With few exceptions, Catholic priests are to live (unmarried) celibate lives, however Pope Francis is interested in changing this policy. See this article here. Although this celibacy restriction has been enforced for over a thousand years, he considers it not a part of official church doctrine.
We can consider this policy from an economics perspective, i.e., we can consider how the policy affects the decisions made by clergy and non-clergy. Indeed, there are many dimensions to this policy that influence the effectiveness of clergy and the operations of the Catholic Church. Here are a few.
1. Opportunity cost of time. Being a good spouse and parent requires time and energy, thus increasing the opportunity cost of other activities. A priest without such family obligations thus has a lower opportunity cost of devoting more time and attention to religious responsibilities. The celibacy restriction thus enables the priest to carry out more and a larger number of clergy responsibilities in the service of church members.
Conclusion: good for the church.
2. Screening into the priesthood. Because having a family is highly desirable for many people, the celibacy restriction imposes a high cost for priests, thus acting as a screening mechanism into the priesthood. Only those who are exceptionally committed a life of priestly service are likely to be willing to voluntarily accept the restriction. The restriction should thus lead to relatively more committed clergy than otherwise as less committed persons would not enter the priesthood. Presumably, having highly committed clergy is good for the church.
However, there are many men who might be quite effective priests as well as effective husbands and fathers. These men will not be allowed to be priests, and their services will be missed. While the commitment of the those that enter the priesthood will be high, there are some with high commitment who also tremendously value the experience of family life that will not enter the priesthood. If being an effective priest depends not just on commitment but on having other character traits that might be correlated with a desire to have a family (e.g., compassion, trust, etc.), then many men who would excellent priests--even better than the average actual priest--might never become priests.
The above discussion clearly applies to heterosexual men considering the priesthood, but it is more complicated for gay men. Because gay marriage has not been a legal option until only until recently (and only in some parts of the world), the cost of the celibacy restriction would have been relatively lower for gays considering the priesthood than for straights considering the priesthood because the value of heterosexual marriage was lower for them. This suggests that the proportion of men choosing the priesthood that are gay might be higher than the proportion of gay men in the rest of the population. Data on this matter are difficult to obtain, but some people have claimed this to be true. If you think having gay clergy is bad given the church's
opposition to homosexuality, then differential screening on sexual
preferences would be bad. However, you might instead believe that the priesthood may be a noble
lifestyle for religiously committed gay men who seek to abide the
church's teachings against homosexuality while still making a
contribution in their religious communities.
Conclusion: unclear, opinions may differ.
3. Priestly human capital. As stated in #1 above, unmarried priests will devote more time to clergy responsibilities, and they can also develop more time developing the skills and talents that would enable them to be effective clergy. For example, they can develop more scriptural knowledge, spend more time on directed learning for effective pastoral care, and so on. This is true for many years after they first became priests. However, it is also reasonable to suppose that marriage and parenting provide experiences and the development of other character traits that can make clergy more effective. If some of these are only obtainable via the intense social relationships found inside families, then unmarried priests will have diminished capabilities relative to married priests because the unmarried priests will not develop those traits that could have only been developed within family settings.
4. Credible signals of commitment. As stated in #2 above, celibacy is extremely costly for many men. Moreover, this cost is publicly known because the celibacy restriction is publicly known. Those that enter the priesthood are, by their decision, sending a public signal to others that their commitment is very high. This public signal enhances the credibility of priests because church members can be confident in the priests' commitment. Church members may be more inclined to trust priests when they are confident in their priests' commitment. This may lead them to participate more at church or be more willing to engage their local priests.
As we should expect from an economic perspective, the celibacy restriction is neither unambiguously good nor unambiguously bad. Even if the policy is considered by the church to be more good than bad overall, it is a policy that still comes with a cost.
Notice as well that the costs and benefits of the celibacy policy change over time. For example, the ability for gay men to legally marry will raise the cost of entering the priesthood for religiously committed gay men, which should decrease the proportion of gay men that enter the priesthood. Of course, celibacy is costly for all men, and it might not be surprising to learn that the Catholic church has experienced a decline in the number of priests over the last many decades despite growth in the number of Catholics. The church has adapted by having an increasing amount of ecclesiastical duties undertaken by deacons and other lay ministers that can be married. Whether Pope Francis will remove or modify the policy is yet to be determined, but if he does we may reasonably infer that he does so because he believes the costs of the policy have become too high.