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Published byGwendolyn Collins Modified over 9 years ago
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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
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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
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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
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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
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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
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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
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