How will goods and services be produced and supplied when there is no economic system?

The workers at the coal mine dig up the coal and leave it at the gates for anyone to pick up free of charge.  The baker bakes the bread and leaves it for anyone who wants it.  And so with the butcher and so on.

Why would the coal miners turn up, the bakers, the butchers, etc?

People work for many reasons.  To have a sense of purpose in the world, involved in the progress of mankind.  Let's face it, work is something to fill a day in with.  Would people simply give up working if there was no economic system?  And do what?  Stare at their navels all day long?  Think what would happen if nobody worked.  Everything would deteriorate rapidly.  Infrastructure—roads, railways, airports, buildings—would decay and collapse.  There would be no food.  Water would be contaminated.  There would be no transport.  The list goes on.  People would not tolerate a decay in the standards of living that they have been used to.  Scientists and health care workers, to give just two examples, work in their respective areas because, on the whole, they care passionately about their fields.  A salary cheque for these intelligent and intellectual people is not the main reason for them having the types of jobs that they have, it's simply a practical neccessity under an economic system.  And remember, under an economic system, there is a conflict of interests for a healthcare provider.  Doctors and nurses provide a valuable service and need to be rewarded fully, but the more money that goes into the pay packets of these people, the less there is for medical equipment and drugs.  That dilemma would not occur in an economy-free society.  And, don't forget that there'd be unlimited resources for drug development, therapies and treatments—searches for cures.  How wonderful for a biochemist to go to his or her laboratory knowing there was nothing to hold him or her back from pushing at the limits of knowledge.  Today, the UK's National Health Service (NHS), providing universal, free-at-the-point-of-use healthcare faces such difficulties, juggling finances; the number of beds on wards that can be afforded.  All of that would be gone.  Over in certain currently poor countries, everybody would have access to all of the medical treatments available anywhere (no drugs costs nor transport costs and so on).  No more blindness for the sake of a simple cataract operation.  With unlimited resources for developing treaments and finding cures, there is the nothing to hold back progress into finding ways to prolong life, perhaps indefinately—immortality (assuming, of course, such a thing is possible within the realm of physics at all).

Who would want to do the dirty jobs?

Anyone who realises that the dirty jobs have to be done.  Anyone who realises that hospital wards must be kept clean, or, given they might find themselves in hospital themselves at any time, they might not get to enjoy as good a recovery thanks to a dirty ward.  But, in an economy-free world comes freedom.  Nobody would have to do the same thing for hours on end, day after day.  With opportunities unlimited, there'd be no such thing as being stuck in a job, with no prospects.  And, with all goods and services free of charge, then, in a sense, the reward for doing a job is your reward; reward yourself with whatever you want (bear in mind that, without an economic system, there is, actually, no such thing as a specified reward for anything, including work done, as there would, by definition, be no economic system to define and determine it, nor would anyone have any need to, let alone be required to, assess what might be an appropriate reward for themselves, for the same reason); not enforced minimum wage subsistance.  But don't worry: with unlimited resources, with science and technology unleashed—progress at break-neck speed—the dirty jobs would soon disappear as better infrastucture was immediately made available.  Just think: worker robots—human-like, too—would really be just around the corner.

Wouldn't people just go crazy and stockpile resources for themselves, selfishly?

What would be the point?  Every good and service would be in plentiful supply for anyone and everyone at no cost.  There would be no point at all in selfishness.  There might initially be instances of what might be called 'waste'.  Somebody might create a giant video wall in their back yard with hundreds of televisions. But, how many, say, washing machines would you really want?  Still, if a house full of washing machines is your 'thing', so be it.

Would people have personal possessions?

Yes, but that would not take the form of stockpiling as mentioned above.  People would be perfectly entitled to have personal possessions.  Most people wouldn't want to share their homes, for example, and, why should they?  Maybe communnal living would evolve in the future, but there is no neccessity for it in an economy-free society.  And there'd be unlimited resources to build homes.

Wouldn't there still be lazy people who would not do anything and just live off everyone else?

Of course.  These people already exist, but they would be much diminished in an economy-free society.  Opportunities would be available for all—education unlimited in resources (including teachers); unlimited employment and so on.  Forget about unemployment: there would be no unemployment.  If a relative few wished to do nothing and live off the rest, so be it.  Good luck to them.

Wouldn't the Earth become polluted? There would be unlimited exploitation of the planet's natural resources, surely?

Don't forget that there would be unlimited progress in all areas, including science and technology.  There would be no stopping the development of cleaner, greener energy and for cleaning up the world, unlike today, where fitting, say, sulphur-reducing equipment to a power plant costs big money.  Today, it costs to be good.  Today, cleaning up polution is a part of the financial equations of businesses and governments.  Today, money used for the environmental good can not be reused for something else, say, product research and development, marketing and so on.

What about national defense and policing?

A country that went it alone and abolished its economy would be an example to the rest of the world.  We need to see ourselves as one species, not as Britons, Americans, Italians, Peurto Ricans, Argentinians, etc.  Let us be united and not divided, lest we become extinct at each other's hands.  Let's have no borders.  Keep an identity if you must but the supply of goods and services must be global and without restrictions.  There has been, every year, since World War II, enough food to feed every man, woman and child on the face of the Earth—and not just a high-energy biscuit and bowl of rice, either.  Yet it costs too much for too many.  Without an economic system, this, of course, would not be an issue.  There would be so many goods and services that there would be more than plenty for everyone; with no need to fight over it.  And, with unlimited science and technology, the exploitation of other worlds—today, just a pipe dream—is brought realistically right into the present.  As stated, selfishness would not make sense.  As for policing, there could be no financial crime.  You can't mug somebody, burgle, swindle or sell drugs and sex for money or any other material gain when money does not exist and goods and services are free of charge; it would be impossible or nonsensical.  There'd likely still be sexual crime, but could that be any worse?  With the availability of whatever goods and services you want—all your needs and wants satisfied—people would be much less likely to be unhappy.  And in a happy society, there would almost certainly be a tendency for less crime.  But there would still be law and people prepared to uphold it, just as there would be scientists and doctors.

Wouldn't abandoning capitalism solve the problem?

Yes, if it was being abandoned in favour of not having any kind of economic system, of course!  But if you mean in favour of some other economic system then no; not at all.  It is the having of anyeconomic system that is the problem.

Footnote.

Economic systems are not mandated by heaven above; nor nature below.  They are man-made entities.  When they are the root of 99% of mankind's problems and hinder the finding of solutions for the remaining 1% of them, why, then, have them?