After characterizing the optimal contracts for the different forms of commitment the question is which contract the firm offers. A firm chooses the contract which
maximizes its expected (residual) profit, given the distribution of good and bad matches and the type-specific distributions of firm profits.
First, compare the full commitment contract and the contract with commitment only to variable compensation. The firm sets different incentives under these forms of commitment, also the base salaries differ. When the base salary is not enforce-able the firm promises a higher base salary for given varienforce-able compensation and effort compared to when it is enforceable. This is necessary to compensate for the possibility that the CEO gets fired.
The first effect of choosing a contract without a fixed base salary is an increase in the expected costs paid to the CEO compared to a contract with an enforceable base salary. For given effort and variable compensation a non-enforceable base salary is larger than the base salary of a contract with a fixed base salary. This is necessary to satisfy the individual rationality constraint of the bad match CEO (3.15). The probability that the bad-match CEO remains at the firm drives the difference between the base salaries under the different forms of commitment. A good match CEO stays at the firm with a higher probability than a bad match CEO. This means that the (expected) base salary for the good-match CEO is larger in a contract without a fixed base salary than in a contract with a fixed base salary.
This higher expected pay for the good match leads to lower expected firm profits for the contracts with an unenforceable base salary.
The second effect is that, for a given participation rate b the contract with commitment only to variable compensation induces higher effort than the full com-mitment contract, since δ(1−Fδe i)
i >0. This potentially increases the firm payoff from the contract with commitment only to the base salary compared to the full com-mitment contract. If the the optimal effort levels of the two match types are close enough under the contract with commitment only to the variable compensation, the firm can design a contract with the expected utility of the good match closer to the reservation utility than under the full commitment contract. This decreases the rent of the CEO and increases the firm profit.
If the contract with commitment only to the variable compensation had no im-pact on the optimal effort level18, δ(1−Fδe i)
i = 0, the firm would always prefer the full commitment contract to the contract with a discretionary base salary. When the possibility of firing the CEO has an effect on optimal effort, the optimal choice of
18This is equivalent to saying that the firing probability is exogenous for the CEO.
the firm depends on whether the first or the second effect dominates.
Now turn to the comparison of the discretionary bonus and the full commitment contract for the first period. Comparing these two contracts is not straightforward, because the marginal productivity of the two match types differs between discre-tionary variable compensation and full commitment. Whereas the base salaries have the same structure, the participation rates of the two contracts differ.
As for the contract with commitment only to variable compensation, the con-tract with commitment only to the base salary induces a higher effort for a given participation rate,b. This means that the firm can potentially induce higher effort levels with the discretionary bonus contract.
An increase in the optimal effort of the two types does, however, not necessarily imply that the firm also receives a higher payoff. The rent the firm pays to the CEO increases in the difference between the effort of the good and the bad match. This implies that, if the contract with discretionary bonus induces higher effort levels than the full commitment contract, but the difference in effort is very large, the firm prefers the full commitment contract.
The effort of the CEO has a second effect on the rent of the good CEO. Effort determines the truncated productivity distributions, µFi , under the contract with discretionary variable compensation. The rent of the good CEO increases when the difference in the µFi s increases. When the difference in the truncated firm distribu-tions under the discretionary bonus contract is very large, the firm prefers the full commitment contract.
This means that the firm prefers the discretionary bonus contract, if under the discretionary bonus contract the optimal effort levels and the means of the truncated productivity distribution,µFi , are more similar than the respective variables under the full commitment contract. At the extreme the discretionary bonus contract induces optimal efforts andµFi s that are identical, which allows the firm to eliminate the rent of the good CEO completely.
A final question concerning the choice of commitment is whether the firm could implement a written contract that has the same characteristics as the partial com-mitment contract. The firm can replicate the partial comcom-mitment contract in this simple setting. Granting the CEO stock options with some strike price,xF, instead of the linear participation of the full commitment contract is identical to the partial commitment contract; stock options and partial commitment are perfect substitutes
in this model. However, even if the firm can write a contract without additional costs, there is still no benefit for both sides in fixing the payoff in the contract. If the match quality additionally depends on other factors that are not contractible such as a strategy change or a new technology it is impossible to replicate the partial commitment contract.