Suppose that there is one manufacturer and one retailer. Final inverse demand is

Question

Suppose that there is one manufacturer and one retailer. Final inverse demand is P(q) = 100-2q. Marginal cost of the manufactuer is 10 and the retailer has a marginal retailing cost of 5 in addition to the wholesale price charged by the manufacturer.

1. Suppose that the manufacturer can offer a two-part tariff (i.e., a fixed fee and a per-unit price).The retailer will accept any tariff which gives him non-negative prots. Find the tariff set by the manufacturer.

2. Suppose that the manufacturer cannot control the price set by the retailer or offer a two-part tariff, but that it would be possible (if the manufacturer wants) to supply another identical retailer who would compete Bertrand with the rst retailer. However, suppose that there is now a xed cost F of supplying each retailer which must be paid by the manufacturer. Find the lowest value of F
for which the manufacturer would rather just supply one retailer, rather than creating competition by supply both.

Explanation / Answer

1) Let tarrif charged be $ t.

then profit of retailer = 10 + 5 - ( 10 + t *(100 - 2q) ) >= 0

so t =< $ 5 / (100 -2q)

2) 10*(100 - 2q) - F >= 0

Hence F =< 10*(100 - 2q)

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