

period 1.

23

In this case, as suggested by (19), we have

P1=R1 = �1(W1; R1)=R1 =

�R1

W1

��1�1(�1)

�1 (1� �1)1��1

=

��(E1L )

��1�1(�1)

�1 (1� �1)1��1;

where, like (20), function �(E1L ) is de�ned as the implicit solution ofR1

W1as a

function of E1L in the following equation

(1 + �1 � �2)�R1

W1

��1��2(�1)

�1

E1L+(�2 � �1)

�R1

W1

��1��2�1(1� �1)

�1��11 � (1� �1)1��1

A (�2)�2 (1� �2)1��2

E1L

= 0:

(1 + �1 � �2)�R1

W1

E1L

��1��2(�1)

�1 +(�2 � �1)

�R1

W1

E1L

��1��2�1(1� �1)

�1��11 � (1� �1)1��1

A (�2)�2 (1� �2)1��2

�E1L

�(�1��2)= 0:

so �0(E1L ) < 0 butE1L �(

E1L ) as a whole is a strictly increasing function of

E1L .

It remains to determine E1L . Note that the total output in period 1 is

Y1(E1; L) = y1

�E1L

�L;

where

y1

�E1L

��

8<: ��11 (1� �1)1��1h

�21��2 � �(

E1L )

E1L

i���1(E1L )

+A�

�21��2

��2(1� �1)

h�(E1L )

E1L � �1

1��1

i���2(E1L )

9=; (1� �2)(�2 � �1)

:

(45)In period 2, both technologies are freely available and the market is perfectlycompetitive.Possibility A1-a. Suppose E2

L � k�2 so that only technology 2 is operated inperiod 2.The market clearing conditions jointly imply that

C2 = AE2�2L1��2

and

P2=R2 = �2(W2; R2)=R2 =

�W2

R2

�1��2A (�2)

�2 (1� �2)1��2

W2

R2=

(1� �2)E2�2L

=(1� �2) �(K0 � E1)

�2L:

In the equilibrium, C1 = Y1, hence (44) implies

24

��

A��(K0

L � E1L )��2

y1(E1L )

!��=

(�1)�1 (1� �1)1��1

�W2

R2

�1��2A (�2)

�2 (1� �2)1��2�R1

W1

��1�1��

�y1(

E1L)

��=

(�1)�1 (1� �1)1��1

��(K0�E1)

L

�1��2+�2�A1���2

��(E1L )

��1�1 ;(46)

which uniquely determines E1L because the left hand side strictly increases withE1L while the right hand side strictly decreases with it. To support such anequilibrium, we require

E1L2 (k�1 ; k�) and

�(K0 � E1)L

� k�2 :

which jointly imply thatK0

L>k�2�+ k�1 :

[[[ observe that in possibility B1-a when � = 1, we have

K0

L����2�1+ 1

�k� >

k�2�+ k�1 :

so it is compatible. However, when the initial endowment can support bothA1-a and B1-a, �rm M will choose B1-a since the latter gives a higher pro�t.In addition, in possibility B1-c when � = 1, we have

[(� + �1) � � (1� �1)] k�1�1�

<K0

L<(� + 1) k�2

��;

and we also require

�� <(1� �1)(1� �2)

�� + �2� + �1

�(<

�2�1

1� �11� �2

)

which is compatible with A1-a only if

k�2�+ k�1 <

(� + 1) k�2��

, �� <k�2k�1=�2�1

1� �11� �2

:

Thus to summarize, B1-c and A1-a are mutually compatible only if

(� + 1) k�2��

>K0

L> maxfk

�2

�+ k�1 ;

[(� + �1) � � (1� �1)] k�1�1�

g

25

and�� <

�2�1

1� �11� �2

:

Note that

k�2�+ k�1 >

[(� + �1) � � (1� �1)] k�1�1�

, 1� �11� �2

> ��:

However, �rm M will prefer B1-c to A1-a when both are feasible.]]]The pro�t is given by

�1 = �1(E1L)W1L;

where

�1(E1L) �

A�

�21��2

��2(1� �1) (1� �2)

