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September 04, 2004

Bilateral Monopoly Average Prices

Suppose we have 1000 buyers and 1000 sellers of a good. Let us compare the
following four situations:

1. Competition (price taking by both sides)

2. Monopoly-- the sellers cartelize, but buyers are price takers.

3. Monopsony-- the buyers cartelize, but sellers are price takers.

4. Bilateral monopoly-- both buyers and sellers cartelize, and then they
bargain, setting a quantity Q* and either a lump sum price T* or a per unit
price P*=T*/Q*....


Certain results are clear, if not well known.

(A) Welfare is highest under price taking and bilateral monopoly, both of which
are efficient.

(B) Sellers are best off under Monopoly or Bilateral Monopoly, depending on
their bargaining power.

(C) Sellers are worst off under Monopsony or Bilateral Monopoly, depending on
their bargaining power. (If their bargaining power is very low, they will get
practically no surplus under Bilateral Monopoly.)

Other questions need formal analysis.

(D) If bargaining splits surplus 50-50, under what conditions does the seller
prefer Bilateral Monopoly to Monopoly?

(E) How does the bilateral monopoly negotiated price P* compare with the
competitive, monopsony, and monopoly prices? In particular, can it be higher
than the monopoly price?

This is related to my ideas on perfect price discrimination, because if perfect
price discrimination results in bilateral monopoly, we have almost this
situation. Indeed, it is practically the same question! What is new is the
question about the average price, which is not the same as the welfare question,
since Q is negotiated too. And, here I implicitly allow redistribution among
the 1000 people on each side of the market.

Posted by erasmuse at September 4, 2004 10:38 AM

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