Ex ante controls 36

5.3. Integrating ex ante and ex post controls We now briefly consider (without explicitly solving) the case in which the

MoF can deter cheating through a combination of ex ante controls and ex post audits. Limiting ourselves to incentive-compatible schemes, the MoF’s problem is to maximise the expected output:

e H , et Max L , H , t L ,, γ c EX () = q ⎡ ⎣ αθ ( H , e H ) − t H ⎤ ⎦ +− ( 1 q )( ⎡ ⎣ αθ L , e L ) − t L − γ z ⎤ ⎦ − c

Subject to IR(L), IR(H) and:

IC(H) Under a combined approach, the most interesting case occurs when the

t H − ψ ⁽⁾ e H ≥ t L − ψ e % − η c − γσ ⁽⁾ P L ⁽⁾

MoF simultaneously uses both types of controls. This may only take place

when λ = 1/η c (c) = [(1 – q)z + λγ]/σP ≤ q. This may be interpreted as linking the

cost-effectiveness of each type of control and comparing their costs (resp. c and [(1 – q)z + λγ]) to their effectiveness in deterring cheating (which depends on η and σP). When the MoF uses both audits and controls in combination, it will thus equate the relative contribution of each type of control. Finally, the optimal level of ex ante controls and probability of ex post audits, as well as the production distortion when i = L and the possible rent when i = H, will be determined simultaneously, so as to satisfy the constraint IC(H) at the lowest cost.