�2 � �1

��(E1L)E1L� �11� �1

��"

��1��2(E1L )

(�1)�1 (1� �1)1��1

� 1

A (�2)�2 (1� �2)1��2

#: (47)

Thus �01(E1L ) > 0:

As a special case, when � = 1, then (46) becomes

�y1(E1L) =

(�1)�1 (1� �1)1��1 (K0�E1)

L

�2��(E1L )

��1�1 :

.Possibility A1-b. Suppose E2

L 2 (k�1 ; k�2) so that both technologies will beoperated in period 2.The market clearing conditions jointly imply that

C2 = aE2 + bL;

where a � �1 (k�1)�1�1 and b � (1� �1) (k�1)

�1 . Observe that

P1R1

=

�R1

W1

��1�1(�1)

�1 (1� �1)1��1=

��(E1L )

��1�1(�1)

�1 (1� �1)1��1P2R2

=1

a=

1

�1 (k�1)�1�1

(44) becomes

��

a�(K0

L � E1L ) + b

y1(E1L )

!��=

P2R2

P1R1

=

�1� �1�1

k�1�(E1L)

�1��1; (48)

26

which can uniquely determine E1L .

Therefore, the pro�t is �1(�E1L

��)W1L. To support this equilibrium, we

require

�(K0

L� E1

L) 2 (k�1 ; k�2)

andE1L2 (k�1 ; k�):

which jointly imply that

k�1�+ k�1 <

K0

L<k�2�+ k�:

[[[ observe that in possibility B1-a when � = 1, we have

K0

L����2�1+ 1

�k� >

k�2�+ k�:

]]]Possibility A1-c. Suppose E2

L 2 (0; k�1 ] so that only technology 1 will beoperated in period 2.Note that

P1R1

=

��(E1L )

��1�1(�1)

�1 (1� �1)1��1

P2R2

=

�R2

W2

��1�1(�1)

�1 (1� �1)1��1

W2

R2=

(1� �1)E2�1L

thus (44) becomes

��

��1(K0

L � E1L )

�1

y1(E1L )

!��=

�(1� �1)�1

�(K0

L� E1

L)�(

E1L)

�1��1(49)

which can uniquely pin down E1L . We require

0 < �(K0

L� E1

L) � k�1

k�1 <E1L

< k�:

which jointly imply that

k�1�+ k�1 <

K0

L<k�1�+ k�:

27

[[[ observe that in possibility B1-a when � = 1, we have

K0

L����2�1+ 1

�k� >

k�1�+ k�:

]]]

As a special case, when � = 1, then (49) becomes

�y1(E1L) = (

K0

L� E1

L)

�(1� �1)�1

�(E1L)

�1��1:

Possibility B for Option 1 : Only technology 2 is operated in period 1.

P1=R1 =

�W1

R1

�1��1(�1)

�1 (1� �1)1��1=

�E1L

�1��2�1A

becauseR1W1

=�1

1� �1A

11��1

�E1L

� 1��2�1�1

:

The pro�t is

�B1 =

A

11��1

�E�1L

��2��11��1

� 1!W1L:

Possibility B1-a. Only technology 2 is adopted in the perfect competitivemarket in period 2.

P2=R2 =

�W2

R2

�1��2A (�2)

�2 (1� �2)1��2=

h(1��2)�2

�(K0�E1)L

i1��2A (�2)

�2 (1� �2)1��2

Then (44) yields:

E�1 =�K0�

�� �2�1

� 11��2+�2�

+ �

(50)

and

E�2 =���� �2�1

� 11��2+�2��

�� �2�1

� 11��2+�2�

+ �

K0:

Thus the pro�t becomes

�B1a =

26640B@A

264 �K0=L��� �2�1

� 11��2+�2�

+ �

375�2��11CA

11��1

� 1

3775W1L:

28

To justify possibility B for option 1, we must have

E�1 � k�L and E�2 � k�2L

which are reduced to

�K0��� �2�1

� 11��2+�2�

+ �

� k�L: (51)

In particular, when � = 1, then (50) becomes

E�1 =K0

� �2�1 + 1;

