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

which were common in Europe at the time.²³

Citizens have a linear inverse demand for the permits. The demand
curve is given by

p(q)=a - bq

where a and b are constants, q is the number of permits allocated by the
agent and p is the price of the permits (or equivalently the tax rate). A
central authority (CA) uses the agent to extract rents from consumers.
He sells offices in an auction for up-front payments, and may demand
a fee, θ, per each permit sold by the agent, which is paid ex post. The
agent can, as in Shleifer and Vishny [1993], issue permits without paying
the CA but may then get caught by the CA, who monitors at the cost
c and penalizes him.²⁴ The penalty is assumed to be constrained by
limited liability on the part of the agent and amounts to t = t.

There are two time periods and the CA maximizes his disposable
income. What the CA cannot extract ex ante it will borrow. However,
the CA cannot borrow more than the net present value of its ex-post
incomes. The CA-specificinterestrateisgivenbyδ.Theoffices are
sold through a first price sealed bid auction. Agents must also borrow
in order to buy the the position. The interest rate to which a potential
agent i can borrow is given by r_i and is privately known. It is assumed
that Ri = iɪ- is uniformly distributed on [0,1].²5 The strategy space
for the n bidders is Rie[0,1] and they are assumed to use linear strategies

²³See e.g. Lipson [1948], Binney [1958], Hill [1970] and Brewer [1988].

²⁴In theory, the CA knows if theft has occurred and would not need to monitor.
However, monitoring may be needed to verify theft. Moreover, it may well be that
the official steals and then promptly leaves the position. To prevent this, the CA
needs to monitor the official.

²⁵For simplicity we normalize the market-interest rate to zero and let the interest
rate be a function of each agent’s default risk solely.

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