On the optimal speed of technology transfer:
how to provide countervailing incentives against
break-up
Ngo Van Long, Antoine Soubeyran and Raphael Soubeyran∗
November 24, 2010

Abstract
This paper studies the properties of joint-venture relationship between
a technologically advanced multinational firm and a local firm operating ina developing economy where the ability to enforce contracts is weak. We
model a dynamic relationship in which at any point of time the local firm
can quit without legal penalties. An early breakup is prevented only if themultinational designs a suitable scheme in which the speed, the acceleration,and the aggregate amount of technology transfer deviate from the first-best,
together with a suitable flow of side payments to encourage the local firm tostay longer. We show that the second-best technology transfer scheme may
involve a phase of deceleration (i.e. the speed is falling) followed by a phaseof acceleration (i.e. the speed is rising), and finally deceleration again.
Date of this version: 24 November 2010.

∗

Long: Department of Economics, McGill University. Email:ngo.long@mcgill.ca. Antoine
Soubeyran: GREQAM, University Aix-Marseille. Raphael Soubeyran: INRA, Montpellier,France.

1

1Introduction

Technology transfer from developed economies to less developed economies has
been one of the key engines of growth of many emerging market economies. A quite
common mode of technology transfer is the setting up of a joint venture between amultinational and a local firm1 . Governments of emerging market economies often
encourage such joint ventures. In fact, the Chinese government does not allow
foreign car manufacturers to have their own subsidiaries in China. It requires
foreign car manufacturers to form joint ventures (JVs) with local firms so that thelatter can benefit from technology transfer. In addition, foreign car manufacturers
must obtain the Chinese government’s permission to form JVs.
A salient feature of international joint ventures is that there are strong incentives for a local firm to breakup the relationship after having received the technology transfer, unless the multinational firm can counter such incentives for breakup
by providing countervailing incentives for the local firm to stay longer to share themutual gains of cooperation.
This paper focuses on two forms of countervailing incentives: (i) direct financial
inducement (e.g., “how much you will receive from me in the future depends on
how long you stay with me), and (ii) manipulation of the speed and accelerationof technology transfer (e.g., “don’t leave me too early, there is a lot you can leanfrom me in the future”.)
If a multinational fails to oﬀer suitable countervailing incentives, a breakup will
occur. Below are two real world cases involving a break-up of relationship.
(a) Easterly (2001, p. 146) recounted that Daewoo Corporation of South Korea
and Bangladesh’s Desh Garment Ltd. signed a collaborative agreement in 1979,
whereby Daewoo would train Desh workers, and Desh Ltd would pay Daewoo 8
percent of its revenue. Desh cancelled the agreement on June 30, 1981 after its
workers and managers have received suﬃcient training. Its production soared from
43,000 shirts in 1980 to 2.3 million in 1987 (interestingly, of the 130 Desh workers
1

Hoekman, Maskus and Saggi (2005) review the principal channels of technology transfer,which are trade in goods, foreign direct investment, licensing, labor turnover and movement ofpeople.

2

trained by Daewoo, 115 eventually left Desh to set up their own firms).
(b) As Branstetter et al. (2006) noted, “when a firm transfers technology to
an aﬃliate, it generally has to instruct local engineers...concerning key elementsof its technology. Some of these elements may have been withheld from the firm’s
patents, in the U.S. and in the foreign country, in order to prevent other parties
from being able to copy its technology by simply reading its patents. When it
transfers this knowledge to local employees, there is a risk that these local employees will defect to a local manufacturer, taking sensitive technology with them.”
They cited an annecdote concerning Taiwan Semiconductor Manufacturing Co.
(TSMC) in a law suit against its mainland Chinese rival, Semiconductor Manufacturing International Corp. (SMIC) for having hired away more than one hundred
employees of TSMC mainland operations, who brought with them valuable trade
secrets. An interesting feature of this anecdote is that TSMC had anticipated thedefection of its employees and therefore had not transferred its most advanced
technology to its mainland Chinese operations.
This paper studies the properties of joint-venture relationship between a technologically advanced multinational firm and a local firm operating in a developing
economy where the ability to enforce contracts is practically non-existent. In ourmodel the multinational firm always honors its promises (because it wants to maintain its reputation in other countries), and it cannot prevent the local firm frombreaking away after receiving its technology transfer. As a result, the multinational firm may have to rely on second-best technology transfer schemes that do
not maximize joint surplus, but that are incentive compatible. This results in a
total amount of technology transfer that is below the first-best level.2
We formulate a dynamic model of relationship in which at any point of time theagent (the local firm) can quit without legal penalties. An interesting feature of2This may be interpreted as the unwillingness to transfer the latest technology. In Glass andSaggi (1998)’s general equilibrium model, the quality of technology that FDI transfers depends
on the size of the technology gap between the North and the South. Empirical work by Coughlin(1983) found that comparing countries that are not favorable to FDI that set up wholly owned
subsidiaries with countries having less restrictive FDI policies, the first group of countries tend toreceive process rather than product technology transfers, and the product technology transfers
tend to concentrate on older products.

3

the model is that the agent’s reservation value is changing over time, because theagent’s knowledge capital increases with the accumulated amount of technology
transfer. The agent’s quitting value (i.e., how much it can earn as a stand-alone
firm over the remaining time horizon) is a non-monotone function of time. Givena planned time path of technology transfer, during the early phase of the relationship, the local firm’s quitting value is rising with time. However, near the endof the time horizon, when the transferred technological knowledge would become
useless because a new product (developed elsewhere) renders the existing productcompletely obsolete, the local firm’s quitting value is falling over time. Becauseof this non-monotonicity of quitting value, the local firm’s optimal quitting time(in the absence of side transfer payments) occurs before the projected end of thefirst-best relationship. Such an early breakup may be prevented if the principal(the multinational) designs a suitable scheme in which both the pace and aggregate amount of technology transfer deviate from the first-best, and a suitable flowof side payments to encourage the local firm to stay longer.
We ask the following questions: (i) When first-best contracts are not implementable, does the second-best scheme involve on average a slower speed of technology transfer, and possibly phases of decreasing speed followed by phases ofincreasing speed? (ii) Is the cumulative amount of technology transfer lower under
the second-best scheme? (iii) Does the side payment increase over time? (iv) Whatis the optimal time to let the local firm break away?
Other questions that can also be discussed using our model are: Does tradeliberalization (e.g. lowering tariﬀs) has unfavorable impact on technology transfer?
Does competition with other local firms has an impact on the technology transfer?
Given that technology transfer in one industry can have beneficial spillovers inother industries, what could the government of the recipient country do to improvesocial welfare by changing the parameters of the second-best schemes? (Section 5
discusses some of these issues).
In modelling the endogenous pace and duration of technology transfer, ourpaper supports the hypothesis that the degree of intellectual property protection
influences the extent of technology transfer (for a survey of empirical evidence, see

