Research Article
An Agency Model to Explain Advance Payment Contract in Supply Chain Management
Business School, Sichuan University, Chengdu, China
Xianyu Wang
Business School, Sichuan University, Chengdu, China
Trade credit has been seen as an important source for the firms to get financial support, especially for which are out of bank credit (Giannetti, 2003). Of course, trade credit is not only used for financial purses, for example it can be used as a certification of products quality (Giannetti et al., 2011). Advance payment (prepayment or early payment) is a kind of trade credit in which the buyers pay the money before the delivery. The scarcity of studies regarding advance payment is surprising, especially since according to IMF (2009) study, advance payment happens in 19-22% of international transactions.
An agency model is developed by Bastos and Pindado (2007), which is for explaining the adveesr selection and moral hazard problems. Following Bastos and Pindado (2007) the research use the agency theory to explore the existing problems with advance payment contract. Previous empirical work has suggested that trade credit can be viewed as a contractual solution to concern product quality (Ng et al., 1999). Just as Pike et al. (2005) point out, the relationship between the advance payment contact and the product quality is more complex. This leads to the first research question: what is the relationship between the advance payment contract and the product quality.
A second way of viewing trade credit is as part of the firms mechanisms to mitigate the overall damage due to the buyers moral hazard?
Repullo and Suarez (2000) think the moral hazard problem between the firms and their lenders can be mitigated by credit trade. Bastos and Pindado (2007) arise a moral hazard model in advance payment model, from the ex-post asymmetric information between sullers and buyers, which gives rise to the possibility that clients will not pay when payment is due. Giannetti et al. (2011) consider to mitigate the buyers moral hazard problem is one of the reasons that the suppliers offer more trade credit. So the second question to explore is: whether can the advance payment mitigate the buyers moral hazard problem or not.
This study proposes a simple agency model to explore the above two questions. The research extends the models from two aspects. First, the trading volume between the supplier and the retailer is the demand quality, other than one (Bastos and Pindado, 2007; Giannetti et al., 2011), which consists with the truth. Second, it is wanted to know how the advance payment influences the product quality, so the product quality can be verified after the contract. The supplier can partly control the product quality by putting effort (Kaya, 2011). So, the product quality is used by a moral hazard parameter. The model can be seen as double sided moral hazard.
METHODOLOGY
As explained above, the demand is dependent on the retailers sales effort e and the suppliers product quality s, as Q = Q (e,s). It is assumed that the cost for retailer of providing effort level e is g(e), where, g(0) = 0, g'(e)>0, g"(e)≥0. The suppliers unit producing cost is influenced by the product quality, it is assumed as c(s), where c(0) = 0, c'(s)>0, c"(s)≥0. The quality equals to zero, means there is no product to provide, so the cost is also zero.
The sales effort and the quality can both enhance the demand, as:
But both margins are decreasing, as:
The sales effort and the product quality can improve each others influence, as:
The products market price p is fixed. The retailer pays A to the supplier before the delivery, so the supplier charges w(A) per unit product. The advance payment discount is dependent on the amount which the retailer pays in advance and the more the retailer pays in advance, the more discount the supplier provides, as w'(A)<0. Let kr(A) denote the opportunity cost of the retailer providing the advanced payment, where kr(0) = 0, kr'(A)>0. Let ks(A) denote the opportunity cost of the supplier getting the advance payment, where ks(0) = 0, ks'(A)>0. As Giannetti et al. (2011) figure out, to some extent, firms have some financial slack or unused credit facilities enabling them to take advantage of the discount offers. So the opportunity cost of the retailer is always less than that of the supplier, kr(A)<ks(A) and the margin of the advance payment for the retailer is less than that for the supplier, kr'(A)<ks'(A).
Following the integrated supply chain model will be explored. The sales effort and the product quality in the integrated supply chain, as the best ones, will be listed as a benchmark.
Under these assumptions, the profit of the whole channel can be expressed as follow:
(1) |
Where, from the second order conditions, it is easy to get the Hessian Matrix is negative. The first best sales effort and the first best product quality can be gotten, when the first order conditions equal to zero. The first best sales effort and the first best product quality can be gotten from the following Eq:
(2) |
(3) |
where, for the advance payment contract, the supplier provides a list pairs of advance payment and whole sale price, as{A, w(A)}, where, and which means the most advance payment is no more than the total transfer amount. The retailer chooses the amount from the list, which he wants to pay in advance.
Under these assumptions, the supplier can decide his product quality and the wholesale price to maximize his profit. The suppliers profit is listed as following:
(4) |
The suppliers first order conditions are as following:
(5) |
(6) |
Because w'(A)<0, ks'(A)>0, from Eq. 5:
(7) |
where, if and only if Eq. 7 is satisfied, the supplier will provide this advance payment contract. From Eq. 6, the supplier will choose a suitable product quality to maximize his profit, so:
The superscript A is used for the parameter under the advance payment contract.
