This is a little Haskell program to illustrate the costly state verification problem in financial economics.

A project run by an entrepreneur can yield a revenue of 0, 2, 4, 6 or 8; each with probabilty 1/5. The entrepreneur borrows money from an investor and writes a contract describing the terms of repayment. There is asymmetric information in the form of costly state verification: once the project is completed the actual revenue received is known only to the entreprenuer and not to the investor. If the investor wants to find out the actual revenue, she has to run an audit which costs her 1 unit of output.

The contract between the entrepreneur and investor specifies, for each value of revenue, the payment to be made to the investor and whether an audit is to be run. It is expected that once the project is complete the entrepreneur will announce a revenue. If the contract does not specify an audit for that revenue level then the entrepreneur simply pays the amount specified in that contract for that revenue level. If the contract specifies an audit for that revenue level then the investor pays 1 unit of output to carry out the audit and then the entrepreneur has to make the payment specified for the actual revenue earned (which is revealed by the audit).

Both the entrepreneur and the investor are risk-neutral, i.e. they care only about their expected earnings. For the investor this is the earning net of any audit cost.

Our goal is to specify a contract which is incentive-compatible --- the entrepreneur announces the actual revenue earned --- and efficient --- there is no other contract which can make one of the parties strictly better off without making the other party worse off.

The present program interactively accepts a contract specification and reports whether it is feasible, incentive-compatible and efficient or not. If it is not incentive compatible it reports the conditions under which the entrepreneur lies. If it is not efficient then the program demonstrates another contract which makes the entrepreneur better off without making the investor any worse.

Incomes, p: [(0.0,0.2),(2.0,0.2),(4.0,0.2),(6.0,0.2),(8.0,0.2)].
Audit cost: 1.0

Enter entrepreneur's payment for each state separated by commas
Put a '*' after a payment to denote a verified state.
For eg: 0*,2*,4,4,4
The audit cost is payed by the investor.
Type 'q' to quit

> 0*,3*,4,5,6
Invalid: Claim greater than income

> 0*,0*,4,5,6
Untruthful: 6.0 -> 4.0, 8.0 -> 4.0

The entrepreneur has an incentive to announce a revenue of 4.0 when her true revenue is 6.0 or 8.0.

> 0*,0*,0*,4*,5
Inefficient
Your contract pays Ent=2.20, Inv=1.00
Try: 0.00*,1.50,1.50,1.50,1.50
which pays Ent=2.80, Inv=1.00

A Pareto superior contract is printed out as evidence of inefficiency.

> 0*,2*,3,3,3
Your contract is efficient

I wrote this program to demonstrate the issues in Section 9.9 of Romer's Advanced Macroeconomics. Warning: the characterization of contracts in the discrete case demonstrated by the program is slightly different from the continuous case discussed in Romer.