4

Mansfield, 1994). In our model, the timing decisions and the pace of technology
transfer play a crucial role. This distinguishes our paper from other papers which
typically use a static framework to analyze technology transfer issues3 . This is
not to deny the usefulness of the static framework. Static models are often aconvenient short-hand description of a dynamic process, or of a long run outcomeof a dynamic process.
Our model is an enrichment of the two-period models of Ethier and Markusen(1996), Markusen (2001), and Roy Chowdhury and Roy Chowdhury (2001). Whilethese three papers oﬀer valuable insights on internalization considerations, our result on the non-monotonicity of quitting value cannot be obtained in such twoperiod models, where, by necessity, things can either go up or go down over time,
not up and then down. This non-monotonicity has important bearing on the multinational’s optimal speed and acceleration of technology transfer. There are two
important considerations here. On the one hand, first-best eﬃciency requires trading oﬀ higher absorption cost associated with faster transfer against higher benefitof knowledge accumulation. On the other hand, a high speed of transfer brings
the local firm’s optimal quitting time closer to the present, which is detrimental
to the multinational.
Ethier and Markusen (1996) presented a model involving a race among sourcecountry firms to develop a new product that becomes outdated after two periods.4
The winning firm has the exclusive right to produce the good in the source country(S), and can produce the good in the host country (H) either by setting up a wholly
owned subsidiary, or by licensing to a local firm. If the licensing contract is for one
period, in the following period the former licensee, having learned the technology,
can set up its own operation to compete against the source-country firm. Twoperiod licensing is ruled out because by assumption the local firm can breakawayin the second period without penalties. Their model captures essential elementsof a situation where source-country firms “continually compete to introduce new
products” and face possible dissipation of their knowledge-based capital. The
3

See for example, Kabiraj and Marjit (2003), Mukherjee and Pennings (2006), in which technology transfer is via licensing, which does not use up real resources.
4
With this assumption, the time horizon of a firm is eﬀectively restricted to two periods.

5authors assume that in the host country there is complete absence of protectionof intellectual property. Their model highlights the interplay of locational andinternalization considerations. It provides a key to understand why there are more
direct investment between similar economies. Their paper does not address theissue of endogenous timing of breakaway by the local partner of a joint venture,
nor the issue of the multinational’s optimal speed and acceleration/deceleration oftechnology transfer that serves to counter the breakaway incentives.
Markusen (2001) proposed a model of contract enforcement between a multinational firm and a local agent. He considered a two-period model where the agent
learns the technology in the first period and can quit (with a penalty) and form
a rival firm in the second period. The multinational can fire the agent after the
first period and hire another agent in the second period. A main result is that ifcontract enforcement induces a shift from exporting to local production, both themultinational firm and the local agent are better oﬀ. Markusen’s paper does notaddress the issue of the optimal speed of technology transfer.
Roy Chowdhury and Roy Chowdhury (2001) built a model of joint venture
breakdown. They used a two-period setting, with a multinational firm and a local
firm. They showed that for intermediate levels of demand, there is a joint venture
formation between these firms in period 1, followed by a joint venture breakdownin period 2 (when the two firms become Cournot rivals). In their model, theincentive for forming a joint venture is that both firms can learn from each other(the local firm acquires the technology while the multinational learns about the
local labor market). The model does not allow the multinational to control the
speed of technology transfer.
In the papers mentioned above, by restricting to two-period models, the question of optimal timing of breakup cannot be studied in rich detail. Among papers
that deal with optimal timing decisions of multinational firms is Buckley and Casson (1981). They analyzed the decision of a foreign firm to switch from the “exporting mode” to the FDI mode (in setting up a wholly owned subsidiary). That
paper did not deal with the problem of opportunistic behavior that would arise if
there were a local partner. Horstmann and Markusen (1996) explored the multi-

6period agency contract between a multinational firm and a local agent (that sells
the multinational’s product) but in their model there was no technology transferfrom the former to the latter. Their focus was to determine when a multinational
would terminate its relationship with the local sales agent and establish its own
sales operation. Rob and Vettas (2003) generated the time paths of exports and
FDI, with emphasis on demand uncertainty and irreversibility. They did not consider the possibility of licensing or joint venture. Horstmann and Markusen (1987)
explored a multinational firm’s timing decision on investing (setting up a wholly
owned subsidiary) in a host country in order to deter entry. Lin and Saggi (1999)
explored a model of timing of entry by two multinationals into a host country
market, under risk of imitation by local firms. There was no contractual issues intheir model; the emphasis was instead on the leader-follower relationship. They
showed that while an increase in imitation risk usually makes FDI less likely, there
exist parameter values that produce the opposite result.
An early paper that discussed the resource cost of transferring technology knowhow was Teece (1977). Teece disagreed with the “common belief that technology
is nothing but a set of blueprints that is usable at nominal cost to all”. He argued
instead that “the cost of transfer, which can be defined to include both transmission and absorption costs, may be considerable when the technology is complex
and the recipient firm does not have the capabilities to absorb the technology”.
His empirical research focused on measuring the costs of transmitting and absorbing all of the “relevant unembodied knowledge”. These costs fall into four groups.
First, there are pre-engineering technological exchanges, where the basic characteristics of the technology are described to the local firm. Second, there are costsof transferring and absorption of the process or product design, which require“considerable consulting and advisory resources”. Third, there are “R&D costs
associated with solving unexpected problems and adapting or modifying technology”. Fourth, there are training costs, which involve extra supervisory personnel.
Teece found that empirically the resources required for international technology
transfer are considerable and concluded that “it is quite inappropriate to regard
existing technology as something that can be made available at zero social cost”

7

(p. 259). Niosi et al. (1995) found that technology transfer costs are significant
and mostly concentrated in training.
The remainder of our paper is structured as follows. Section 2 introduces a
simple basic model where a constant speed of technology transfer is chosen andcharacterizes the first-best pace of technology transfer when contracts are perfectly
enforceable, so that a joint-venture breakup is not allowed. (The case where boththe speed and the acceleration can be changed over time is presented in Appendix
5.) Section 3 shows that if breakup can happen without penalties, and the local
firm faces a credit constraint, then the first-best pace of technology transfer is
not an equilibrium outcome, because the multinational would want to modify
the pace of technology transfer in order to (partially) counter the incentives ofbreakaway. We find that the equilibrium outcome under credit constraint andimperfect property rights involves generally a slower pace of technology transfer,and also results in a lower cumulative technology transfer. In Appendix 5, weshow that the second-best technology transfer scheme may involve a phase of
deceleration (i.e. the speed is falling) followed by a phase of acceleration (i.e. thespeed is rising), and finally deceleration again. Section 4 discusses some policy
implications. The Appendices contain proofs.

2

The Basic Model

2.1

Assumptions and Notation

We consider a developing country in which a good can be produced using local
inputs (such as labor and raw material) and technological knowledge which can betransferred from a foreign firm. Unlike most existing models which assume thatthe technology transfer can happen immediately, we take the view that there areabsorption costs and training costs which rise at an increasing rate with the speedof technology transfer, and which make an once-over technology transfer unprofitable. We therefore explicitly introduce time as a crucial element in our model.
We take time to be a continuous variable,  ∈ [0  ]. Here  is an exogenously

given terminal time of the game. It can be interpreted as the time beyond which
8the product ceases to be valuable (cf. the product cycle theory of Vernon).
Let () denote the rate of technology transfer at time  The state of technological knowledge of the local firm at time  is denoted by () where() =Z 

( )

(1)

0

The (reduced-form) “gross profit” of the joint venture at time  is assumed to
be a function of () alone. It is denoted by (()) where () is a continuous,concave and strictly increasing function, with  = 0 if  = 0. This gross profit does
not include “absorption cost” which is denoted by (()). We assume that ()is continuous, strictly convex and increasing in , with (0) = 0. This implies
that for all   0, marginal absorption cost is greater than average absorption
cost,  0  . We also assume that there is an upper bound on , denoted bymax  0.
Let us make the following specific assumptions:
Assumption A1: (a) The diﬀerence between marginal absorption cost and average absorption cost,  0 () − (), is positive and increasing in  for all   0.

(b)   0 (0)   0 (0) ≥ 0.

