Fragmentation Mode of Entry

In this case MNC chooses to fragment the production in such a way that it conducts the manufacturing of core parts in its own country (thus bringing in embodied technology to the LDC) and complete the assembling part in the LDC. As men-tioned earlier the MNC can adopt two alternative strategies namely:

Complete Copy Protection strategy—The MNC undertakes anti-copying investment such that entry of the fake producer is prevented ensuring monopoly profit for the MNC. We assume that x^cp_frag be the level of anti-copying investment which completely prohibits the illegal copying of the MNCs product and thus rules out the entry of fakefirm in the LDC market.

The total cost function under Complete Copy Protection (CP) strategy is c^cp_frag¼ wq þ A þ tq þ x^cpfrag: ð5Þ where w is the per unit cost of assembling the semifinished product in the LDC¹¹ and t is the per unit transport cost to transfer the intermediate product to the LDC.

For simplicity it is assumed to be same as the transport cost of thefinished product when the MNC is simply exporting the product.

The profit of the MNC in this case will be Ycp

frag ¼YcpðmÞ frag 
x^cp_frag

¼ ph ^cpfrag ðw þ tÞi

q^cp_frag A 
x^cpfrag: ð6Þ The monopoly profit, price, and quantity will be

Ycp

frag ¼fa  ðw þ tÞg²

4  A 
x^cpfrag; q^cpfrag¼a w  t

2 ; p^cpfrag¼aþ w þ t

2 : ð7Þ

10Where Social Welfare is maximized at g = 0.

11It is assumed that w < c due to cheap labor in the LDC.

The social welfare in this case will be

SW^exp_frag^ðcpÞ¼ Consumer Surplus þ Government Surplus

¼fa  ðw þ tÞg²

8  CðgÞ: ð8Þ

Accommodating Strategy—In this case anti-copying investment x^acfrag is under-taken by the MNC in such a way that the fake producer can enter and operate in the market. The MNC acts as a price leader with the fake producer acting as a follower.

Let kh(x^ac_frag) be the probability of copying the original product where 0\k\1; 0\hðxÞ\1; h⁰ðxÞ\0; h⁰⁰ðxÞ [ 0 : 0\khðxÞ\1; hðxÞ ¼ 1 for x ¼ 0;

Lt hðx^acfragÞ

x!1 ! 0 and k is the exogenously given copying parameter.¹² Thus in the accommodating strategy complete deterrence of the pirate is ruled out. The model also makes the following assumption:

A1: hðxÞh⁰⁰ðxÞ  fh⁰ðxÞg²[ 0

The probability that the fake producer will be detected is g where g is the local government’s monitoring rate of IPR. Therefore, the probability of entry of the fake producer can be written as kh(x^ac_frag)(1− g) and the probability of detection of the fake producer isn1khðx^acfragÞð1gÞo

.

The total cost function of the MNC is given by c^ac_frag¼ wq þ A þ tq þ x^acfrag

The profit of the MNC when the fake producer enters and operates in the market Yac

frag ¼ ph ^ac_frag ðw þ tÞi

q^ac_frag A  x^ac_frag: ð9Þ For the fake producer profit is defined as:

Yfake

frag ¼ p^acfragq^fake_frag1 2q^{2 fake}_frag

 

 F: ð10Þ

where the cost functions of the fakefirm is Cðq^fakefragÞ ¼ q^2fake_frag

2 þ F: ð10aÞ

and F be the sunk cost.

12‘k’ is assumed to be a fraction because under fragmentation mode of entry as full technology transfer is not taking place afirm cannot copy the product with certainty if the firm is not investing in anti-copying investment.

Solving the price leadership game by backward induction method we first determine the FOC of profit maximization of the fake producer and equate it to zero

@p^fake_frag

@q^fake_frag ¼ 0 ) p^acfrag¼ q^fakefrag: ð11Þ

The residual demand function for the MNC will be

q^ac_frag¼ a  p^acfrag q^fakefrag: ð12Þ Replacing Eq. (11) in (9) and solving for the profit maximizing equilibrium values we get¹³

In case the fake producer gets detected due to IPR protection exercised by the local government then the profit equation of the MNC will be

YacðmÞ From the two profit functions for the MNC given in Eqs. (13) and (14) the expected profit function for the MNC can be given as

Y_acðexpÞ Maximizing (15) MNC determines the optimal value of anti-copying investment (
x^ac_frag) which satisfies (16).¹⁴

13The duopoly profit of MNC under fragmentation with AC strategy will be positive if and only if a > 2(w + t).

