Two-Step Distribution: Why the Middleman? Manufacturer sells to retailer at price p. –Retailer then sells to consumer at price P r. 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 P m. –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

Case I: Manufacturer Sells thru Middleman Retailer’s total revenue = TR r = P r 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 =TR m =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 P r = a – bx = ¾ a + ¼ mc Profit retailer = (P r – p) x = 1 / 16 (a – mc) 2 /b Profit mfr = (p – mc) x = 1 / 8 (a – mc) 2 /b Profit total = 3 / 16 (a – mc) 2 /b

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

Middleman or Sell Direct??? When manufacturer sells thru middleman Profit mfr = 1 / 8 (a – mc) 2 /b When manufacturer sells direct Profit mfr = 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 dP m /dmc = ½ vs dP r /dmc = ¼

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 Profits total = (P – mc)x = [(a – mc) – bx]x MProfits total = (a – mc) – 2bx (= 0 for maximum) x = ½ (a – mc)/b P = a – bx = ½ (a + mc) Profits total = (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

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 “Profits retailer ” = (P – p) x = ¼ (a – mc) 2 /b= F max –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 Profit mfr = 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