Assumption A2: The upper bound max is suﬃciently great, such that
 0 (max ) −(max ) 0 (0)

max
2

(2)

Assumption A3: The elasticity of marginal contribution of technology to profit
is less than or equal to unity:1+

 00 ()≥0
 0 ()(3)

Remark 1: Assumption A1(a) implies that
 00 () −  0 ()−1 + ()−2  0(4)

Clearly, the function () = (1) where   1 satisfies A1(a). Assumption

9

A1(b) means that the return (over the life-time of the joint venture) of a very small
technology transfer is higher than its marginal cost. Assumption A3 implies that0 () is increasing in . We use this assumption to prove the optimal solution
is unique (see Proposition 1 below) and to show that the equilibrium outcome
under credit constraint and imperfect property rights results in a lower cumulativetechnology transfer (see section 3.4). Clearly, the function () = ()  where0   ≤ 1 and   0 satisfies A3.

We assume that the foreign firm and the local firm form a joint venture. We

first consider the ideal case where contracts can be enforced costlessly. In this casethe joint venture chooses a time path of technology transfer and production thatmaximizes the joint surplus. In analyzing this ideal case, our focus is on eﬃciency.
The surplus sharing rule under this first-best scenario is not important for our
purposes.
After characterising the first-best (eﬃcient) time path of technology transfer,
we discuss whether this path can be achieved if the local firm can at any time breakaway from the joint venture and become a stand-alone entity that captures all
the post-breakaway profit (we assume that after the breakaway, the joint venture
vanishes, and the multinational firm leaves the host country). The answer will
depend on what kind of contracts are feasible, in particular, on whether the local
firm has access to a perfect credit market, and whether the multinational is entitled
to compensation by the local firm after the breakaway (i.e. whether property
rights are perfectly enforceable). In the absence of a perfect credit market and aperfect property rights regime, we show that the foreign firm must design a secondbest contract. We show that the second-best contract involves a slower pace oftechnology transfer, and a lower level of cumulative technology transfer. We argue
that this outcome could be detrimental to the host country.

10

2.2

The first-best solution

For simplicity, we assume that the discount rate is zero. The joint-surplus maximization problem is to choose a time path () over the time horizon  to maximize
 =

Z 
0

[(()) − (())] (5)subject to ̇() = (), (0) = 0 = 0 and 0 ≤  ≤ max .

Let us simplify the problem by restricting the set of admissible time paths oftechnology transfer, so that it consists of the following two-parameter family ofpiece-wise constant functions (the case where () is not constrained to be piecewise constant is analysed in the Appendix).
() =(

 if  ∈ [0  ]0 if  ∈ (   ](6)where  is the “technology-transfer-stopping time”, beyond which there will be nofurther technology transfer, and  is a constant transfer rate, to be chosen. Afterthe time  , the level of technological knowledge of the joint venture is a constant,denoted by  where ≡ 

(7)

The optimization problem of the joint venture then reduces to that of choosing
two numbers  and  to maximize (  ) =Z 0[() − ()]  + [ −  ]  ( )(8)subject to 0 ≤  ≤ max and 0 ≤  ≤  .

Proposition 1: The solution of the (first-best) optimization problem (8) of thejoint venture exists, is unique, and has the following properties:(i) The rate of technology transfer ∗ during the time interval [0 ∗ ] is strictly
positive and strictly below the upper bound max .
(ii) The stopping time ∗ is strictly positive and is smaller than the time horizon11

(iii) The marginal benefit (over the remaining time horizon) of the technologicalknowledge stock at the stopping time ∗ is just equal to the average absorption cost:( − ∗ )0 (∗ ∗ ) =(∗ )∗(9)(iv) At the optimal technology transfer rate ∗ , the excess of the marginal absorption cost over the average absorption cost is just equal to average of the marginalcontribution of technology to profit over the transfer phase:(∗ )1 ( ) −
=
∗
∗
0

∗

Z ∗ ∙0¸∗( ) (10)

Proof : See Appendix 1.
Remark 2: Since ()  0 for any   0 and (0) = 0, the assumption that
() = 0 when  = 0 implies that, for any   0, there exists an initial timeinterval called the “loss-making phase” over which the joint venture’s net cash
flow, () − (), is negative. This phase ends at time + () which is defined,

for any given   0, as follows:½¾ () ≡ min   sup { ∈ [0  ] : ()  ()}
+

(11)



Example 1: Assume () =  × (1)  where   0, 0   ≤ 1 and() = () where   1 and   0. Then using equations (9) and (10) we
get:

∗ =
and

µ

¶
( − 1) ( + 1)
1 + ( − 1) ( + 1)

∗

 =

µ


 ( − 1) ( + 1)¾
½ ³
 ´ 1 ∗ −∗ ( ) = min  ( ) 

+

∗

12

1
¶ −



(∗ ) −

(12)

(13)

Thus the cumulative transfer is∗ ∗ =µ ( − 1) ( + 1)

1
µ
¶ −

( − 1) ( + 1)
1 + ( − 1) ( + 1)


¶ −

(14)

In the rest of the paper, we will illustrate our results with the three following
numerical examples:

2.3

∗

∗

+ (∗ )Example 1a = 30  = 1  = 2  = 1  = 2

40

20

10

Example 1b
 = 30  = 12   = 2  = 1  = 2' 50418

2

Example 1c
 = 30  = 1  = 54   = 1  = 01

' 39

10

10

Implementation of the first best when the local firmcannot break away

Denote by  (∗  ∗ ) the net profit of the joint venture under the first-best solution.
Let us assume that the local firm would form a joint venture with the foreign firm
only if the payoﬀ to the owner of the local firm is at least equal to its reservationlevel  . We consider only the case where    (∗  ∗ ). Assume there are manypotential local firms. Then the foreign firm will oﬀer the local firm the payoﬀ  ,and keep to itself the diﬀerence  (∗  ∗ ) −  .

Suppose it is possible to enforce a contract that specifies that the joint venture

will not be dissolved before the end of the fixed time horizon  . Then the foreign
firm will be able to implement the first best technology transfer scheme that we
found above. In the following sections, we turn to the more interesting case where
the local firm is not bound to any long-term contract.

13

3

Joint venture contracts when the local firm
can break away

We now turn to the real world situation where the local firm can break away at
any time, taking with it the technological knowledge that has been transferred,without having to compensate the multinational. For simplicity, we assume thatafter the breakaway, the multinational is unable to produce in the host country.
The local firm can break away at any time 0 ≤  ≤  and become a stand-alone

firm in the local market, benefiting from the cumulative amount of technology

transfer up to that date,  ( ). In this section, we assume the following market
failures:
Credit market failure (C1): The local firm cannot borrow any money, hence themultinational has to bear all the losses of the joint venture during the loss-making
phase [0 + ()], where + () is as defined by equation (11) (the multinational firm
is not subject to any credit constraint). The multinational firm cannot ask the
local firm to post a bond which the latter would have to forfeit if it breaks away(the local firm cannot raise money for such a bond).
Property rights failure (C2): The multinational cannot get any compensation
payments from the local firm after the breakaway time  .
Without the credit market failure, the multinational firm would be able to ask
the local firm to pay as soon as it receives any technology transfer. Without theproperty rights failure, the prospect of having to compensate the multinational
would deter the local firm from breaking away. Let us make clear the meaning of(C1) and (C2) above by describing the payoﬀ function of the multinational andthat of the local firm.
We assume that the multinational firm can credibly commit to honor any contract it oﬀers. This assumption seems reasonable, because multinational firms
operate in many countries and over a long time horizon, so it has an interest in
keeping a good reputation. Then we can without loss of generality suppose thatthe multinational oﬀers a contract which specifies that it collects all the profits of
the joint venture, and pays the local firm a flow of side payments () for all 