(51) becomesK0

� �2�1 + 1� k�L: (52)

and

�B1a =

2640@A" K0=L

� �2�1 + 1

#�2��11A 11��1

� 1

375W1L:

Possibility B1-b. Only technology 2 in period 1 and only technology 1 inperiod 2.Then (44) becomes

L(1��)(�2��1)�A��1E��2+(1��2)1 = ���1+��1 [(K0 � E1)]1��1+��1 ; (53)

which uniquely determines E1. Moreover

@E�1@�

< 0;@E�1@A

� 0; @E�1

@L� 0; @E

�1

@�� 0; @E

�1

@K0> 0;

where "=" holds only when � = 1, in which case we also have

E�1 =K0

1 + �;E�2 =

��K0

1 + �:

We requireK0

1 + �� k�L;

��K0

1 + �� k�1L:

which can hold only when

k� [1 + �] � K0

L� k�1 [1 + �]

��;

29

which is impossible because �� > 1.When � < 1, we require

E1 � k�L and �(K0 � E1) � k�1L:

��A��1�E1L

���2+(1��2)= [�(K0 � E1)]1��1+��1

thus we must have

��A��1 (k�)��2+(1��2) � [�(K0 � E1)]1��1+��1 � [k�1 ]

1��1+��1 :

And the related pro�t is

�B1b =

A

11��1

�E�1L

��2��11��1

� 1!W1L:

Possibility B1-c. Only technology 2 in period 1 (that is,E�1

L 2 (k�1 ; k�)

). Both technologies are adopted in the perfect competitive market in period2.(that is, �(K0�E�

1 )L 2 (k�1 ; k�2) )

(44) becomes.�a�(

K0

L� E1

L) + b

���=

A1��

�� (k�1)�1�1 �E1

L

�(1��2)+��2 ; (54)

which uniquely determines E1L . In particular, when � = 1, we have

E1L

=a�K0

L + b

�� (k�1)�1�1 + a�

E2L

=�(K0 � E�1 )

L=

K0

L �� � (1� �1)k�1

� + �1

Recall a � �1 (k�1)�1�1 and b � (1� �1) (k�1)

�1

hence the pro�t is given by

�B1c =

0@A 11��1

a�K0

L + b

�� (k�1)�1�1 + a�

!�2��11��1

� 1

1AW1L:

We require

[(� + �1) � � (1� �1)] k�1�1�

<K0

L<[(� + �1) �] k

� � (1� �1)k�1�1�

(� + 1) k�1��

<K0

L<(� + 1) k�2

��

30

which jointly imply that

[(� + �1) � � (1� �1)] k�1�1�

<K0

L<(� + 1) k�2

��:

The above set is not empty i¤

(1

�<)� <

(1� �1)(1� �2)

��2 + �

� + �1

�1

�(55)

Comparing B1-a and B1-c: Suppose (55) is satis�ed,

K0

L�

���2�1+ 1

�k�

[(� + �1) � � (1� �1)] k�1�1�

<K0

L<(� + 1) k�2

��

they are compatible if and only if���2�1+ 1

�k� <

(� + 1) k�2��

;

which is impossible because���2�1+ 1

���2 (1� �1)

�1�2 � �21 + �2 � �22

� 1�2��1

<(� + 1)

��:

Thus B1-a and B1-c are mutually exclusive.Comparing B1-c and A2,

[(� + �1) � � (1� �1)] k�1�1�

<K0

L<(� + 1) k�2

��;

K0

L� (1 + �)

��

"�2 (1� �1)

�1�2 � �21 + �2 � �22

��1�2

��1 �1� �11� �2

�1��1# 1�2��1

A�1

�2��1

�� <(1� �1)(1� �2)

��2 + �

� + �1

�;

which is impossible because

�2 (1� �1)�1�2 � �21 + �2 � �22

> 1:

Thus A2 and B1-c are mutually exclusive.

Option 2: Start Technology 2 in Period 2.

