Optimal Pricing of Green Agriculture Products in a Marketing-Mix Program

Preselling refers to the sales strategy that the sellers begin to accept orders before the products officially hit the market. The consumers are often required to pay a part or all the price in advance [4]. In the early days, preselling was mostly adopted in industries with limited supply of products/services, namely, ticketing, clothing, and reservation services [6].

Preselling is increasingly popular among sellers, owing to the uncertainty of market demand. Through preselling, the seller can learn the product demand timely, and adjust the production plan and selling price as per the number of orders.

Weng and Parlar [7] were the first to study the correlation between preselling and production decision. They analyzed the connotations of preselling and its impact on production decision. Considering the stochasticity of preselling demand, Tang et al. [8] discussed how the update of presale information affects the seller interests. Through modeling and empirical analysis, Moe and Peter [9] measured the impact of the presale of new product on the prediction of market demand. Bernstein and DeCroix [10] investigated how the acquisition of different kinds of demand information in advance affect corporate profit and the benefit brought by flexible allocation of resources. Under uncertain supply and demand, Cho and Tang [11] verified the impact of three sales strategies on manufacturer profit: preselling, regular selling, and dynamic selling, and optimize the conditions for each strategy. Based on the demand in the preselling period, Papier [12] improved the resource allocation in enterprises with limited production capacity, evaluated the value of preselling information, and proposed the optimal way to utilize such information. Karle and Möller [13] suggested that information disclosure helps to reduce the mismatch between consumer preferences and product features, enabling the seller to offer greater discount and boost the sales in preselling period.

The impact of preselling model on seller pricing has long been a research hotspot. Xie and Shugan [14] proposed a normative model, which optimizes the price decision by issuing early announcements to clarify the pre-order conditions. Desiraju and Shugan [15], Shugan and Xie [16] also explored the price decision under the preselling model. Moe and Peter [9] measured the impact of the preselling of new product on the prediction of market demand, with the aid of models and empirical data.  Kuthambalayan et al. [17] evaluated the effect of preselling discount on seller profit in a production environment, featured by short cycle, multiple product categories, changing demand, and limited production capacity. Under the constraint of production capacity, Huang et al. [18] constructed a two-stage pricing model for preselling, and deduced the optimal price decisions in the preselling period and the regular selling period.

In addition, Alexandrov and Bedre-Defolie [19] likened the preselling model to the bundling model, and formulated the optimal price decision. Drawing on the laws of the futures market, Noparumpa et al. [20] analyzed the pricing strategies of winemakers, especially under uncertain quality. Xiao et al. [21] investigated the equilibrium pricing strategies and price commitment scheme of the seller under dynamic price, in the light of uncertain product quality and consumer fitness in the preselling period. Under the framework of rational expectation, Peng et al. [22] studied price guarantee policies through preorder-dependent social learning. Wei and Zhang [5] introduced the preorder contingent production (PCP) strategy to curb the negative influence of strategic consumer behavior in preselling market. Niu and Yang [23] discussed the impact of preselling strategies on a three-echelon supply chain, when the upstream enterprises launch a new product for strategic consumers under social influence.

Inspired by the previous studies, this paper characterizes the consumer decisions in the preselling and spot selling periods, and optimize the price decisions of the seller, in consideration of the difference in consumer behaviors and the driving effect of high-quality green agricultural products.

4.1 Consumer behavior and demand realization

According to the classic theory on consumer choice, a consumer will make purchase at price p only if his/her net utility, v-p, is nonnegative [1]. Hence, the purchase probability is Prob(v>p₁) in the preselling period, and Prob(σv>p₂) in the spot selling period. The demand q₂ in the spot selling period can be derived from the preorders q₁ in the preselling period:

$q_{2}=\left(p_{1}-\frac{p_{2}}{\sigma}\right)^{+} \cdot \frac{q_{1}}{1-p_{1}}$     (1)

4.2 Optimal dynamic price decisions

This subsection optimizes the seller’s dynamic price decisions through standard backward induction. Firstly, the optimal spot price was obtained first for the spot selling period. The seller profit in the spot selling period can be maximized by solving:

$\pi_{2}\left(p_{1}, p_{2}\right)$$=\max _{p_{1}>p_{2} / \sigma}\left(p_{2}+k\right) \cdot q_{2}$$=\max _{p_{1}>p_{2} / \sigma}\left(p_{2}+k\right) \cdot\left(p_{1}-\frac{p_{2}}{\sigma}\right) \cdot \frac{q_{1}}{1-p_{1}}$     (2)

Whereas $\frac{\partial^{2} \pi_{2}}{\partial p_{2}^{2}}=\frac{-2 \cdot q_{1}}{1-p_{1}}<0$ and $\frac{\partial \pi_{2}}{\partial p_{2}}=\frac{q_{1}}{1-p_{1}} \cdot\left(p_{1}-2 \frac{p_{2}}{\sigma}-\frac{k}{\sigma}\right)$, the seller’s optimal price decision and corresponding profit can be obtained as in Lemma 1.

LEMMA 1. In the spot selling period, the seller will set his/her price at $p_{2}=\frac{\sigma p_{1}-k}{2},$ produce $q_{2}=\left(\frac{p_{1}+k / \sigma}{2}\right) \cdot \frac{q_{1}}{1-p_{1}}$ units of product, and obtain the maximum spot selling profit $\pi_{2}=\frac{\sigma\left(p_{1}+k / \sigma\right)^{2} q_{1}}{4\left(1-p_{1}\right)}$.