14

until the local firm breakaway.
After the breakaway, if C2 does not hold, the multinational can successfully
ask for a flow of compensation payment  () from the local firm, to be paid from to  . In the rest of this paper we analyse diﬀerent situations where the flows
() and () are constrained.
The total payoﬀs of the multinational firm and of the local firm are, respectively,

 ≡

Z 
0

[( ()) − ( ()) −  ()]  +

and
 ≡

Z

 () 

(15)



Z

 ()  +Z[( ()) −  ()] 

(16)



0

The payoﬀ implications of the market failures (C1) and (C2) are described
below.
C1: The local firm cannot borrow: In this case, at all time , the local firm’s
cumulative net cash flow up to time , denoted by  () must be non-negative.
Thus

0 ≤  () ≡

⎧
⎪
⎪
⎨

R
⎪
⎪
⎩  ( )  +
0

R

0
R



 ( ) 

if  ∈ [0  ](17)

[( ( )) −  ( )]  if  ∈ (   ]C2: The multinational cannot obtain from the local firm any compensation
payment after the breakaway time: () = 0 for  ∈ (   ](18)

The goals of this section are (a) to show that when both constraints (17) and(18) hold the first-best technology transfer scheme is in general not achievable, and(b) to characterize the second-best technology transfer scheme. In a later section,
we will point out that if one of these two assumptions is completely removed, the15

first-best can be recovered.

3.1

Technology transfer with two market imperfections

We now consider the case where the local firm can break away, there is no credit
market, and the multinational cannot get any side payment after the breakaway.
Using the constraint that () = 0 and the fact that ( ()) ≥ 0, the borrowing

constraint C1, condition (17), can be simplified to0≤Z

 ( )  for all  ∈ [0  ] 

(19)

0

For simplicity, from this point we assume that the reservation value  is 0. Thenthe participation constraint  ≥  is satisfied when the borrowing constraint(19) holds.

Then, the program of the multinational can be written as
max  = ()Z 0[( ()) − ( ()) −  ()] (20)

subject to 0 ≤  ≤  0 ≤  ≤ max , the incentive constraint∙¸Z  = arg max  =
 ( )  + ( − )(())


(21)

0

and the credit constraint0≤Z

 ( )  if  ∈ [0  ] 

(22)

0

Here

Z 

( ) (23)

 if  ∈ [0 min (   )]0 if  ∈ (min (   )   ](24)

() =

0and() =

(

16

3.2

The local firm’s secure payoﬀ

Let us consider what would happen if during the profit-making phase, the multinational firm takes 100% of the profit and does not make any side transfer to the
local firm. Under this scenario, clearly the local firm has an incentive to breakaway at or before the time  (after  , it has nothing to lose by breaking away).
The local firm wants to choose a breakaway time  ∈ [0  ]. Given that () = 0
identically, the payoﬀ to the local firm if it breaks away at time  is0 (  ) = ( −  )(( ))where( ) =( if   
 if  ≥ 

(25)

(26)

Here the superscript 0 in 0 indicates that the local firm’s share of profit before
the breakaway time is identically zero. Given (  ), the local firm knows that if
it breaks away at time  , it will get ( −  )( ). If it breaks away at someearlier time    , it will get ( −  )( ). The local firm must choose  in[0  ], to maximize

(  ) ≡ ( −  )( ) where  ∈ [0  ](27)

Lemma 1: Given that () = 0 identically (i.e. there is no side transfer from themultinational to the local firm),(i) If( −  ) 0 ( ) − ( ) ≥ 0(28)

the local firm will break away at the planned transfer-stopping time  , and earns
the payoﬀ ( −  )( ).
(ii) If( −  ) 0 ( ) − ( )  0(29)

the local firm will break away at a unique b () strictly earlier than the planned
17transfer-stopping time   and earn the (secure) payoﬀ ())(b ())
  () ≡ ( − b(30)

 ()) − (b ()) = 0( − b ()) 0 (b(31)(iii) In both cases, a small increase in  will increase the local firm’s payoﬀ by£¤ −b ()  0 (b ())b ()  0 where, in the first case, b () =  , and in thesecond case, b () satisfied the interior first order condition:
Proof: The function (  ) is strictly concave over (0  )  because 2 (  )= ( −  ) 00 ( )2 − 2 0 ( )  0( )2(32)

Consider the derivative of (  ) with respect to  ;(  )= ( −  ) 0 ( ) − ( )


(33)

Thus if ( −  ) 0 ( ) − ( ) ≥ 0 then, due to the strict concavity of (  )in   we know ( −  )0 ( ) − ( )  0 for all    , and it follows

that the local firm will choose  =  . If ( −  )0 ( ) − ( )  0 then(  ) attains its maximum at some    . To prove (iii), note that in thecase of b =  (corner solution), if after a small increase in , the corner solution£¤b =  remains optimal, then   () =  − b () 0 (b ())b () whereb ()   , diﬀerentiation of (30) () =  . In the case of an interior solution, bgives  () =

£
¤
 −b
 ()  0 (b ())b ()©
ª + ( − b ()) 0 (b ()) − (b ())
(34)

But the term inside the curly brackets {} is zero. This concludes the proof.

18

Remark 3: Strictly speaking, the (secure) profit should be written as (  ))(b (  )))  (  ) ≡ ( − b(35)

However, this formalism is quite unnecessary.

Example 2: Use the specification of example 1. Independently of the value of, if   +1
 condition (29) is satisfied, and the local firm will break away atb =   . If  ≤   , condition (28) is satisfied, and the local firm will
+1

+1

break away at b
 =  (see Appendix 2).

Using the parameters of example 1a, the interior-breakaway condition (29)becomes   15. In Figure 1, the curve  (∗   ) where ∗ = 40 shows thatthe multinational payoﬀ under the first-best scenario is single-peaked in  , andits optimal  is ∗ = 20 Now, given ∗ = 40 and ∗ = 20, under the imperfectproperty rights regime, the local firm can break away at time  and earns apayoﬀ (∗   ). We find that (∗   ) is non-monotone in  : if the local firm
(firm ) breaks away too early, it has too little knowledge capital to take away.
If it breaks away too late, it has a lot of knowledge capital to take away, but
too little remaining time before the end of the time horizon. The local firm will
break away at b
 (∗ ) = 15. This shows that the first-best scheme in example 1a,(∗  ∗ ) = (40 20)  is not implementable (in the absence of any side payment).

20000

15000
R(h*, t B)
V(h*,ts)

10000

5000
V(h*,ts)-R(h*,ts)
0

|

0

5

10

^t B 1519

t*s= 20

25

30

ts

Fig. 1: Case where the local firm breaks away before the first besttransfer-stopping time.
(b (∗ )  ∗ )( = 30  = 1,  = 2,  = 1  = 2  = ∗ = 20).
Using the parameters of example 1c condition (28) becomes  ≤ 15. Thisshows that the first-best scheme in example 1c, (∗  ∗ ) = (39 10) is implementable(but the multinational does not get the profit that it would get if the joint venture
were a wholly owned subsidiary). The local firm will break away at time b (∗ ) =∗ = 10.

1000

R(h*,ts)V(h*,ts)
0
10

20

30

ts

V(h*,ts)-R(h*,ts)-1000

Fig. 2: Case where the local firm breaks away at the first best transfer-stopping
time (b (∗ ) = ∗ = 10).
( = 30  = 1,  = 54 ,  = 1  = 01  = ∗ ' 39)

Figure 2 illustrates the case where the local firm would prefer that the transfer
stops later than the first-best stopping-time, so that when it breaks away it will
get a higher stock of knowledge. The local firm’s preferred transfer stopping-timeis  = 15. But, since the multinational chooses to stop the technology transfer at∗ = 10, the local firm has an incentive to break away at the same time.
20

3.3

Incentive compatible contract under credit constraint

Given that the local firm must have non-negative cash flow at all time, and that,in the absence of transfer payment from the multinational, it can secure the profit  () = ( − b ())(b ()) by breaking away at an optimal day, the multinational firm must design a contract (with transfer payments) that maximizes its
payoﬀ, subject to the constraint that the local firm earns at least   ().