14Second-order condition requires thath⁰⁰ðxÞ [ 0.

kh⁰ð
x^acfragÞð1  gÞ fa  ðw þ tÞg²

4 fa  2ðw þ tÞg² 8

" #

¼ 1: ð16Þ

Proposition 1 In the Fragmentation mode of entry, under Accommodating Strategy the anti-copying investment undertaken by the MNC (
x^ac_frag) is inversely related to IPR protection rate (g) and transport cost (t).

Proof See Appendix1.

Thus if the local LDC government’s provision of IPR protection or the transport cost of transferring the semifinished good from the DC to the LDC increases then the MNC will reduce its anti-copying investment in case of AC strategy. There is a substitutability between local government’s provisions of IPR protection vis-á-vis that of MNCfirm. Alternatively, a rise in t increases the marginal cost of assem-bling the product for LDC. Thus profitability requires a cut in anti-copying investment by the MNC.

The expected profit function for the fake firm will be YfakeðexpÞ

where G is the lump sum penalty which the fake firm has to pay the local LDC government if it gets detected.

Replacing the values from Eq. (13) we get

Y_fakeðexpÞ

(i) Fakefirm will not operate under Fragmentation for g 2 ½g^_frag; 1 where g^_frag is defined in Eq. (18).

(ii) g^_fragincreases with t and decreases with penalty level G where

g^_frag¼

(iii) Profit of the fake producer decreases unambiguously with the IPR moni-toring rate if the assumption A1 holds.¹⁵

Proof See Appendix1.

That is if g g^_fragthen fakefirm does not enter. In other words for a sufficiently high value of g the MNC enjoys monopoly profit and also does not have to undertake any anti-copying investment. Second, a high penalty lowers the prof-itability and deters the entry of fake firm. Alternatively as t increases, per unit transport cost for MNC increases, raising the price. A higher price increases the profitability of fake producer. Hence g^fragrises, implying that a high monitoring rate is required to deter entry of fake producer.

The profit of the fake producer decreases with ‘g’ the IPR monitoring rate if the assumption A1 holds. A rise in g reduces the expected profit of the fake firm at an unchanged level of anti-copying investment. However, from Proposition 1 we know that a rise in g reduces the anti-copying investment thereby increasing the fakefirm’s profit. But the overall effect will be negative if condition A1 holds.

The social welfare¹⁶ will be

SW^ac_frag^ðexpÞ¼ Consumer Surplus þYfake

frag þ Government Surplus Now Consumer Surplus is given as

CS^exp_frag^ðacÞ¼ ð1  gÞkh x^acfrag

 f3a 2ðw þ tÞg²

32 þn1 khðx^acfragÞð1  gÞo

8 fa ðw þ tÞg²F

The Government Surplus can be given as

Government Surplus¼ khðx^acfragÞgG  CðgÞ

where G is the local LDC government’s earning received when the fake firm gets detected and C(g) is the cost of providing IPR protection.

Summing up Consumer Surplus, profit of the fake firm (which retains its entire profit in the LDC) and Government Surplus we get the Social Welfare of the AC strategy as

15A1 rules out the situation where a stringent IPR monitoring rate improves the profit of the fake firm.

16It may be argued that since fakefirm is not socially desirable so its profit should be excluded from Social Welfare calculations. However, since the fakefirm generates a surplus in the host country so its profit is included in the above calculations. Even if we exclude the fake firm from social welfare calculations, the results remain essentially the same.

SW^acðexpÞ_frag ¼ða  w  tÞ²

Comparative Study of Copy Protection and Accommodating Strategies under Fragmentation Mode of Entry

Comparing (7) and (15) wefind Ycp

Equation (20) shows that if equilibrium value of
x^acfragis greater than or equal to

x^cpfrag the AC strategy is always dominated by the CP strategy.

Again differentiating (20) with respect to‘g’

@ðQcp

The above result shows that AC strategy in the fragmented mode of Entry becomes more profitable as ‘g’ goes up. Thus for
x^ac_frag\
x^cp_frag let us assume that there exists a value of g say~gfragsuch thatQcp

frag¼QacðexpÞ

frag . Solving for that value of g we get the following results.

~gfrag¼ 1 4ð
x^cpfrag
x^acfragÞ

khð
x^acfragÞ^{a22ðw þ tÞ}₂ ²¼ 1 8ð
x^cpfrag
x^acfragÞ

khð
x^acfragÞða² 2ðw þ tÞ²Þ ð22Þ

Therefore depending on the value of‘g’ we get the following strategy choice for the MNC when it considers the fragmented mode of entry.¹⁷ Otherwise complete copy protection strategy will be a dominated strategy for all values of g. Table1 summarizes the result.

Since ^@SW^acðexpÞ_frag

@g \0 the social welfare under AC strategy is maximized at g¼ ~gfrag.