A good example of a libertarian government is the United States government circa the 19th century, when it strongly adhered to the principle of Laissez Faire, and when the United States saw itself become the world's industrial super-power. Instead of wading into more historical examples to try to prove my case about libertarianism and efficiency, I want to explain my theoretical reasoning.
The underlying reason why a libertarian econo-political system is the most efficient one is that conflict is expensive. Conflict drains and diverts resources from productive uses and disrupts productive systems through acts of destruction. We humans seek to attain and accumulate resources in the most efficient possible manner for our individual self. When the most efficient manner available is attaining the resources from other individuals through coercion or theft (including fraud), it tends to reduce the overall efficiency of society because those individuals who lost their resources to the coercion and/or theft will divert their resources to attempting to prevent future losses of resources by such means.
One example of this dynamic in effect is taxes. Tax receipts are coerced from the population at the threat of imprisonment/fines. People spend considerable amounts of time and resources trying to find ways to minimize the taxes they are forced pay. For example, they may hire an accountant to file their taxes in a way that minimizes their taxable income, or they may look for ways to move their money offshore outside the reach and sight of government agents.
None of these activities aimed at reducing how much they are taxed increases the overall efficiency of society. This type of mis-allocation of resources manifests itself whenever there is conflict amongst the participants of a society (in this case between state and citizen), so obviously, as this line of reasoning goes, the less conflict a society has, the better it is for its level of efficiency.
So the next question we face is how to reduce conflict. One option is simply putting everyone into bondage, deny them their right to privacy, and ensure that they have no choice but to obey the government. This could conceivably reduce the incentive of the citizen to resist the state's dictums to the point that conflict is reduced, but this would also give awesome powers to the government over the people, and therefore make the potential rewards of attaining the position of political leader of such a state enormous, which itself could create conditions that increase the likelihood of conflict.
It therefore seems likely that an all powerful state would create a cold war like environment where each political faction is focused on increasing their political/military strength in order to increase the probability of seizing power.
All of this political jockeying uses up resources of course, diverting them from productive purposes, and therefore mitigating whatever efficiency advantage that an all powerful state would confer from reducing citizen vs state conflict.
Furthermore, the resources required to maintain a bureaucracy that keeps the population under absolute control and surveillance would be enormous. For these reasons, I conclude that a society with an all powerful government that pervades every facet of that society cannot be economically efficient.
So the question now is, if we go to the opposite extreme, and have a society that has a small libertarian government in place rather than an all powerful pervasive one, will coercion from other, non-state, facets of society replace government coercion? Wouldn't mafias and other non-state actors simply take the place of the government?
I argue no, because there's a distinct advantage that a government has when trying to prosecute and outlaw acts of initiated coercion and fraud, over trying to prosecute other types of crime (e.g. narcotics consumption, tax evasion, etc), and that is that they have the victim on their side.
It is not just Government vs Law-breaker, in the case of a libertarian government, it is always Government + Victim vs Law Breaker. A libertarian government need only be more powerful than the next most powerful center of power in the country, in order to guarantee that no citizen is above the law. The citizens will do the bulk of the job of surveilling and reporting crime, as a natural consequence of the fact that the only crime in a libertarian society is one where a citizen is a victim and therefore has a strong incentive to report it, requiring of the government only to administer justice.
I believe this advantage of libertarianism in efficiently reducing conflict in society makes it the best form of government for maximizing efficiency in a society.