In the absence of side payments, if the local firm stays with the joint venturebuntil a later date    (), it loses an amount   ()−( − )( ). Therefore,

if the multinational wishes to induce the local firm to break away no sooner than , it has to pay the local firm a compensation  equal to the loss of delaying thebreakaway,   () − ( −  )( ).

bMore precisely, given any desired date    (), we can show that there exists

a multiplicity of flows of side payments  () (see Appendix 4) such that (a) the

local firm, responding to such incentives, will choose to break away at time  and(b) the total side payment is minimal with respect to the incentive constraint andthe borrowing constraint. All these solutions satisfy
Z  ()

 ()  = 0 and

0

Z 


 ()

 ()  + ( −  )( ) =   ()(36)These flows have the same present value. The only diﬀerence between the various
incentive-compatible flows  () is how the flow is spread out between b
 () and . The intuition is as follows.

Firm  (the multinational) can oﬀer to pay firm  (the local firm) a lump
sum  at a contractual time  if  actually breaks away at time  or at anylater date, so that firm ’s total payoﬀ is  + ( −  )( ). If  breaks away

at any time  before  , it will simply get the payoﬀ (  ) = ( −  )( ).
Since  can always ensure the payoﬀ   () by breaking away at time b (), firm’s oﬀer would be accepted only if  + ( −  )( ) ≥   ().

Alternatively, instead of giving the lump sum  at the time  , firm  canspread the payment of this total amount over time, from time b () to time ,and still ensure that firm  has no incentive to break away before  . Recall that21 =   () − (  ), and that (  ) is decreasing in  for all   b
 (). So,
for any sequence of dates {1  2  3     } where b ()  1   = 
 , itholds that

 = [  () − ( 1 )]+ [( 1 ) − ( 2 )] +  + [( −1 ) − (  )]

(37)
(38)

≡ 1 + 2 +  + 

where each  is positive. Firm  can then oﬀer the following contract to firm :
I will pay you  at time  if up to time  you are still part of the joint venture.
Clearly, breaking away at any time  ≤ 
 does not give firm  any advantage incomparison to staying in the joint venture until time .

The above argument supposes that payments are made in small amounts at alarge number of discrete points of time. We can take the limit as the size of thesetime intervals go to zero, and  goes to infinity. This yields a continuous flow () such that  () = − ()  0 for  ∈ (b () 
 ]. Remark that this flow is




2

increasing in  because ( ) is concave in , () = −  ()
 0.
2

All the above side transfer payments schemes have the same eﬀect on the local

firm’s quitting time. We can therefore focus, without loss of generality, on thefollowing particular flow of side payments (which concentrates at a point of time,i.e. the flow becomes a mass). The multinational oﬀers to pay the local firm
a lump sum amount  ≥ 0 if the latter breaks away at a specified time  .

Since the multinational does not want to overpay the local firm, the lump sum will be just enough to make the local firm indiﬀerent between (a) breaking
away at b
 () thus earning the secured pay-oﬀ   (), and (b) breaking away¤£
at the contractual breakaway time  , thus earning  +  −  ( ). Thus£¤
 +  −  ( ) =   (). Therefore the side payment written in the contractis
e ( ) =(0
if   

£
¤


  () −  −  ( ) if  = (39)

Let us now make use of the incentive constraint (39) to determine the multi-

22national’s optimal choice of both  and  to maximize its own payoﬀ:
Z 

e =

0

£
¤

[() − ()]  +  −  ( ) −   ()(40)

The first order condition with respect to 
 is
 e
 0  = ( −  )  (  ) − ( ) = 0



(41)

This condition has the same form as the first best condition (see equation (9)),
except of course the value  is in general not the same. The first order condition
with respect to  is e  ()
=
−
=0




or
Z 
0

(42)

¤
£ 0 
¡  ¢ 0  (  ) −  0 ( )  + ( −  )   ¤£
 ( ) = 0
 ( ))b−  −b ( )  0 ( b(43)

Example 3: Using the parameters of example 1b, b
 () = 10 then   () =√40 10.
800
V(h,t*s)600
V_ L(h)

V(h,t*s)-V_ L(h)
400

200

0
0

2

4

h* 6

8

23

10

12

14

h

Fig. 3: The secure value of the local firm and the pace of technology transfer.
( = 30  = 1,  = 12 ,  = 1  = 2  = ∗ = 18)
Figure 3 illustrates that, given the first best transfer-stopping time ∗ = 18, if
the local firm can secure   () (which is increasing in ), the multinational has
an incentive to reduce the pace of technology transfer to  ' 393 lower than∗ ' 504.

3.4

Comparison with the first best

In this sub-section, we show that the second-best scheme described above implies
that i) the multinational will choose a slower transfer rate   ∗ and ii) the
cumulative technology transfer is also lower. We prove this for the general case(where the profit function () is concave), and provide an explicit solution forthe case of a linear profit function () = ,   0 in Appendix 3.
First, let us show that the two equations (41) and (43) yield (   ) with




∗
∗ ∗
∗ and    , where (   ) is the solution of the system of firstorder conditions in the first best case studied in Section 2. For easy reference, we
reproduce that system below:

=


Z ∗

[ 0 (∗  ) −  0 (∗ )]  + ( − ∗ )0 (∗ ∗ ) ∗ = 0

(44)


= ( − ∗ )∗  0 (∗ ) − (∗ ) = 0


(45)

0

To show that   ∗ and    , we use the following method. Let  be anindicator, which can take any value between zero and 1. Consider the following
system of equations:
1 ≡

Z 

(46)

2 ≡ ( − )0 () − () = 0(47)[  0 ( ) −  0 ()]  + ( − ) 0 () 0¤£ ())b () = 0−  − b () 0 (b24Clearly, if  = 1, the system (46)-(47) is equivalent to the system of equations(41)-(43) and thus yield ( ) = (   ), and if  = 0, the system (46)-(47) isequivalent to the system of equations (45)-(44) and thus yield (³) = (∗  ´∗ ).
For an arbitrary  ∈ [0 1], the solution of the system is denoted by e() e() .
We now show that e() is decreasing in  and e() is increasing in . Let 11

be the partial derivative of 1 with respect to , 22 be the partial derivative of2 with respect to , 12 be the partial derivative of 1 with respect to , etc.
Then we have the following system of equations:

Then

#
"
#" # "
11 12 e

−1

=
21 22 e0e−1 22=
11 22 − 21 12e1 21=11 22 − 21 12

(48)

(49)
(50)

Now, by the second order condition, 11 22 − 21 12  0 Hence e isnegative if and only if −1 22  0
Now£¤1 = −  − b ()  0 (b ())b ()  0(51)

() is decreasing inand by the second order condition 22  0. This proves that e.

We now show that 21  0, where21 = − 0 + ( − )( 00 +  0 )(52)

Using (47),− 0 + ( − ) 0 = − 0 +

()
0


(53)

where the strict inequality follows from the assumption on (): average cost issmaller than marginal cost. It follows that 21  0. This proves that e() isincreasing in .