31

The market structure is perfectly competitive in period 1 with only technol-ogy 1 in operation. Thus

P1R1

=

�R1

W1

��1�1(�1)

�1 (1� �1)1��1R1W1

=�1

1� �1L

E1

P1 =(R1)

�1 W 1��11

(�1)�1 (1� �1)1��1

C1 = E�11 L1��1 :

In period 2, there are two possibilities: Possibility A is that only technology 2is operated in period 2. Possibility B is that both technologies are operated inperiod 2.Possibility A for Option 2: only technology 2 is operated in period

2

P2 =(R2)

�1 W 1��12

(�1)�1 (1� �1)1��1

P2R2

=

�R2

W2

��1�1(�1)

�1 (1� �1)1��1

R2W2

=�1

1� �1A

11��1

�E2L

� 1��2�1�1

C2 = A [�(K0 � E1)]�2 L1��2

(44) implies

��

�A [�(K0 � E1)]�2 L1��2

E�11 L1��1

���=

0@ L�1��2�1�1

A1

1��1E1E1��2�1�12

1A1��1

(56)

which is reduced to

E1��1+��11 �A1�� = L(�2��1)(1��)�(��1)�2(K0 � E1)1��2+��2 : (57)

Thus E�1 can be uniquely determined by (57). In addition, we have

@E�1@�

< 0;@E�1@A

� 0; @E�1

@L� 0; @E

�1

@�� 0; @E

�1

@K0> 0;

32

where "=" holds if and only if � = 1, in which case

E�1 =K0

1 + �;E�2 =

��K0

1 + �;

R1W1

=�1 (1 + �)

(1� �1)L

K0;R2W2

=�1

1� �1A

11��1

���K0

L (1 + �)

� 1��2�1�1

;

�2 =

A

11��1

���K0

(1 + �)L

��2��11��1

� 1!LW2

�A2eR = �

0@1� "A� K0��

L (1 + �)

��2��1#� 11��1

1ALW1

To ensure a non-negative pro�t, we require

K0

L� (1 + �)

��A�

1�2��1 : (58)

To justify that �rm M can serve the whole market in period 2 with technology2, we require

E�2 � k�L;

which means

K0

L� (1 + �)

��

"�2 (1� �1)

�1�2 � �21 + �2 � �22

��1�2

��1 �1� �11� �2

�1��1# 1�2��1

A�1

�2��1 ;

(59)which automatically ensures (58) because

�2 (1� �1)�1�2 � �21 + �2 � �22

> 1 and��1�2

��1 �1� �11� �2

�1��1> 1:

For more general � 2 [0; 1), we have

�A2eR =

"L

�1��2�1�1

��1��2�1�1 E�1 [(K0 � E�1 )]

1��2�1�1

���K0

(1 + �)L

��2��11��1

�A�1

1��1

!#LW1:

Now we can compare �A2eR with the pro�t in possibility B for option1, �B1. Inparticular, when � = 1, we have

�A2eR > �B1a ,

� + 1�

0@A" 1

� �2�1 + 1

#�2��11A 11��1

(K0=L)�2��11��1 > �

"A

���

(1 + �)

��2��1#� 11��1

(K0=L)��2��1

1��1

33

which holds if and only if

x1 < (K0=L)�2��11��1 < x2 (60)

where

x1;2 � (1 + �)�p�

2

A

�1

��2�1+1

��2��1! 11��1

� � (1 + �)2 � 4�

0@ (1 + �)

��h� �2�1 + 1

i1A

�2��11��1

> 0

Therefore, when (60) holds,�A2eR�B1

> 1; otherwise�A2eR�B1

� 1. Recall, we have torequire (51) and (59). Therefore, when K0=L is su¢ ciently large, it is betterto operate technology 2 immediately (in period 1) than to delay to period 2.Recall that under Possibility B1-c, we require

K0

L� #1 �

���2�1+ 1

�k�: (61)

and now under Possibility A2, we require (59):

K0

L� (1 + �)

��k�:

Thus they are comparable only when (61) is satis�ed. De�ne

�1;2 � A1��11��2

26642h� �2�1 + 1

i 1��21��1

k�

(1 + �)�p�

3775(1��1)(�2��1)