The next step is to analyze the seller decision on preselling price. From Lemma 1, the seller’s total profit π from the two periods can be expressed as:

$\pi=\max \left\{\pi_{1}+\pi_{2}\right\}=\max \left\{p_{1} q_{1}+\pi_{2}\right\}$     (3)

Drawing on the classic demand curve theory, the demand in the preselling period was described as q₁=a-bp₁, where a is the market size, and b is the price sensitivity of consumers. Then, the optimal price decision-making problem of the seller was transformed into the maximization of seller profit by optimizing p₁:

$\pi\left(p_{1}\right)=\max \left\{p_{1}\left(a-b p_{1}\right)+\frac{\sigma\left(p_{1}+k / \sigma\right)^{2}}{4\left(1-p_{1}\right)} \cdot\left(a-b p_{1}\right)\right\}$     (4)

The first and second derivatives of profit with respect to price can be respectively obtained as:

$\frac{\partial \pi}{\partial p_{1}}=a-2 b p_{1}+\frac{\sigma}{4} \cdot\left[\frac{2\left(a-b p_{1}\right)\left(p_{1}+k / \sigma\right)}{\left(1-p_{1}\right)}+\frac{\left(p_{1}+k / \sigma\right)^{2}(a-b)}{\left(1-p_{1}\right)^{2}}\right]$     (5)

$\frac{\partial^{2} \pi}{\partial p_{1}^{2}}=-2 b+\frac{\sigma}{2\left(1-p_{1}\right)^{2}} \cdot\left[\left(1-p_{1}\right)\left(a-2 b p_{1}-b k / \sigma\right)\right.$$\left.+\left(a-b p_{1}\right)\left(p_{1}+k / \sigma\right)+\frac{(a-b)\left(p_{1}+k / \sigma\right)(1+k / \sigma)}{1-p_{1}}\right]$     (6)

To satisfy the above assumption, the market size was set to a=1. For simplicity, the value of b was set to 1 to derive an analytical solution. Then, it can be obtained that $\frac{\partial^{2} \pi}{\partial p_{1}^{2}}=-\frac{3}{2}<0$, i.e. there exists an optimal preselling price that maximizes the profit under $\frac{\partial \pi}{\partial p_{1}}=0$. Then, the optimal price and profit of the seller can be summed up as the following proposition.

Proposition 1. If σ>2k/(k+1), the preselling price and spot selling price can be respectively expressed as:

$p_{1}^{*}=\frac{k+2}{4-\sigma}$     (7)

$p_{2}^{*}=\frac{\sigma k+\sigma-2 k}{4-\sigma}$     (8)

In the two periods, the market demand can be respectively expected as:

$q_{1}^{*}=\frac{2-k-\sigma}{4-\sigma}$     (9)

$q_{2}^{*}=\frac{1+2 k / \sigma}{4-\sigma}$     (10)

Under the above circumstances, the optimal seller’s total profit can be expected as:

$\pi^{*}=\frac{1+k^{2} / \sigma+k}{4-\sigma}$     (11)

In Proposition 1, the critical condition σ>2k/(k+1) indicates that the spot selling consumers have a high valuation of the products. This is consistent with our assumption that the high-quality green agriculture products have a driving effect.

Corollary 1. (1) ∂p₁^*/∂k>0, ∂p₂^*/∂k<0; (2) ∂p₁^*/∂σ>0, ∂p₂^*/∂σ>0.

Corollary 1 shows that the seller can raise his/her preselling price and lower the spot selling price, if the product has a prominent driving effect.

Different consumers have different demands for the specific properties of the products. To improve net profit per unit of product, the seller tends to focus on the few high valuation consumers by raising the preselling price, and then attract the remaining consumers by offering a low spot selling price.

In addition, the seller can raise both prices, if the product is perceived by consumers as worthy of waiting for in the supermarket. Such a product is the said high-quality green agricultural product with a high value of σ, which can attract more consumers to the supermarket.

In this way, the seller can capture the high-end consumers with a high preselling price, and the ordinary ones with a low spot selling price. Needless to say, the spot price increases with the product value $\sigma$ perceived by consumers.

Corollary 2. ∂π^*/∂k>0, ∂π^*/∂σ>0.

Corollary 2 shows that the seller’s total profit increases with the driving effect factor k, as well as the valuation discount factor σ. As required by China’s national policy, enterprises ought to promote the HQD of agriculture. The primary requirement of HQD is to continuously improve the quality of products/services. Without high-quality products, it is impossible to enhance brand influence, not to mention cultivating the driving effect of products.

This paper mainly solves the optimal price decision-making problem of the seller for both preselling and spot selling. Special considerations were given to the different value perceptions of consumers in the two sales channels, as well as the driving effect of high-quality green agricultural products. The results show that the seller could raise the preselling price and lower the spot selling price, if the product has a prominent driving effect; the seller could raise both preselling and spot selling prices, if the product is perceived by consumers as worthy of waiting for in the supermarket; such a marketing-mix program is suitable for products popular among most consumers. These findings help enhance the awareness of HQD among enterprises of green agricultural products, enabling them to make more profit with the proposed marketing-mix program. The future research will explore the optimal price decision-making problem with statistic demand and production of green agriculture products.