Understanding Two-Step Distribution: Middleman's Role and Profit Optimization

1. Two-Step Distribution: Why the Middleman? • Manufacturer sells to retailer at price p. • Retailer then sells to consumer at price Pr. • Manufacturer’s marginal cost is constant = mc • Retailer’s marginal cost is simply p (he has no additional marginal cost of retailing) or • Mfr sells direct to consumer at price Pm . • In addition to marginal cost of production, mc, mfr has marginal cost of retailing = k. • Consumer demand given by P = a – b x where x = quantity bought at price P

2. Case I: Manufacturer Sells thru Middleman • Retailer’s total revenue = TRr = Pr x = (a-bx)x • Manufacturer figures retailer equates his marginal revenue (MR =a–2 bx) to his marginal cost (MC = p) p = a – 2 b x • Manufacturer’s total revenue =TRm=px=(a-2bx)x • Mfr equates his marginal revenue (MR = a - 4bx) to his marginal cost (mc). • Then a – 4 bx = mc ; x = (a – mc)/4b and • p = a – 2bx = ½ a + ½ mc • Pr = a – bx = ¾ a + ¼ mc • Profitretailer = (Pr– p) x = 1/16 (a – mc)2 /b • Profitmfr = (p – mc) x = 1/8 (a – mc)2 /b • Profittotal = 3/16 (a – mc)2 /b

3. Case II: Manufacturer Sells Direct to Consumer • Manufacturer’s total revenue = TR = Pm x = (a-bx)x • Manufacturer equates marginal revenue (= a – 2bx) to marginal cost (= mc + k). Then x = ½ (a – mc – k)/b Pm = a – b x = ½ (a + mc + k) Profitmfr = (Pm – mc – k) x = ¼ (a – mc – k)2/b

4. Middleman or Sell Direct??? • When manufacturer sells thru middleman • Profitmfr = 1/8 (a – mc)2 /b • When manufacturer sells direct • Profitmfr = ¼ (a – mc – k)2/b • Manufacturer will sell thru middleman when k > [1 – 1/sqrt(2)] (a – mc) = .29 (a – mc) • As manufacturing productivity increases, mc falls and retailing is increasingly turned over to middlemen  growth of retail sector relative to mfg sector • More of mfg cost reduction is passed on to consumers when manufacturer sells direct dPm/dmc = ½ vs dPr/dmc = ¼

5. Franchise the Middleman? • Even when k<.29(a-mc), the manufacturer may prefer to sell thru a middleman • Can he charge a fixed franchise fee, F, that transfers the middleman’s profits to himself? • If he can, then (just about) all profits are his • Profitstotal = (P – mc)x = [(a – mc) – bx]x • MProfitstotal = (a – mc) – 2bx (= 0 for maximum) • x = ½ (a – mc)/b • P = a – bx = ½ (a + mc) • Profitstotal = (P – mc) x = ¼ (a – mc)2/b • From before, retailer will want to sell • x = ½ (a – p)/b • To get retailer to sell profit maximizing x = ½ (a-mc)/b, manufacturer must set wholesale price, p, to his own marginal cost of production, mc

6. Negotiate a Franchise Fee • The maximum franchise fee the manufacturer can charge equals the retailer’s profits when P = ½ (a+mc), p = mc, and x = ½ (a – mc)/b • “Profitsretailer” = (P – p) x = ¼ (a – mc)2/b= Fmax • In this case, all of the manufacture’s earnings come from the franchise fee. • The retailer may know that the best the manufacturer can do without him is Profitmfr = ¼ (a – mc – k)2/b • There’s room for negotiation! • In fact, if k > .29 (a – mc), the manufacturer needs the retailer • The retailer may be able to negotiate a fee to carry the manufacturer’s line • However, if p is set to mc to maximize total profits, the manufacturer still depends on F for his profits