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 xwhere x = quantity bought at price P

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

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

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

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

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