37.4 Decentralized Channels
37.4.1 (Jiang and Tian 2022) Reactive capacity on product quality and profitability in uncertain markets
Under “pull” contracts, the retailer designs the product quality and makes the wholesales and retail pricing decisions, but the risk of excess production is assumed by the upstream suppliers or contract manufacturers, rather than brand-owning retailers or OEMs.
How much improvement in reactive capacity will benefit the supplier and how much it will benefit the retailer?
Model
Production Setup
A supply chain where before the selling season, a brand-owning retailer designs a production quality \(q\) and offers a wholesale price \(w\) to outsource its production to ta supplier.
At the beginning of the selling seasons, the retailer will decide how many units \(Q\) of the product to order from the supplier and choose its retail price \(p\)
Supplier’s marginal cost = \(k q^2\)
Market uncertainty setup
Then consumer utility from product with quality \(q\) at price \(p\) is \(u = q \theta - p\)
where \(\theta\) is the consumer’s WTP
Assume that the market uncertainty is about the distribution of the consumer’s rather than about the total number of consumers in the market. Then a fraction of \(\alpha \in (0,1)\) of consumers have \(\theta = \theta_H\)
Time setup
Supplier’s production lead time \(T\) = total production time + shipping and handling
\(T = T_S + \frac{N}{c}\) quantity independent time + quantity dependent time
Denote A as the acceptable delivery time. The supplier will have to manufacture the product before the selling season if \(T_s > A\) and could produce some units during the selling season other wise
The market outcome \(T_S > A\) is equal to \(T_S = A\)
Model
The supplier’s reactive capacity is measured by \(\bar{Q}\), which is the maximum quantity (number of units) of the product that the supplier can produce and deliver to the retailer within the selling season
\(T = T_S + \frac{Q}{c} \le A\) Hence, \(\bar{Q} = (A - T_s)c\)
The supplier’s reactive capacity, \(\bar{Q}\) is driven by both the amount of production capacity \(c\) and how reactive and flexible that capacity is (\(T_s\))
Whether is it the retailer or the supplier that bears the inventory risk?
Timeline
Before selling seasons
Retailer decides product quality and wholesale price
Supplier: pre-season inventory I
Within the selling seasons
\(\alpha\) is known to the retailers
Retailer: product quantity \(Q\)
Supplier:
\(Q \le I\) revenue \(w Q\)
\(Q>I\) decide \(I' \le \bar{Q}\) to produce within A
Retailer: selling price
Consumer: purchase decisions
Analysis
Without market uncertainty (\(\alpha = \alpha_g = \alpha_b\))
With market uncertainty
Extreme cases
- When \(\alpha_b \ge \frac{\theta_L}{\theta_H}\) even the bad market has many high-valuation consumers, the retailer will find it optimal to charge a high price to target only high-valuation consumer regardless of the market state
In-between cases
Low reactive capacity
Medium reactive capacity
Opportunistic targeting with stock-out: the retailer sets the wholesale price low at the supplier’s marginal cost and the supplier will produce the risk-free inventory of \(I = ag\)
Opportunistic targeting with overstock: the retailer chooses a high wholesale price to induce the supplier to optimally produce a higher pre-season inventory of \(I = 1 - \bar{Q}\)
High reactive capacity: the supplier has enough time to produce during the selling season within the acceptable delivery time. Anticipating the supplier’s high ability to fulfill its order, the retailers will target only high valuation costumers at a high retail price
37.4.2 (Hu, Zheng, and Pan 2022) Wholesale vs. Agency
Literature
Distribution channels
Previously examine wholesale contract and downstream consequences (double marginalization problem)
This paper examines channel efficiency of agency contract.
Strategic contract choices: wholesale vs. agency
Retail pass-through
Model setup
\(n \ge 2\) competing suppliers selling substitutable products to consumers through a dominant online retailer \(r\)
Each supplier has a unique product
Assume same marginal cost across supplier, e-tailer has marginal cost for each unit of products demanded by costumers
Demand structure
Consider the demand of product is given by continuous \(q_i(p)\)
where \(p\) = market prices
Common assumptions:
- Demand is downward sloping
- Demand function is symmetric
Let \(\gamma >0\) be the product substitutability for specific demand function
\(\lambda(p) = - \frac{q(p)}{q'(p)}\) be a measure of sensitivity of demand
Additional assumptions on \(\lambda(p)\)
- profit functions are quasi-concave
- elasticity of demand decreases with \(p\) increases
Game Structure
Wholesale
- Supplier announces wholesale price \(w_i\)
- E-tailer sets selling price \(p_i\) for each product
Agency
- E-tailer sets revenue share rate \(1 - \alpha\)
- Suppliers can choose to accept and sell directly to costumers on e-tailer platform, setting retail prices \(p_i\)