1��2

:

Lemma 5 Suppose � = 1. [1] When A > �1, option B1-a is better than option

A2 if K0

L 2 [#1; x1) [ (x2;1) and the opposite is true if K0

L 2 (x1; x2). Thesetwo options are indi¤erent for the �rm M when K0

L = x1 or x2. [2] WhenA 2 (�2; �1), option B1-a is better than option A2 if K0

L 2 (x2;1) and theopposite is true if K0

L 2 (#1; x2). These two options are indi¤erent for the �rmM when K0

L = x2; [3] When A < �2, option B1-a is better than option A2whenever K0

L 2 (#1;1):

Possibility B for Option 2: both technologies are operated in pe-riod 2

34

P2 =(R2)

�1 W 1��12

(�1)�1 (1� �1)1��1

P2R2

=

�R2

W2

��1�1(�1)

�1 (1� �1)1��1R2W2

= �(E2L)

Euler equation (44) becomes

��

bY (�(K0 � E1); L;�( �(K0�E1)L ))

E�11 L1��1

!��=P2=R2P1=R1

=

�W2

R2

R1W1

�1��1;

where function bY (:; :; :) is de�ned in (18). This implies��

bY (�(K0 � E1); L;�( �(K0�E1)L ))

E�11 L1��1

!��=

1

�( �(K0�E1)L )

�11� �1

L

E1

!1��1;

(62)which uniquely determines E1, and hence everything else. We need to imposethat

�(K0 � E1)L

2 (k�1 ; k�):

thusk�1�<K0

L<k�

�+E1L

The related present discounted pro�t is

�eR =A�

�21��2

��2(1� �1) (1� �2)

�2 � �1

��(E2L)E2L� �11� �1

�� (63)"

�(E2L )�1��2

(�1)�1 (1� �1)1��1

� 1

A (�2)�2 (1� �2)1��2

#1

��(E2L )

�11� �1

L

E1LW1:

This implies that, for any given K0, �eR strictly increases when E2 increases andE1 decreases, thus

�eR <A�

�21��2

��2(1� �1) (1� �2)

�2 � �1

��(k�)k� � �1

1� �1

��"

�(k�)�1��2

(�1)�1 (1� �1)1��1

� 1

A (�2)�2 (1� �2)1��2

#1

��(k�)

�11� �1

1K0

L � k�

�

LW1

35

In particular, when � = 1, (62) becomes

�� bY �1(�(K0 � E1); L;�(�(K0 � E1)

L)) =

1

E1

1

�( �(K0�E1)L )

�11� �1

!1��1When comparing option B2 and B1a, suppose the initial endowment can supportboth options, then it can be shown that option B1a will bring a higher discountedpresent value of pro�t. The reason is that, not only the current value of pro�t inperiod 2 will be larger under option B1a, but also that the discounted rate willbe smaller under option B1a. To see the latter, note that in order to transformthe period-2 current value of pro�t into discounted present value at period 1in the units of period-1 wage, the e¤ective discounting multiplier is W2

R2=W1

R1,

which is larger under option B1a because more capital is used in period 2 forgiven initial capital endowment.

Proposition 6 Suppose � = 1 , � � (1��1)(1��2)

h�2+��+�1

i1� and

K0

L 2 [#1;1). The

dynamic market equilibrium is the following: [1] When A > �1, option B1-a isrealized if K0

L 2 [#1; x1) [ (x2;1) and option A2 is realized if K0

L 2 (x1; x2).There are two equilibria (option B1-a and option A2) when K0

L = x1 or x2. [2]When A 2 (�2; �1), option B1-a is realized if K0

L 2 (x2;1) and the option A2 isrealized if K0

L 2 [#1; x2). There are two equilibria (option B1-a and option A2)when K0

L = x2; [3] When A < �2, option B1-a is realized whenever K0

L 2 [#1;1):

