21.9 Distribution Channels
McGuire and Staelin (1983)
Assumptions:
- Two manufacturing (wholesaling) firms differentiated and competing products: Upstream firms (manufacturers) and downstream channel members (retailers)
3 types of structure:
- Both manufacturers with privately owned retailers (4 players: 2 manufacturers, 2 retailers)
- Both vertically integrated (2 manufacturers)
- Mix: one manufacturer with a private retailer, and one manufacturer with vertically integrated company store (3 players)
Each retail outlet has a downward sloping demand curve:
\[ q_i = f_i(p_1,p_2) \]
Under decentralized system (4 players), the Nash equilibrium demand curve is a function of wholesale prices:
\[ q_i^* = g_i (w_1, w_2) \]
More rules:
- Assume 2 retailers respond, but not the competing manufacturer
And unobserved wholesale prices and market is not restrictive, and Nash equilibrium whole prices is still possible.
Under mixed structure, the two retailers compete, and non-integrated firm account for all responses in the market
Under integrated structure, this is a two-person game, where each chooses the retail price
Decision variables are prices (not quantities)
Under what conditions a manufacturer want to have intermediaries
Retail demand functions are assumed to be linear in prices
Demand functions are
\[ q_1' = \mu S [ 1 - \frac{\beta}{1 - \theta} p_1' + \frac{\beta \theta}{1- \theta}p_2'] \]
\[ q_2' = (1- \mu) S [ 1+ \frac{\beta \theta}{1- \theta} p_1' - \frac{\beta}{1- \theta} p_2'] \]
where
\(0 \le \mu , \theta \le 1; \beta, S >0\)
S is a scale factor, which equals industry demand (\(q' \equiv q_1' + q_2'\)) when prices are 0.
\(\mu\) = absolute difference in demand
\(\theta\) = substutability of products (reflected by the cross elasticities), or the ratio of the rate of change of quantity with respect to the competitor’s price to the rate of change of quantity with respect to own price.
\(\theta = 0\) means independent demands (firms are monopolists)
\(\theta \to 1\) means maximally substitutable
3 more conditions:
\[ P = \{ p_1', p_2' | p_i' -m' - s' \ge 0, i = 1,2; (1-\theta) - \beta p_1' \beta \theta p_2' \ge 0, (1- \theta) + \beta \theta p_1' - \beta p_2' \ge 0 \} \]
where \(m', s'\) are fixed manufacturing and selling costs per unit
To have a set of \(P\), then
\[ \beta \le \frac{1}{m' + s'} \]
and to have industry demand no increase with increases in either price then
\[ \frac{\theta}{1 + \theta} \le \mu \le \frac{1}{1 + \theta} \]
After rescaling, the industry demand is
\[ q = 2 (1- \theta) (p_1+ p_2) \]
Results:
When each manufacturer is a monopolist (\(\theta = 0\)), it’s twice as profitable for each to sell through its own channel
When demand is maximally affected by the actions of the competing retailers (\(\theta \to 1\)), it’s 3 times as profitable to have private dealers.
The breakeven point happens at \(\theta = .708\)
In conclusion, the optimal distribution system depends of the degree of substitubability at the retail level.
Jeuland and Shugan (2008)
Quantity discounts is offered because
Cost-based economies of scale
Demand based - large purchases tend to be more price sensitive
Strategic reason- single sourcing
Channel Coordination (this is where this paper contributes to the literature
K. S. Moorthy (1987)
- Price discrimination - second degree
Geylani, Dukes, and Srinivasan (2007)
Jerath and Zhang (2010)