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This paper obtains optimal settings of each parameter on a supply chain composed of a rational manufacturer and a fair retailer. Through the establishment of model under information symmetry and information asymmetry, in which the effort level of retailer can’t be observed by manufacturer, the impact of retailer’s fairness on his effort level and manufacturer’s utility are explored and investigated. From the comparison, this paper find that retailer’s effort level and manufacturer’s utility under information asymmetry are higher than those under information symmetry, and the difference is directly proportional to the degree of retailer’s fairness. Retailer’s fairness has positive effect on his effort level and manufacture’s utility under information asymmetry, and manufacturers tend to cooperate with the retailer who has higher degree of fairness.

In recent years, the improvement of the supply chain performances has become a key point of researches in the Supply Chain Management. Retailers are more and more developing familiarity with the market especially customers, they often organize various promotions to attract potential customers and expand sales. Therefore, how retailers can increase promotional effort level so as to improve the whole performance of supply chain has been the target of many scholars. For example, Wen, C.Z., Ji J. H. studied the coordination problem of supply chain assuming the retailer sales efforts to be verifiable. But actually, retailer’s effort level cannot be observed by the manufacturer [

Consider a supply chain made up of one manufacturer M and one retailer R, in which the manufacturer as the leading party is completely rational and the retailer is the follower with fairness. Production cost is c, manufacturer sells products to retailer at a wholesale price w, retailer sells products to consumers at a price p. p is an exogenous variable and it has no influence on market demand. w ? c > 0 means that the marginal profit of manufacturer is greater than zero and p − w > 0 shows that the marginal profit of retailer is greater than zero. Assuming the market demand function is

In terms of theoretical description of fairness, the representative model is the F-S model (Fehr and Schmidt, 1999) [

in which

Assuming the retailer’s effort is observable so the manufacturer can force the retailer to choose any effort level e. In this contract the manufacturer puts forward parameters

Constructing Lagrange function based on (1) and (2) as follow:

We can get the optimal solution according to (3).

Theorem 1: The optimal setting of each parameter under information symmetry as follows:

In the case of information symmetry, the retailer’s effort level is determined by the manufacturer, which is not affected by his own fairness.

Actually, the effort level

We can deduce e_{2} through the partial derivative of (8) towards e:

Combining (9), (7) and (6) we get the following theorem.

Theorem 2: The optimal setting of each parameter under information asymmetry follows:

Under information asymmetry, every parameter is directly linked to the retailer’s fairness. As the degree of fairness of the retailer becomes higher, the manufacturer will lower the wholesale price w to increase the retailer’s promotion effort level. Facing different retailers with different fairness, the various combinations of w and e can maximize the manufacture’s utility.

Under information symmetry,

Theorem 3: Under information symmetry, the effort level of the retailer would not be influenced by his fairness; under information asymmetry, the retailer’s promotional effort is proportional to the degree of his fairness.

Under information symmetry, the effort level of the retailer is determined by the manufacturer. So, his fairness degree has no influence on his sales effort. Under information asymmetry, although the manufacturer cannot force the retailer to choose the effort level which is most beneficial to him, the retailer, due to a lower wholesale price offered by the manufacturer will put more efforts on sales in order to maximize his own utility. Besides, his higher degree of fairness will drive higher his effort level, that is to say, the retailer's promotional effort is proportional to the degree of his fairness.

Under information symmetry, the manufacturer’s utility is

So

We only discuss the case

Under information asymmetry, the manufacturer’s utility is

So,

Since

Theorem 4: Under information symmetry, the manufacturer’s utility is inversely proportional to the retailer’s fairness; under information asymmetry, it is proportional to the retailer’s fairness.

Firstly, compare the difference between the retailer’s effort level in two different cases: information symmetry and information asymmetry. From (5) and (11) we can get

Secondly, compare the manufacturer’s utility under the two information status. From (13) and (15) we can get

Introducing

Theorem 5: Compared to information symmetry, under information asymmetry the retailer’s effort level is higher; in both cases the difference of retailer’s promotion effort level is proportional to the fairness.

Theorem 6: Compared to information symmetry, under information asymmetry the manufacturer’s utility is higher; in both cases the difference of manufacturer’s utility is proportional to the retailer’s fairness.

In asymmetric information, since the manufacturer can’t observe the retailer’s effort level, he has to lower the wholesale price according to the retailer’s fairness degree to incite the retailer to make greater efforts than that he does in symmetric information case. Although the manufacturer must pay certain incentive costs (lower the wholesale price), his additional returns which increased due to the retailer’s higher effort level are higher than the incentive costs; the manufacturer’s utility is therefore improved. The retailer’s fairness has influence on his own effort level only under information asymmetry, in such case the manufacturer will lower the wholesale price to drive the retailer to pay more sales efforts to maximize his utility. Under information symmetry and information asymmetry, if the retailer has a low fairness preference, the difference of his effort level and the difference of the manufacturer’s utility are both small. In real situation, the retailer’s sales effort level cannot usually be observed but the retailer’s fairness has positive value and it can make his own effort level and the manufacture’s utility higher. Therefore, in the supply chain where retailers have fairness preference, manufacturers tend to cooperate with the retailer who has higher degree of fairness.

Under information symmetry, the retailer’s fairness has no influence on his own effort level and it is inversely proportional to the manufacturer’s utility; under information asymmetry the retailer’s fairness has positive influence on his own effort level and it is proportional to the manufacturer’s utility. From a series of analyses we concluded that under the condition of information symmetry and asymmetry both the difference of retailer’s promotion effort level and the difference of manufacture’s utility are proportional to the retailer’s fairness. Due to the positive value of fairness, under information asymmetry manufacturers prefer to cooperate with the retailer who has higher degree of fairness.

Guangxing Wei,Yao Tang, (2016) Supply Chain Contract Incorporating Fairness under Asymmetric Information. Open Journal of Social Sciences,04,35-39. doi: 10.4236/jss.2016.47005