Transaction Cost, Technology Transfer, and Mode of Organization

Abstract

We develop a monopolistically competitive model for a closed economy without contract incompleteness. We show that if superior technology is not allowed to be transferred, integration would be the best mode of organization given that the transaction cost of intermediate input is not sufficiently small. However, transferability of technology calls for adding the dimension of factor intensity of input. We then prove that integration could be the better option only when input production technology is capital intensive. Thus, we validate the empirical claim of Antras (2003) from a perspective other than incomplete contract.

We are thankful to Avik Chakrabarti, Lei Yang for their constructive comments on an earlier draft of the paper. Comments from an anonymous referee are also acknowledged with thanks. Sugata Marjit acknowledges without implicating, the Reserve Bank of India (RBI) endowment at the CSSSC for financial support. The usual disclaimer applies.

Appendix

Integrating final good producer (G) maximizes the following profit function in absence of technology transfer.

$$ \pi_{G,\;I} (i) = p(i)x(i) - r^{\beta } w^{1 - \beta } \gamma x(i) - f_{c} r^{\beta } w^{1 - \beta } $$

(A.1)

We further know that,

$$ x(i) = EP^{\sigma - 1} p(i)^{ - \sigma } $$

(A.2)

From (A.2) one gets,

$$ \frac{x(i)}{{\frac{\partial x(i)}{\partial p(i)}}} = - \frac{p}{\sigma } $$

(A.3)

The first-order condition implies

$$ \begin{gathered} p(i) - r^{\beta } w^{1 - \beta } \gamma = \frac{p(i)}{\sigma } \hfill \\ p(i) = r^{\beta } w^{1 - \beta } \frac{\gamma }{\alpha } \hfill \\ \end{gathered} $$

(A.4)

Plugging (A.2) and (A.4) in (A.1), the profit equation reduces to

$$ \pi_{G,I} (i) = F\alpha^{\sigma } \gamma^{1 - \sigma } \left[ {\frac{1}{\sigma - 1}} \right]\left[ {r^{\beta } w^{1 - \beta } } \right]^{1 - \sigma } - f_{c} r^{\beta } w^{1 - \beta } $$

(A.5)

This is the same equation that we have in text as (13).

Following the same technique, we can derive the profit maximizing equilibrium price for G when input is sourced from stand-alone supplier.

$$ p(i) = r^{\beta } w^{1 - \beta } \frac{\mu }{\alpha } $$

(A.6)

In what follows, the profit for G with outsourced intermediate input becomes,

$$ \begin{aligned} \pi_{G,I} (i) = & p(i)x(i) - r^{\beta } w^{1 - \beta } \mu x(i) - f_{c} r^{\beta } w^{1 - \beta } \\ \Rightarrow \pi_{G,O} (i) = & F\alpha^{\sigma } \mu^{1 - \sigma } \left[ {\frac{1}{\sigma - 1}} \right]\left[ {r^{\beta } w^{1 - \beta } } \right]^{1 - \sigma } - f_{c} r^{\beta } w^{1 - \beta } \\ \end{aligned} $$

(A.7)

This equation is identical with (12′) of the main text.

However, with technology transfer (TT) the total cost function for producing intermediate input would be:

$$ C = (r^{\beta } w^{1 - \beta } )(1 + \phi (\beta ))x(i) + f_{c} r^{\beta } w^{1 - \beta } $$

(A.8)

Therefore the profit equation becomes,

$$ \pi_{G,I} (i) = p(i)x(i) - r^{\beta } w^{1 - \beta } x(i)(1 + \phi (\beta )) - f_{c} r^{\beta } w^{1 - \beta } $$

(A.9)

Above equation gives us the new profit-maximizing equilibrium price as

$$ p(i) = r^{\beta } w^{1 - \beta } \frac{(1 + \phi (\beta ))}{\alpha } $$

(A.10)

Plugging (A.2), (A.8) ,and (A.10) into (A.9) one gets the equation identical with (16) of the main body of the paper.

$$ \pi_{G,I,TT} (i) = F\alpha^{\sigma } (1 + \phi (\beta ))^{1 - \sigma } \left[ {\frac{1}{\sigma - 1}} \right]\left[ {r^{\beta } w^{1 - \beta } } \right]^{1 - \sigma } - f_{c} r^{\beta } w^{1 - \beta } $$

(A.11)