How is the market going to equitably distribute resources?

Who said anything about equitable?  

Utimately the rules of nature and the market system is connected. I can best summarize the connection between markets and nature by borrowing the title of Darwins famous book "Survival of the fittest". Those without wealth, resources or can't adapt will suffer and probably die off.

The rules of survival, the market, and natural selection are all the related. People that can adapt and have access to the necessary resources will survive. Those without will perish. We can see this all the time in business. Successful businesses that provide good or services that meet the demands of tje market survive and flourish, those that don't go bankrupt. Businesses also need to adapt to the changing market. For instance during much of the 20th century, camera film manufactures and processors flourished. Kodak was part of the dow 30 for many decades. When film was replaced by digital photography, these companies no longer served the market. Some adapted and some went bankrupt.

Market forces will bring about changes, but they aren't going to save humanity from the trouble ahead. The only option is to adapt or die. Those that believe that Communism and socialism can solve the problem are dead wrong. Our planet's history has been dominated by the market system since life began about 2 billion years ago. During this time, nature has never developed an eco. system based upon the ideas of communism. It has always been based upon a market system and always will be. In the end the rules of the market system will prevail, it just won't be one that is any regards, equitable.

5. Malnutriention resulting in wide spread of pandemic diseases (The dark ages during the little ice age).

There are two ways around it, according to Diamond.  

One is to be such a small society that everyone can understand the problem and everyone has a stake in the solution.  

The other is a central government strong enough to force compliance.  

Byzantium (Eastern Roman Empire) was the only society that ever simplified itself on purpose.   At its nadir it was almost completely destroyed.  Byzantium had 1/3rd of its population killed by plagues, the currency was so debased that it became no longer used and their empire was at one point almost completely overrun by Visigoths and Arab Muslim invaders yet they were able to recover from their nadir in the 700s and survive till the 13th century (600 years!) even though they faced almost constant invasions from the Muslim empires to the east and goths and other barbarians to the north and west.  They were able to do this through a number of clever simplification maneuvers.  

1.  The Government had run out of money to pay soldiers so instead they gave them land in exchange for hereditary military service organized in "themes" or military districts.  The soldiers were responsible for purchasing and providing their own rations, equipment, and uniforms.  This got rid of almost all the military bureaucracy and a large part of the taxation complexity.  Can you imagine the government devolving the military into local farm owner's gun clubs purchasing their own heavy military equipment?  It reflects an amount of trust in the people by the government that is unthinkable today.

2. The civil administrations were merged into the military.  There was no distinction between the military and the local governments.  The Military ran the courts, the police, and local government functions.  No Posse Comitatus but the military was the equivalent of these local farm owner's gun clubs and would therefore be far more trusted with their authority by the people.

3.  They gutted all the glamour of their central government to keep things together.  At one point they paid the army by melting down 20,000 pounds of gold from the emporer's throne room.  Equivalent to selling off most public lands and buildings.  Administrative ranks and honors were done away with.  

4. Cities contracted to densly packed fortified hilltops.  That would mean abandoning the suburbs.

5. Aristocratic life (what rich educated people were doing) was focused around the imperial court.  Meaning that rich educated people mainly passed the time by hanging out at city hall with the politicians,  drinking wine, wearing fancy clothes and gossiping but otherwise didn't have many luxuries, compared to Roman times.

6.  Education was simplified.  Basic math, reading and science were the order of the day.  New books were mostly the lives of Saints, the ancient traditions were preserved and copied.

Tainter points out that a) a government can wreck itself by trying by all means to sustain itself and b) complexity in problem solving destroys governments slowly, subtly over long period of time and that simplification is very hard because so many have tied their interests to growing and maintaining the complexity of the centralized power structure.