25

Let us compare the total quantity of technology transfer in the first best casee () ≡ ≡ ∗ ∗ and the quantity in the second best case   ≡   . Let 
∗





e
()e
(). Then

e ()

e
() ee() e=× () +× ()


Using (49) and (50)

h
i
e

−1
e
=
22 − e21 

11 22 − 21 12

(54)

(55)

e
Since
−1 i 0 and 11 22 − 21 12  0, 
is negative if and only ifhe22 − e21 is negative. This term can be rewritten as
i
h
³
´
i
h
0
00
00
0
0
e
e
e
e
e
e
e
e
22 − 21 =  − + ( − ) −  ( − )  +  − 

Then

£
¤
e
21 = e  0 − ( − e) 0 − e 0 
22 − e

(56)

(57)

Using assumption A3 ( 0 () +  00 () > 0 for all  > 0) we have

Using (46) we obtainZ 
1 h 0 e ie  ( )  ≤ e
 0 ()
e
 0³ ´ hie +e ≥  0 (ee 0 ()) − ( − e) 0 )  0 (e
b
 (e
))b
 (e
)
 −b
 (e
e


Then, if   0³ ´e e   0 (ee 0 ()) − ( − e) 0 

(58)

(59)

(60)

Using this inequality and (57) we conclude that, for   0,This proves that     ∗ .

e21  0
22 − e

The following proposition summarizes the finding of this section:
26

(61)

Proposition 2: To counter the local firm’s opportunistic behavior, the multinational firm designs a second best scheme that involves a slower rate of technology
transfer (thus reducing the local firm’s secure payoﬀ) and a lower total cumulative technology transfer. It also oﬀers side payments to the local firm to delay thebreakaway time. The side payments can be in the form of a continuous flow that
increases with time, or a lump sum payable at a contracted breakaway time.
Example 4: Use the parameters of example 1a.
V(h,t*s)15000
V(h,tcB )10000

V_ L(h)

5000

V(h,tcB ) -V
_ L(h)_ L(h)
V(h,t*s)-V

0
0

10

|
hc 20

30

h*= 4050hFig. 4: The secure value of the local firm and the pace of technology transfer.
( = 30  = 1,  = 2,  = 1  = 2)
Figure 4 shows that the maximum joint profit is smaller in the second-best
scheme (see the two curves at the top of figure 4, from the dash curve to thethick curve). To counter the local firm’s incentive to quit early (at b (∗ ) = 10),the multinational firm reduces the pace of technology transfer from ∗ = 40 to ' 168 (see the two curves at the bottom of figure 3, from the dash curve to thethick curve) while increasing the technology transfer stopping time from ∗ = 20
¡  ¢
¡ ¢
to 
'
258
In
this
case,
the
multinational
firm
gets




−


 



27

4

Implications of tariﬀ policies, wages policies
and spillover eﬀects

4.1

Tariﬀ policies and wages policies

Our model can be regarded as a reduced form version of a model with richer details
and implications on tariﬀ policies and wage policies. To see this, suppose that thejoint venture sells in the local market a product for which a perfect substitute isavailable at the price  = (1+) where  is the exogenously given world price and is the tariﬀ rate. The output of the joint venture is a Cobb-Douglas functionof two inputs, technology  and labor . Assume that labor earns a constantwage rate  (equal to the wage in the alternative employment, say subsistence
agriculture). Given (), the joint venture chooses () to maximize instantaneous
profitΠ( ) = (1 + )   1− − (62)This yields the labor demand function∙(1 + )
=


¸1



(63)

Substituting this into the profit function Π, we get£¤1Π = (1 + )

µ

1−


¶

1−(1) 

(64)

µ

¶

(65)

It follows that our  in example 1 is£¤1
 = (1 + )1−

1−(1)An increase in the tariﬀ rate will raise  which leads to an increase in both the paceof transfer ∗ and the aggregate technology transfer ∗ ∗ in the first-best transfer
scheme. The second best amount of transfer also increases, because  increases(see Appendix 3). Similarly, a smaller wage rate will lead to more technology
transfer.
28

A developing country must consider the trade-oﬀ between the static eﬃciency
loss of a tariﬀ and the dynamic gain generated by technology transfer (and its
spillover eﬀects).

4.2

Spillover eﬀects in a Cournot duopoly

Our model can also be regarded as a reduced form version of a model of Cournot
competition with spillover eﬀects. Suppose that there are two local firms, denotedby  (the local firm which forms the joint venture with the multinational) and .
The two firms compete à la Cournot and the inverse demand function is linear, () =  −    0. The quantities they produce are respectively denoted and  . Assume that the technology transferred is cost-reducing. When firm  has
accumulated an amount of technology , its marginal cost is  () =  −  () with  ≥  (max  ). The second local firm  benefits from spillover eﬀects. Its

marginal cost is  () =  −  (), where  is the strength of the spillover√
eﬀects. For simplicity, assume that  () = ,   0. The profits of the local
firms  and  are, respectivelyΠ (    ) = ( () −  −  )  

(66)

and
(67)
Π (    ) = ( () −  −  )  
£ ¤Now assume that  ∈ 12  1 . Under this assumption, both firms produce in equi-

librium. The equilibrium quantities are
∗ =

√
√
1
1
(2 − )  and ∗ = (2 − 1) 
3
3

(68)

Substituting these quantities in the profit functions, we getΠ ( ∗  ∗ ) =1(2 − 1)2 
9

29

(69)

and
Π ( ∗  ∗ ) =1(2 − )2 
9(70)

The profit function of the local firm  is the same as in example 1 with=

1(2 − )2 
9(71)

An increase in the strength of spillover eﬀects  will reduce  which leads to adecrease in both the pace of technology transfer ∗ and the aggregate technology
transfer  ∗ = ∗ ∗ . The second best amount of technology transfer also decreases.

5

Concluding Remarks

Our model provides a theoretical formulation of the problem of choice of the pace oftechnology transfer from a multinational firm to a joint venture in a host country.
We have shown that when the host country cannot enforce joint venture contract,
the multinational will generally have an incentive to reduce the overall pace oftechnology transfer and the cumulative amount of technology transfer. Moreover,in Appendix 5, we show that the second-best technology transfer scheme may
involve a phase of deceleration (i.e. the speed is falling) followed by a phase ofacceleration (i.e. the speed is rising), and finally deceleration again.
A major implication of our model is that if the host country’s legal system is
not suﬃciently strong to prevent breakaway by local firms, the multinational will
reduce the rate of technology transfer. To the extent that technology transfers in
one industry have positive spillover eﬀects to other industries in the host country,
this country loses out by its inability to enforce contracts.
Our model can be used to examine the stability of relationships, such as
employer-employee contracts, where the employee can learn from working in thefirm and leave the firm once he has accumulated suﬃcient human capital.

