Asymmetric Information 1:pre-contract

Example1:Selling One Unit
Asymmetric information for seller
c = seller’s cost (publicly known)
v = buyer’s value (privately known)
p = offer price
F(p) = the probability that v is lower than p
seller guesses buyer’s value as distribution(here, we assume it is uniform on interval 〔0,vbar〕
seller’s optimal strategy is to make the offer p which maximizes benefit of seller

(p-c)(1-F(p))=(net profit)(probability that v is higher than p)=(p-c)(1-p/vbar)

And p=(c+vbar)/2 maximizes it. But it is inefficiently high.

This mechanism is:
It is difficult for seller to optimize their benefit. And if seller cannot perfectly commit, it is also difficult to optimize. But If buyer makes offer, it is easy to optimize.

If seller has multiple units, he can make more money through quantity discounts. If so, the price for a low number of units will be inefficiently high.

Example2: Red Tape and Corruption

Player: entrepreneurs(E) and bureaucrat(B)
Rule:
B sells licenses to E, and it values 10 for E
E’s wealth is privately knowledge w=10(probability q), w=5(probability 1-q)
B’s price is 5 (if q<0.5), and 10 (if q>0.5)
B have red tape which impose additional cost t to E, but no cost for B.
With red tape t=5, B can charge a price of 5, and charge a bribe of 5-e.
E’s expecting wealth is
Without red tape
If q<0.5
:10-5=5
If q>0.5
:10+10q+5(1-q)-10=5q+5
Outcome
Payoff

Result: red tape is profitable.


Case: Oil Field Organization
If there are common pool problem, it predicts
(i) Excessive drilling
(ii) More concentrated ownership leads to smaller inefficiencies

And it was almost proved in different number of owner and different jurisdictions.