Here is Melanchthon on Romans 13 from the Dispositio orationis in Epistolam Pauli ad Romanos with the next two paragraphs added.

Translation

Romans 13

Proposition: “Let everyone be subject to his own magistracy.”^[1]  [Paul] adds reasons taken from the dignity of magistracy, and from the punishment that avenges the scorn of magistracy. Here, it is again apparent that Paul teaches the commandments about morals in a different way from how philosophers teach them. For he teaches us about the will of God, because πολιτεία [politeia, “polity,” “constitution,” “government”] is a divine ordinance, just as the changes of time—winter, summer, day, night, and the continual courses and movements of the stars—have been created by God and are preserved by him. In the same way, God has ordained and preserves πολιτειίαν [politeian], magistrates, and laws in the world.

There have been many fanatical men, even in our time, who have contended that a Christian is not permitted to hold a magistracy, because the gospel frequently prohibits vengeance. They have therefore thought that magistracy is robbery and unjust violence. Paul fortifies us against this impious and seditious opinion, and teaches that magistracy is a divine ordinance or a good work of God. The result of this is that those who hold a magistracy are engaged in a lawful and honorable office.

No one has the requisite words to do adequate justice to how many uses this teaching affords both to magistrates and to subjects. For magistrates can perform the duties of their offices with a good conscience when they know that their type of life and their administration are pleasing to God. And they are bold to await and seek help from God (since they act in his stead), in order that he may defend and govern his ministers. No armies, no citadels are able better to fortify princes in the midst of so many dangers and traps of the devil as this trust in divine help. Next, no reason more effectively moves the minds of men to obey the magistrate than if they know that he is a minister of God and must be respected, just as other sacred things must be, and that this obedience is performed not for me, but for God. As we honor sacred ceremonies because they have been commended to us by the Word of God, so pious minds honor the magistrate, because he has been commended by the Word of God, and they recognize that the blessings of God, justice, and tranquility come to us through them.  

In addition to these points, they understand that magistracy cannot be overthrown by human violence, because they know that it is defended by God. And because punishment or vengeance is the work of God, they in no way doubt that those who are seditious will pay the penalty. In this way, the teaching of Paul nourishes reverence toward magistrates and laws. What similar thing do we read in Plato’s Republic? Paul teaches that laws and magistrates are an ordinance of God. Plato condemns the form of the commonwealth that actually existed in his day; he fashions a πολιτειίαν [politeian] that is new and in no way harmonious with the judgment of human reason; and he reviles kings as if he were a jester.

And we have the books of certain men written in recent years in which princes are falsely mocked, and often [this] type of life is even taken to task,^[2] as if it conflicted with the gospel. And all men are naturally moved, when the consider the vices of princes and when they behold the changes of regimes, to suspect that political jurisdictions^[3] are both established and maintained by human violence without the plan of God. This passage of Paul should be set in opposition against scandals of this kind, so that it may habituate us sincerely hold magistrates in reverence and to esteem them highly. And I would wish those tho teach the gospel to treat and explain this passage carefully and regularly. But as to the fact that vengeance is prohibited in other passages, this ought to be understood only of private vengeance. For here magistrates are expressly given an exception, which magistrates exercise in order that we may know that political administration is truly the work of God.

There is also emphasis in the phrase, “They have been ordained.” For “ordinance” signifies the form of political jurisdiction, that is, laws, courts, punishments, and contracts. Therefore, he approves not only of magistracies, but also of laws and the form of the commonwealth as a whole, namely, of marriage, the division of property, contracts, and courts. He includes all of these, so that we may know that we can use civil things with a good conscience, just as one must use food, clothing, air, and light. Nor, indeed, should we judge civil ordinances (laws, contracts, courts, magistracies) to be less necessary for bodily life than clothing, or the air that we breathe, is. Therefore, it is not only with magistrates, but with human nature as a whole that the Anabaptists and others wage war, who disparage public laws; who condemn courts; who dream that it is piety or, really, perfection to part with private property and to transfer it to common possession. I myself know how many great men have judged badly concerning these matters, and how easy it is to err on this topic. Therefore, I thought that the reader ought to be advised to fortify his heart with this passage against the fanatical opinions that the Devil sows, both to render the gospel hateful and, by arousing seditions, to destroy churches and commonwealths. 

Under this pretext, Christian teaching was hateful to great men among the gentiles, because they judged that, once vengeance had been prohibited, magistracies and courts were destroyed, impunity was granted to the wicked and criminal, and the bonds of peace and civil society were cut. In addition to these things, they thought that a sort of Platonic communal sharing of property was commanded in the gospel, which is absolutely inconsistent with the nature of the human race.

Here, our writers labor to make a refutation. Some reply that these commandments (not to exercise vengeance, to share property communally) pertain to the perfect, and they make different groups, some for the imperfect, others for the perfect. But this does not satisfy the adversaries. And as long as the opinion persists in the church that perfection is located in works of this kind, matter for disturbances will never be lacking. For fanatical men arise who disapprove of the office of magistrates and who condemn the customary interactions of civil life. Such opinions, once they have been spread among the ignorant, trouble the consciences of many, and arouse the greatest commotions.