From the retailers aspect, he will choose his sales effort and the advance payment amount to maximize his profit and the retailers profit is as following:
(8) |
The retailers first best conditions are as following:
(9) |
(10) |
where, the retailer will choose his sales effort to maximize his profit, that is:
The condition for that the retailer chooses to pay in advance is Eq. 9 more than zero. So, it can get:
(11) |
Proposition 1: If the opportunity cost margins of the supplier and the retailer satisfies kr(A)<-w'(A) Q(e,s)<ks'(A), both the supplier and the retailer will agree with the advance payment contract.
Proposition 1 shows the financial conditions for the advance payment. Then the influence of advance payment on product quality and the sales effort will be discussed.
Figure 1 shows how the advance payment influences the product quality and the sales effort. Figure 1a shows how the product quality changes with the advance payment. Figure 1b shows how the sales effort changes with the advance payment.
In Fig. 1a, s° is the product quality when the advance payment is zero, which means there is no advance payment. In Fig. 1b, e° is the sales effort when the advance payment is zero, which means there is no advance payment.
Proposition 2: The product quality will be improved under the advance payment contract.
Proof: Under Eq. 5:
where, from Eq. 6, the second order condition of the product quality is as following:
(12) |
Fig. 1(a-b): | Influence of the advance payment (a) Relationship between the product quality and the advance payment, (b) Relationship between the sales effort and the advance payment |
So the draft Fig. 1 for the relationship between the product quality and the advance payment can be shown as Fig. 1a.
From Fig. 1a, it can be clearly gotten as s<sA, so the advance payment contract can improve the product quality.
Proposition 3: The retailers moral hazard can be mitigated by advance payment.
Proof: Under Eq. 9:
where, From Eq. 10, the second order condition of the sales effort is as following:
(13) |
Because and the second:
d order condition, so:
when e<eA and:
when e>eA:
So the draft Fig. 1 for the relationship between the sales effort and the advance payment can be shown as Fig. 1b.
From Fig. 1b, it can be clearly gotten as eA>e0, so the advance payment contract can mitigate the retailers moral hazard.
The product quality and the sales effort cannot reach the first best, so the supply chain cant be coordinated by the advance payment contract.
Proposition 4: Advance payment cannot coordinate this supply chain alone.
COORDINATION CONTRACT
From the previous analysis, the advance payment contract cant coordinate the supply chain. In this section, the effort is made to design a contract to coordinate it. As Hou et al. (2009) mention, the revenue- sharing contract can align the two parties interests and actions by having the retailer share a portion of his revenue with the supplier.
Considering the revenue sharing contract, the supplier charges wr(A) per unit purchased plus the retailer gives the supplier a percentage of the revenue. Let α be the fraction of revenue the supplier earns, so 1-α be the fraction of revenue the retailer keeps. The advance payment A should be dependent on the total transfer amount, it is simplified to be A(Q), where A(0) = 0, A'(Q)>0.
The suppliers profit function is:
(14) |
And the fist order condition is:
(15) |
The retailers profit function is:
(16) |
The first order condition is:
(17) |
By comparing 15 with 3, 17 with 2, the optimal contract parameters are as following:
(18) |
(19) |
Considering Eq. 18, because A'(Q)>0 and ks'>kr', so . Because A(0), so:
(20) |
Considering 19, because w'<0:
so:
(21) |
The supplier should get a non-negative profit, so:
(22) |
Proposition 5: The supply chain can be coordinated, when Eq. 19-22 are satisfied.
This research extends the previous models from two aspects. First, the trading volume between the supplier and the retailer is the demand quality, other than one (Bastos and Pindado, 2007; Giannetti et al., 2011), which consists with the truth. Second, the product quality is considered to be verified after the contract. The supplier can partly control the product quality by putting effort (Kaya, 2011). So the product quality is used by a moral hazard parameter. The model explored can be seen as double sided moral hazard.
Three main results are reached. First, conditions from the financial aspect for advance payment are listed, which is referred to the opportunity cost margins of the supplier and the retailer. Second, the advance payment do mitigate the moral hazard of the retailer and improve the product quality, but cant make them first best. Third, a revenue sharing contract with advance payment is given to coordinate the supply chain.
The product quality not only can be seen as a moral hazard factor (Kaya, 2011), but also can be seen as the asymmetric information (Bastos and Pindado, 2007). There will be different results if the product quality considered as the asymmetric information. Of course, the better results will be reached by considering both. Other limitation in this model, is the demand quantity equals to the order quantity. Although it happens in reality, the contract usually has been designed before ordering.
This research gets the support of the National Natural Science Foundation of China (No. 71071103).