30

Appendices (Not for publication)
Appendix 1: Proof of Proposition 1
The choice set Ω defined by Ω = {(  ) : 0 ≤  ≤ max and 0 ≤  ≤  } is acompact set. The objective function (8) is continuous in the variables   overthe compact set Ω. By Weierstrass theorem, there exists a maximum, which wedenote by (∗  ∗ ).
Next, we show that the maximum must be in the interior of the admissible setΩ. Since (0) = (0) = 0 and   0 (0)   0 (0) ≥ 0, the function  (  ) is strictly

positive for some positive  suﬃciently close to zero, for all  . Since  (0  ) = 0

and  ( 0) = 0, it follows that the optimum must occurs at some ∗  0 and∗  0. To prove (i) and (ii) above, it remains to show that an optimum cannot
occur at any point on the line  =  nor on the line  = max . To take into
account the constraints  −  ≥ 0 and max −  ≥ 0, we introduce the associatedLagrange multipliers  ≥ 0 and  ≥ 0. The Lagrangian is
=

Z 
0

[() − ()]  + ( −  ) ( ) + ( −  ) + (max − )(A.1)

The first order conditions are[ − ∗ ]  0 (∗ ∗ ) ∗ − (∗ ) −  = 0,

(A.2)

( − ∗ ) = 0  ≥ 0  − ∗ ≥ 0Z 0

[ 0 (∗ ) −  0 (∗ )]  + ( − ∗ ) 0 (∗ ∗ ) ∗ −  = 0,

(A.3)

(max − ) = 0  ≥ 0 max − ∗ ≥ 0

Since (∗ )  0, condition (A.2) implies that  − ∗  0. (The intuition behind
this result is simple: there is no point to transfer technology near the end of thetime horizon  ). Thus  = 0 and hence (A.2) reduces to( − ∗ ) 0 (∗ ∗ ) =31

(∗ )
∗(A.4)

To show that ∗  max , let us suppose that ∗ = max . Then, using (A.4), and∗ = max , condition (A.3) gives
(max ) ∗(max ) ∗0∗ 0 (max )∗ −

≤

(
)
−
 +
max


∗
max 
Z Z 
 0 (0)(∗ )200=
 (max )   (0)
 =
2
0
0

(A.5)

which violates assumption A1. Thus ∗  max . This concludes the proof that(∗  ∗ ) is in the interior of Ω.
It follows thatZ 0

[ 0 (∗ )]  =  0 (∗ )∗ − ( − ∗ ) 0 (∗ ∗ ) ∗¸∙
(∗ ) ∗0 ∗=  ( ) −
∗

(A.6)

It remains to verify the second order conditions. Recall that the FOCs at aninterior maximum is1 ≡  = ( −  ) 0 ( )  − () = 0

2 ≡  =Z 0[ 0 ()]  + ( −  )0 ( )  −   0 () = 0

(A.7)
(A.8)

The SOCs are

22 =

Z 
0

11 = − 0 ( )  + ( −  ) 00 ( ) ()2  0¤£ 2 00  ()  −   00 () + ( −  ) 00 ( ) ( )2  0∆ ≡ 11 22 − (12 )2  0(A.9)(A.10)(A.11)

Clearly 11  0 and 22  0. It remains to check that ∆  0 at (∗  ∗ ). Note that
12 = ( −  ) 00 ( )  + [( −  ) 0 ( ) −  0 ()] =32(A.12)

∙

¸
()
0
( −  ) ( )  +−  ()  0

00(A.13)(making use of (A.4)).
Consider the curve  = () defined by (A.7) in the space (  ) where  ismeasured along the horizontal axis. The slope of this curve is0 () =


12
0
| = −

11(A.14)

()(A.15)

Along this curve( −  ) 0 ( ) =as  → 0,  →  , and as  → 0,  → e
 where e is defined by  0 (0) = () .

Next consider the curve  = () defined by (A.8). The slope of this curve is22| = −
0
12(A.16)¸
0 () 0 () 0 ( )

+
(
−

=
)

  0 (0) 0 (0) 0 (0)(A.17)

0 () =Along this curve
Z  ∙
0

³ ´
0
0 b
b
b
As  → 0,  → 2 , and as  → 0, →  where  is defined by   (0) =   e. Thus the curve () must intersect
Since  0 ()  (), it follows that b
the curve () from above (at least once). At that intersection, the slope of the() curve must be more negative (i.e. steeper) than the slope of the () curve,that is

22
12
−
12
11

(A.18)

11 22  (12 )2(A.19)−
hence

Thus the SOC is satisfied at that intersection.
Finally, we can show that under assumption A3, the two curves () and ()intersect exactly once, that is, we show that ∆  0 whenever the FOCS are33

satisfied. It is easy to see that A3 implies that  0 () is an increasing function of.
We note the following facts. First,
∙
∙
¸2
¸
()
()
0
00
0
(12 ) = [( −  ) ( )  ] +−  () +2( − ) ( ) −  ()
(A.20)
2

2

00

Secondly,11 22 ©
ª( −  ) 00 ( ) ()2 − 0 ( ) ©
ª× ( −  ) 00 ( ) ( )2 −  00 ()

(A.21)(A.22)

2= [( −  ) 00 ( )  ] +  00 () 0 ( ) − ( −  )  0 ( )  00 ( ) ( )2 −  00 () 00 ( )  ()2 ( −  )2

= [( −  )00 ( )  ] − ( −  )  00 ( )  [0 ( )  +  00 ()]+ 00 () 0 ( ) 

Hence
∙
µ
¶¸
()
0
00
0
(A.23)∆ ≥ − ( −  )  ( )   ( )  +  () − 2  () −

00

¸2
()
0
+ () ( )  −−  ()
00∙

0(A.24)

Using the ³implication of´ assumption A1 stated in (4), which can be written as 00 ()   0 () − (), we have


∙µ
¸
¶
()
0
00
∆ 
 () −− ( −  )  ( ) 

∙
¶¸
µ
()
0
0
×  ( )  −  () −³´It remains to show that  0 ( )  >  0 () − ().
34

(A.25)(A.26)

With (A.6), we know that∙¸Z 
(∗ ) ∗0 ∗ ( ) − =[ 0 (∗ )] ∗
0(A.27)If A3 holds,  0 (∗ ) is increasing in  (remark 1). Then ( )  >0

Z 

[ 0 (∗ )] (A.28)

0

We conclude that ∆  0.
Appendix 2: The local firm’s optimal breakaway time
Consider the isoelastic profit function () = (1)  where 0    1. Thenequation (31) gives a unique b () that is independent of  :1 (A.29)1  −1  =   (1 + )(A.30) −11  =   (1 + )(A.31)( −  ) −1  =

so

or

ie




∙

¸

1+
=0
−



(A.32)


1+

(A.33)

thenThis is independent of .

b =Appendix 3: The incentive compatible contract when () is linear
The first order condition ((41) and (43))of the program can be rewritten as( −  ) −  () = 0
¡  ¢220   − 

()
+
(
−

)
−

= 0

 
2
4
35

(A.34)(A.35)

Equivalently,( −  ) −  () = 0
¡  ¢2∙¸2  ()0+ −  () − 
= 0
2

4

(A.36)(A.37)

Replacing  () =   , we haveh
 −1 i
 = 0
( −  ) − ¡  ¢2
∙
¸

1 −1
2


−
−  1 −

= 0
2

4

(A.38)(A.39)

If   0−1( −  ) = ¡  ¢2
∙
¸

1 −1
2
1
−
  − 
−

= 0


2

4

(A.40)

−1( −  ) = (A.42)(A.41)Or,¡  ¢22  − 
= 0
[
−
1]
(
−

)
−



2
4

(A.43)The solution is:

 =

q
 − 1 + ( − 1)2 +  − 12¡  ¢−1( − ) =  

2 − 1

(A.44)(A.45)

The contractual breakaway time is
−1+

 =

p
( − 1)2 + ( − 05)2( − 1)  ∗ =
2 − 12 − 136(A.46)

This implies that− − =p( − 1)2 + ( − 05)≡02 − 12 − 1(A.47)

where   0 and−10(A.48)The transfer rate is∙( − 
)
 =



¸1(−1)∙=(2 − 1)¸1(−1)

 ∗(A.49)

because   1.
The optimal lump sum  is£¤  ∗∗ =   () −  −  (  ) =

¤
£
¤
£
 
 ( )) −  − 
 −b ( ) ( b (  )(A.50)(A.51)

To prove that  ∗∗  0 it suﬃces to show that b ( )  
 . Using Lemma 1,

0  

 
part (i), we know that b ( )  
 if ( −  ) (  ) − (  )  0. Since 
is linear, this condition reduces to ( −  ) −    0(A.52)

  2


(A.53)

i.e.

