Hidden Costs of Offshore Outsourcing: an Analysis of Offshoring Decisions

Abstract

Offshore outsourcing has grown as a form of industrial organisation to increase profitability of firms. However, offshoring may be less lucrative than envisaged, due to the presence of hidden costs. We study the strategic interaction amongst onshore Cournot firms in the decision to offshore when they receive signals about offshore hidden costs. The analysis helps suggest policy implications for countries which are potential offshoring locations. We find the precision of signals and the range of possible hidden costs to be crucial in determining offshoring destinations. Updating of information about hidden costs leads to different equilibria including herding in offshoring.

Appendices

Appendix A: Proof of Observation 1

We simplify equation 8 and write it as:

$$F(C_{h},C_{d})q_{1}^{HS}+\delta[G(C_{h},C_{d})]q_{1}^{HC}(C_{h},C_{d}) \geq F(C_{h},C_{l},C_{d})q_{1}^{LS}+\delta[G(C_{h})]q_{1}^{HC}(C_{h}) $$

where, $F(C_{h},C_{d})=[P^{HS}-(\bar {C}+C_{h})]$ and P ^HS is a function of C _d and C _h . $G(C_{h},C_{d})=[P^{HC}(C_{d},C_{h})-(\bar {C}+C_{h})]$ and similarly for the others.

Now, that gives the lower bound for $q_{1}^{HS}$ i.e.

$$F(C_{h},C_{d})q_{1}^{HS} \geq F(C_{h},C_{l},C_{d})q_{1}^{LS}+\delta[G(C_{h})]q_{1}^{HC}(C_{h}) -\delta[G(C_{h},C_{d})]q_{1}^{HC}(C_{h},C_{d}) $$

Differentiating this expression wrt C _l we get:

$$F_{C_{l}}()q_{1}^{LS}+F()q_{1C_{l}}^{LS} $$

Now, for a given demand function and the costs of production C _h , $q_{1}^{HS}$ is the profit maximising Stackelberg output. For any increases in output the revenues increase less than the costs. Hence at the given cost C _h it becomes more and more unprofitable to produce more output. Hence for conventional demand functions with decreasing marginal revenue this expression comes out to be positive.

So, as C _l decreases, the RHS reduces in value. Hence the inequality holds more strongly. Thus the higher is (C _h − C _l ) the stronger the possibility of the high type to reveal his true hidden cost. Hence observation 1 stands proved.

Appendix B: Proof of Observation 2

Qualitative proof of one IC binding in the pooling equilibrium: ICH:

$$\begin{array}{@{}rcl@{}} [P^{P}-(\bar{C}+C_{h})]q^{p} \\ +(1-\bar{p})[\delta\{P^{HC}(C_{d},C_{h})-(\bar{C}+C_{h})\}q_{1}^{HC}(C_{h},C_{d})] \\ +\bar{p}[\delta\{P^{HC}(C_{h})-(\bar{C}+C_{h})\}q_{1}^{HC}(C_{h})] \\ \geq [P^{HS}-(\bar{C}+C_{h})]q_{1}^{HS}+\delta[P^{HC}(C_{h})-(\bar{C}+C_{h})]q_{1}^{HC}(C_{h}) \end{array} $$

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i.e.:

$$\begin{array}{@{}rcl@{}} [P^{P}-(\bar{C}+C_{h})]q^{p} \\ \geq [P^{HS}-(\bar{C}+C_{h})]q_{1}^{HS}+\delta[P^{HC}(C_{h})-(\bar{C}+C_{h})]q_{1}^{HC}(C_{h}) \\ -(1-\bar{p})[\delta\{P^{HC}(C_{d},C_{h})-(\bar{C}+C_{h})\}q_{1}^{HC}(C_{h},C_{d})] \\ -\bar{p}[\delta\{P^{HC}(C_{h})-(\bar{C}+C_{h})\}q_{1}^{HC}(C_{h})] \end{array} $$

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ICL:

$$\begin{array}{@{}rcl@{}} [P^{P}-(\bar{C}+C_{l})]q^{p} \\ +(1-\bar{p})[\delta\{P^{LC}(C_{d},C_{l})-(\bar{C}+C_{l})\}q_{1}^{LC}(C_{l},C_{d})] \\ +\bar{p}[\delta\{P^{LC}(C_{l})-(\bar{C}+C_{l})\}q_{1}^{LC}(C_{l})] \\ \geq [P^{LS}-(\bar{C}+C_{l})]q_{1}^{LS}+\delta[P^{LC}(C_{l})-(\bar{C}+C_{l})]q_{1}^{LC}(C_{l}) \end{array} $$

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i.e.:

$$\begin{array}{@{}rcl@{}} [P^{P}-(\bar{C}+C_{l})]q^{p} \\ \geq [P^{LS}-(\bar{C}+C_{l})]q_{1}^{LS}+\delta[P^{LC}(C_{l})-(\bar{C}+C_{l})]q_{1}^{LC}(C_{l}) \\ -(1-\bar{p})[\delta\{P^{LC}(C_{d},C_{l})-(\bar{C}+C_{l})\}q_{1}^{LC}(C_{l},C_{d})] \\ -\bar{p}[\delta\{P^{LC}(C_{l})-(\bar{C}+C_{l})\}q_{1}^{LC}(C_{l})] \end{array} $$

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Now it may be noted that LHS of the ICH is less than LHS of ICL. Similarly RHS of ICH is less than RHS of ICL. Thus, the IC of the high type alone guarantees the low type IC as well. It is easy to note that as C _l increases profitability of the low hidden cost type falls. Hence leaving C _h unchanged, one gets a situation where both inequalities are simultaneously satisfied.

Proof of Observation 2:

Following on from above:

$$\begin{array}{@{}rcl@{}} [P^{P}-(\bar{C}+C_{h})]q^{p} \geq [P^{LS}-(\bar{C}+C_{l})]q_{1}^{LS}+\delta[P^{LC}(C_{l})-(\bar{C}+C_{l})]q_{1}^{LC}(C_{l}) \\ -(1-\bar{p})[\delta\{P^{LC}(C_{d},C_{l})-(\bar{C}+C_{l})\}q_{1}^{LC}(C_{l},C_{d})] \\ -\bar{p}[\delta\{P^{LC}(C_{l})-(\bar{C}+C_{l})\}q_{1}^{LC}(C_{l})] \end{array} $$

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For a lower C _h ,the LHS increases and we have strict inequality. Hence the ICs become stronger. [Proved] □