Optimal Rent Extraction in Pre-Industrial England and France – Default Risk and Monitoring Costs

Bi(Ri) = α_iR_iπ* where Riπ* is the expected value of the office.

The decisions in the model are taken in the following order: first,
the CA selects the system of rent extraction through the fee θ, followed
by potential agents bidding for the office. Then, the theft and moni-
toring decisions are made. After that, the agent chooses the quantity,
q, and finally, the potential penalties are enforced. The game is solved
by backward induction starting at stage four when the agent sells the
permits.

III.A. Stage Four: the Market for Permits

The agent’s problem is to maximize his profit with respect to the number
of permits provided

maxπ =(a - bq)q - θq.                   (2)

^q

The fee per permit, θ, which the agent has to pay to the CA is determined

by the CA. The equilibrium number of permits is equal to

q*(θ) = ^a-^θ                        (3)

2b

and the equilibrium price is given by

p∙(θ) =   + θ.                              (4)

2

Thus, the profit for the agent is equal to

∏NT (θ) =    4   ''                           (5)

where the superscript NT denotes a no theft case. In the case of theft,
the agent issues permits without compensating the CA. Hence, the agent
receives the profit

T  ^a2

^П = 4b
where the superscript T denotes theft.

15

<<   13   14   15   16   17   18   19   >>

More intriguing information