4 Industrial Policy

The previous positive analysis implies that there is scope for industrial policiesin some cases because there exist discrepancies in the outcomes between the�rst best case (all technologies are publicly and freely available so the marketis perfect competitive) and the market equilibrium when the knowledge to bestoperate the new technology (which is more capital intensive) �rst becomes ac-cessible to only a subset of the investors who can form coalition as a singlemonopolist and such knowledge becomes publicly information only after it isoperated for a while. The sole source of market ine¢ ciency comes from the factthat the new technology is not publicly available until it is operated for a whileby the �rst mover. The magnitude of this ine¢ ciency, however, endogenouslyand non-monotonically depends on the endowment structure. More speci�cally,e¢ ciency will be restored when capital endowment is su¢ ciently large or su¢ -ciently small. Therefore, welfare-enhancing industrial policies could be in twoforms: one is to change the endogenous monopoly market structure, the otheris to change the relative factor prices faced by �rms. We will discuss these twoalternatives one by one.

36

4.1 Changing the Market Structure

The monopoly in this model is due to the fact that the new technology andhow to operate it pro�tably in the local context is only privately known at thebeginning and imitation takes time before it becomes fully publicly available.Who acquires this information advantage is taken as given in this paper. An-titrust law does not necessarily help or even makes things worse because it candelay the implementation of the new technology even further, as the potentialinvestor who has private information to this technology would simply hold theidea without implementing it. Antitrust laws may work only after the �rstmover already enters.A more e¢ cient way, theoretically speaking, is for government to help collect

and disseminate the information about the new technology and the relevant in-formation how to operate it pro�tably such as the information on marketing, onsearching for the right market and right customer group, etc. For example, thegovernment may support the training programs for workers and entrepreneurs,collect the general market information as public service, reduce the regulationsand lower the entry barrier for new �rms, etc.Of course information collection is costly and it is impossible for the gov-

ernment to collect all the information for all the in�nite technologies on thecandidate menu. So in addition to the aforementioned industry-neutral generalpolicies, the government may also take some industrial policies that are moreindustry-speci�c. Given that the government may not know better than theindividual �rms when selecting the most promising technology before collectingthe relevant information, it is desirable for the government to conduct timelysurveys from a widely covered group of potential investors asking about whichnew industry and what kind of information they are most interested in, andthen the government could help collect the speci�c information or provide thenecessary public goods that are most commonly demanded.8

To the extent that the government may not be able to collect the full informa-tion partly because investors/producers may have heterogeneous characteristicsand therefore may need di¤erent types of information, it is desirable to rewardthe individual �rms who take the initiatives to explore actively rather than waitpassively for the government help. In that sense, the temporary monopoly rentcan partly compensate the �rst mover cost. When the incurred information costis su¢ ciently small, the technology upgrading can be achieved by the marketwithout government support, although the monopoly causes some social ine¢ -ciency as described in the model. This partly explains why industrial upgradingsometimes takes place without active industrial policies. However, when theincurred cost is too large, partly because the monopoly power is by nature not

8Lin and Monge (2010) provide a very concrete six-step policy precedures for the govern-ment in the developing countries to identify the right industrial target and then facilitateindustrial upgrading. For example, a rule of thumb is to check what are the most prosperousindustries in those economies whose GDP per capita is about twice larger. Those industries areon average more likely to be the industries consistent with your latent comparative advantage.

37

legally protected, appropriate government intervention would be necessary tohelp overcome this upgrading hurdle.Another useful way is to encourage foreign direct investment, and thus facili-

tate the technology di¤usion subject to the market incentives. Essentially it notonly helps facilitating the technology di¤usion and learning, but also increasethe number of potential �rst movers and reduces the likelihood or the durationof the monopoly.Despite the importance, some of these recommendations of industrial poli-

cies and the caveats are not entirely new. According to our model, what seemsinsu¢ ciently emphasized in the literature, is the set of policies aiming to rec-tify the relative factor prices so as to indirectly facilitate the adoption of newtechnology and simultaneously induce the timely abandonment of the obsoletetechnology, which we now turn to.