This condition is satisfied, because, from (A.46)
−1+


=


p
( − 1)2 + ( − 05)12 − 1
2(A.54)

where the strict inequality follows fromp
2 ( − 1)2 + ( − 05)  1
37(A.55)

i.e.

£¤
4 ( − 1)2 + ( − 05)  1(A.56)

which is true because   1.)

Appendix 4: Properties of side transfer schemesbbConsider a given contractual breakaway time  with    (), where  ()is the “default breakaway time” found in Lemma 1, i.e, the time the local firm
would choose to break away in the absence of the flow (). Given  , the multinational will choose the minimal total flow of side payment that satisfies the incentive
constraint, the participation constraint and the borrowing constraint. Formally,
the multinational finds a function () that solves:
min
()

"Z 


#

 () 0

(A.57)

such that (a) the flow induces the local firm to choose  , i.e. such that
 = arg max


∙
¸
Z 
 =
 ()  + ( −  )(( ))(A.58)0and (b) the side payment at any time  is non-negative, i.e.

0≤

Z

0

£
¤
 ( )  if  ∈ 0  (A.59)

Let  () denote a solution of this program.(We allow the function  () to havea mass at isolated points.)
Lemma 2: A flow of side payments  () is optimal if and only if the following
conditions are satisfied.
(a) the local firm receives no payment prior to its “default breakaway time”b ():Z  () ()  = 0

(A.60)

0(b) the sum of the accumulated side payments and the local firm’s stand-alone38

profit after  just equals its secured profit   () :
Z 
0


b
b
 ()  + ( −  )( ) = ( −  ())( ()) ≡   ()(A.61)(c) and, for any time  where b () ≤  ≤ 
 , the total payoﬀ to the local firm

is inferior to its secured profit   ():0≤
Proof:Z  ()

 ( )  ≤ ( − b ())(b ()) − ( −  )( )(A.62)(i) Proof of suﬃciency: It is easy to verify that when  () satisfies conditions(A.60), (A.61) and (A.62) it is a solution of (A.57).
(ii) Proof of necessity: Consider a solution of (A.57). We show that it mustsatisfy conditions (A.60), (A.61) and (A.62).
To show the necessity of condition (A.61), suppose that  () does not satisfy
condition (A.61). If the left-hand side of (A.61) is strictly smaller than   (), thelocal would not choose  and hence the incentive constraint (A.58) is violated. If
the left-hand side of (A.61) is strictly greater than   (), then the multinational
can reduces it costs by oﬀering less side payments.
Next, we show the necessity of condition (A.62). If  () does not satisfy theleft inequality of condition (A.62) then condition (A.59) is not satisfied. If  ()does not satisfy the right inequality part of condition (A.62), then there exists e£¤within the interval b
 ()   such thatZ  ()

 ()   ( − b ())(b ()) − ( − e )(e )(A.63)

From the incentive constraint (A.58), from the local firm’s point of view, by defi
enition of  ,  does not dominate  , i.e.
Z 




 ()  ≥ ( − e )(e ) − ( −  )(( ))39(A.64)

Adding inequalities (A.63) and (A.64) we have
Z 





0


() +( − )(( )) Z  ()0 () +( −b ())(b ()) (A.65)

Thus  () fails to minimize the total flow of side payments

R 
0

 () .

Finally, we show the necessity of (A.60). Suppose that  () does not satisfy
condition (A.60), i.e.

Z  () ()   0

(A.66)

0

Using the incentive constraint (A.58), we obtain
Z 



0




()  + ( −  )(( ))≥Z  ()0 ()  + ( − b ())(b ())

 ())
 ( − b ())(b(A.67)

R 
This implies that  () does not minimize the total flow of side payments 0   () .
Appendix 5: The case where speed and acceleration are not constant.
We now assume that (i) the multination can vary the speed and accelerationof the technology transfer, and (ii) the parties can renegotiate at any time .
Furthermore, we suppose that the local firm’s bargaining power is  ∈ [0 1]. Thenthe local firm can ask (for the remaining period from  to  ) for a payment such thatb (()) +  = ( − ) 

∙Z 


¸
[(() − (()]  − ( − ) b (()) 

Here ( − ) b (()) is the payoﬀ that it can get outside the relationship from 

to  .

Assuming that the multinational wishes to design an incentive scheme suchthat the local firm never quits. The multinational’s programme is:½¾Z  (1 − )[(( )) − (( ))]  ()≥0040and the non quitting constraint is:( − ) b (())+

∙Z 


¸
[(( )) − (( ))]  − ( − ) b (()) ≥ ( − ) b (())  for all  ∈ [0 This is a special case of dynamic games between a leader and a follower. (SeeDockner, Jorgensen, Long and Sorger, 2000, Long 2010, Long and Sorger, 2010).

The problem can be written as follows:
The multinational’s objective function is
max

Z 
0

[(( )) − (( ))]  − (A.68)

subject to̇() = ()(A.69)

(0) = 0 (fixed),(A.70)

the "succesful renegotiation" constraint (i.e. the multinational must promise to
pay the local firm at least its payoﬀ under successul negotiation), ≥ ( − ) b (())+

∙Z 


¸
[(( )) − (( ))]  − ( − ) b (()) for all  ∈ [0  ] (A.71)and the non quitting constraint,b (()) for all  ∈ [0  ]  ≥ ( − ) 

(A.72)

We will transform this problem into a standard optimal control problem. To
do this, we define a new state variable () such that
() = ( − )(1 − )b (()) + 

41

Z 


[(( )) − (( ))]  

Then we require(())− [(()) − (())] (A.73)
̇() = ( −)(1−)b 0 (())()−(1−)band( ) = 0 (fixed).

(A.74)We define a second new state variable  () such that

Then we requireand () = ( − ) b (()) ̇ () = −b (()) + ( − ) 
b0 (()) ()

(A.75)

 ( ) = 0 (fixed).

(A.76)

Then the constraint (A.71) takes the form of a constraint on the state variable: − () ≥ 0

(A.77)and the constraint (A.72) takes the form of a constraint on the state variable  : −  () ≥ 0

(A.78)The optimal control problem is then to choose the time path of the control
variable  and the “control parameter”  to maximize the objective function(A.68) subject to the two transition equations, eqs. (A.69) and (A.73), the boundary conditions (A.70) and (A.74), and the constraint (A.77). Let (), () and () be the co-state variables associated with the state variables (), () and () respectively, and let ()  () ≥ 0 be the multipliers associated with the con-straint (A.77) and the constraint (??), respectively. Using Hestenes Theorem (seee.g. Leonard and Long, 1992), we can find the necessary conditions. (Suﬃciency42

is covered in the file LARS-suﬃciency), using the Lagrangian functionª©
 () −  [() − ()] = () − () +  +  ( − )(1 − )b 0 () − (1 − )b
ª
©
+ −b
 (()) + ( − ) 
b0 (()) ()+ [ − ] +  [ −  ]Proposition B-1: The second best program is very diﬀerent from the first best
program, and can be characterized as follows. If  ()  0 over [0  ),(i) The (second-best) function () is at first concave and then becomes convex
over at least one time interval (0  00 ) implying that ̇()  0 over (0  00 ) i.e.
the principal promises a phase of acceleration of human capital accumulation inorder to induce the agent to stay longer.
(ii) There exists    , such that over the interval [   ], () will be falling(̇  0).
(iii) There exists 0   , such that over the interval [0  ], () will be falling(̇  0).
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