Diseño de Interiores

The primary objective of this paper is to examine the relationship between product differentiation and the irrelevance of input prices for the entrants’ make-or-buy decisions. We find that Sappington’s main result on the irrelevance of input prices is sensitive to the particular level of product differentiation in the Hotelling model. Specifically, Sappington’s results concerning the irrelevance of input prices depend on the limitations of the standard Hotelling location model for product differentiation. It is shown that even under the Hotelling framework, allowing for product differentiation in more than one characteristic undermines Sappington’s main result concerning the irrelevance of input prices for make-or-buy decisions. Allowing product differentiation in more than one characteristic produces results similar to those of Gayle and Weisman (2007a). The representative consumer approach also provides similar qualitative

results. Our findings serve to establish that input prices for make-or-buy decisions are irrelevant if the incumbent and the entrant produce identical products, and relevant if the firms produce differentiated products. The policy implications of these results are important. Unless the incumbent’s and entrant’s products are perfectly homogeneous, regulatory agencies should seek to set efficient prices to minimize efficiency distortions.

The models employed in this study treat product differentiation as independent from the actions of firms since the product differentiation definition relies on consumer preferences.

However, in reality firms exert significant effort and go to great expense to differentiate their products from those of their rivals. Thus, employing models where the degree of product differentiation is endogenous to the firms may be a fruitful avenue for future research.

Appendix A - Proofs for Lemmas and Propositions

Proof of Proposition 1:

See Sappington (2005, pp. 1632-1633).

Proof of Lemma 1:

The location of the consumer that is indifferent between purchasing from the incumbent and the entrant satisfies the following equation:

(1 )

The profits of the incumbent and the entrant are given, respectively, by

( )

^I ₂^{I E E ;}

Maximizing (A4) and (A5) with respect to P and_M^I P , respectively, then solving the first _M^E order conditions simultaneously yields

( ) ( )

Substituting (A6) and (A7) into (A2) and (A3), respectively, then multiplying the resulting equations by N yields:

Substituting (A6) and (A8) into (A4), and (A7) and (A9) into (A5) yields:

( ) ( )

²

The proof follows steps similar to those of Lemma 1. The difference arises from the definition of profits. For the buy decision, the incumbent makes profits from the production of the upstream input which is basically a function of the entrant’s quantity and its downstream production. On the other hand, when the entrant buys the upstream input, w replaces as the entrant’s upstream marginal cost. Therefore, if the entrant buys the upstream input from the incumbent, the incumbent’s profits are:

( )

^E ₂^{E I I}

Maximizing (A12) and (A13) with respect to and , respectively, then solving the first-order conditions simultaneously yields:

Substituting (A14) and (A15) into (A2) and (A3), respectively, then multiplying the resulting equations by N yields:

(A12) and (A15) and (A17) into equation ields:

and (A19) reveals that the condition for the entrant’s efficient make-or-buy decision,

P

A comparison of (A11)

E E

he proof is straightforward. As stated in the body of the essay, for w ^I, the entrant

earns z buy the input. In the case where the e t makes the

and both firms charge a price of p=c^I, and the entrant’ profits are

( )1 ( ) 0.

E cI cE D cI

Π = − > Hence, the entrant prefers to make the input if it is the least-cost

E I

input both firms will charge price p=c^E, and the entra es zero profit while the incumbent

M 2

supplier. This establishes part (a). In the case where t is in rent to either option. To show this in the case where c , obs if the entrant chooses to make the

nt mak

makes positive profit of 1

( ) ( )

I cE cI D cE

Π = − . However, if the entrant buys the input, then the

market price is p=w, the entran nce again zero and the incumbent’s profit is

( ) ( )

B I

I w c D w

Π = − . Hence the entrant is indifferent to the make-or-buy decision. This

M 2

t’s profit is o

mma 3:

e upstream input itself, the profits of the incumbent and the entrant

)

A28) into the demand system provides:

( ) ( )( ) ( )

( ) ( )( ) ( )

ps similar to those of Lemma 3. As before, the difference derives from th

P

The proof follows ste

e definition of profits. For the buy decision the incumbent makes profits from both the production of the upstream input which is basically a function of the entrant’s quantity and its downstream production. However, when the entrant buys the upstream input, w replaces c_u^E as the entrant’s upstream marginal cost. Hence, if the entrant buys the upstream input from the incumbent, the profits are:

Substituting (A35) and (A36) into the demand system yields:

( ) ( ) ^{( )} ( ) ( )( ) ( )

Substituting (A35), (A37) and (A38) into (A33), and (A36) and (A38) into (A34) yields:

( )

A comparison of (A32) and (A40) reveals that the condition for the entrant’s efficient make-or-buy decision.

(

^{2b bI E d2}

)( )

^{cuE <}

(

^{2b bI E d2}

) ^{( )}

^{w d c}

(

^{uI w}

Hence, the entrant buys the upstream input from the incumbent when which implies that

The entrant prefers to make the upstream input when Π < Π which implies that ^E_B

( ) (

2 ²

)(

Appendix B - The Irrelevancy of Input Prices in a Sequential Game

Sappington (2005) employs the Hotelling model to demonstrate the irrelevance of input prices in a simultaneous game framework. One possible extension would be to examine the concept in a sequential game framework. In the sequential framework, we assume that the incumbent firm is the leader and the entrant is the follower. The remaining assumptions are identical to those in Sappington (2005).

We will present the entrant’s equilibrium values only. When the entrant makes the upstream input, the entrant’s equilibrium price, output, and profit are given by:

( ) ( )

Conversely, when the entrant chooses to buy the upstream input from the incumbent, the entrant’s equilibrium price, output, and profit are given by:

( ) (

A comparison of (B3) and (B6) reveals the conditions for the entrant’s efficient make-or-buy decision. Specifically, the entrant prefers to make the upstream input itself if Π > Π and ^E_M ^E_B buy the input from the incumbent if Π < Π . Therefore the entrant makes the upstream input ^E_M ^E_B when , and the entrant prefers to buy the upstream input from the incumbent if and only if Hence, in comparison with the simultaneous game framework, the sequential game structure affects only the equilibrium values, but not the irrelevance of the input prices. Hence, Sappington’s result on input irrelevance is robust to the change from a simultaneous-move to a sequential-game framework.

I

cu >c

I E.

u <cu E u

c

In document DOCTORADO EN DISEÑO. La conformación del campo disciplinar del diseño de interiores en Ecuador. Catherine Cabanilla León (página 88-97)