4.2 Changing the Relative Factor Prices

Our model suggests that when to implement the new technology and how muchthe monopolist wants to produce both depend on the relative prices of capitaland labor, which is an important novel feature of this paper. Recall in ourgeneral equilibrium model, the monopolist may produce less than the socialoptimal because it fears that the rising rental price of capital relative to the wagewould erode its monopoly pro�t if it increases its output (hence the demand forproduction factors). Correspondingly, there are several ways to improve theeconomic e¢ ciency by rectifying the relative factor prices.One way is to subsidize the capital cost for the monopolist of the new tech-

nology to the extent that the monopolist is willing to produce the social optimalamount. The subsidy could be in the form of loan credit or investment credit.Tax holidays could also help the capital accumulate faster and hence facilitatesthe adoption of the new technology. The rationale is di¤erent from the creditconstraint argument.Another way is to impose labor income taxes to discourage the employment

in the labor-intensive industry so that the old labor-intensive industry shrinksto the optimal level, and the production scale of the new technology is expandedas the result of the changing market-clearing factor prices.From a dynamic point of view, it may be desirable to encourage saving and

capital accumulation by, for example, levying consumption tax, such that thepotential ine¢ ciency could be mitigated or even alleviated even if monopolyexists. Moreover, it also facilitate industrial upgrading.For small economies, would it help improve economic e¢ ciency by liberaliz-

ing the capital account and allowing for international capital �ow? Not neces-sarily. First of all, although the monopolist behavior could no longer a¤ect theprice of the international capital market, yet the potential monopolist could stillindirectly control the wage rate by changing its own output because the labordemand would shift across the two technologies unless there is a su¢ ciently largepool of surplus labor, which is less likely in small economies. Moreover, interna-tional capital �ow weakens the resource constraint but the budget constraint for

38

the households may not change much, therefore the general equilibrium e¤ectis not clear.

5 Conclusion

In this paper, we develop a two-factor dynamic general equilibrium model to ex-amine the industrial upgrading process, where the market structure may changeendogenously depending on when the �rst mover chooses to start operating thenew technology, which is initially privately accessible but becomes publicly avail-able after one period lag. We show that endowment structure plays a very im-portant role in determining the magnitude of the monopoly rent, thus a¤ectingwhether or not and when the new technology will be implemented. In particular,when the (initial) capital endowment is su¢ ciently scarce or su¢ ciently abun-dant, the equilibrium allocation (not prices) always achieves economic e¢ ciency,no matter whether the new technology is privately or publicly available, henceindependent from the market structure. The reason why monopoly may alsoachieve the �rst best allocation is because, di¤erent from the standard partialequilibrium analysis, the demand curve is not exogenous in the general equilib-rium. It turns out that the negative price e¤ect due to the price markup andthe positive income e¤ect due to the extra monopoly rent exactly cancel outeach other. This is true in both static and dynamic economies.However, ine¢ ciency arises when the capital endowment falls onto some

intermediate range, in which case both technologies are operating in the equi-librium and the potential monopolist will produce less than the social optimalamount. This is not because of the textbook partial-equilibirum argument thatthe monopolist reduces the supply of the output at given demand curve, butmainly because it wants to indirectly depress the rental price of capital relativeto wage by demanding less capital in its production in a general-equilibriumfashion. In addition, in the static equilibrium, the cuto¤ value for capital abovewhich the new technology starts operating is the same no matter whether thistechnology is privately or publicly known, but the cuto¤ value for capital abovewhich the old industry completely exits is larger in monopoly than in the per-fect competition case. This static result may suggest that the monopoly of thenew technology creates distortions mainly by making the old industry exist "toolate" rather than delaying the �rst adoption of the new technology. In the dy-namic model, we show there are cases in which the potential monopolist wouldchoose to delay operating the new technology but the new technology wouldbe operating throughout the time if the new technology is initially publiclyavailable.Based on the positive analysis, we discuss how the market equilibrium may

be improved by adopting industrial policies. One set of industrial policies isto try to alleviate the source that may cause monopoly while at the same timemaintaining su¢ ciently strong incentives for private �rms to adopt the newtechnologies in time and also fully exploit it. The other set of industrial policiesis to rectify the relative factors price without trying to change the endogenous

39

market structure.

40

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