Transcript Two-Step Distribution: Why the Middleman?

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
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Mfr sells direct to consumer at price Pm .
– In addition to marginal cost of production,
mc, mfr has marginal cost of retailing = k.
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Consumer demand given by
P=a–bx
where x = quantity bought at price P
Case I: Manufacturer Sells thru Middleman
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Retailer’s total revenue = TRr = Pr x = (a-bx)x
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Manufacturer figures retailer equates his marginal
revenue (MR =a–2 bx) to his marginal cost (MC = p)
p=a–2bx
 Manufacturer’s total revenue =TRm=px=(a-2bx)x
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Mfr equates his marginal revenue (MR = a - 4bx) to his
marginal cost (mc).
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Then a – 4 bx = mc ; x = (a – mc)/4b and
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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
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
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Middleman or Sell Direct???
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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
Franchise the Middleman?
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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
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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
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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