Look at three ways of helping poor people to buy food, clothing, and
shelter.  The first ay is to pass laws setting price ceilings to keep
these basic goods affordable. The second is to have the government
disctribute coupons that give poor people a discount when they buy
these necessities.  The third is for the government to distribute
income to poor people.  Which program is more likely to have a Pareto
efficient outcome? Describe why the other programs are not likely to
be Pareto efficient?

It would seem that the answer is that the discount coupons/vouchers option
(like food stamps) would be most Pareto efficient.

Obviously, price ceilings/caps are Pareto inefficient. They discourage
producers from satisfying consumer demand, including the consumption
of the poor.  So moving from equilibrium to price ceilings would be
Pareto inefficient.

Someone told me welfare was clearly Pareto inefficient, but I don't
see why it is.

Vouchers/coupons/food stamps would seem to stimulate demand without
being overly inflationary.

So which is more Pareto efficient, coupons or welfare?

Why?

Also, what is the difference between Pareto efficient allocations and
a Pareto efficient market?  On my sparknotes chart, it says, "Pareto
Efficiency:In an efficient market, there are no possible trades that
will make one party better off without making another party worse
off."

Please cite a site or sites if possible.

Thank you.

The coupons would not be most efficient.

What would happen is that people would sell them for money, and use
that to buy what they /really/ want.

Since they would be selling them at a discount, the 'poor' would land
up consuming less of what they really want than giving them cash.

They would fall short of the Optimum Optimorum

There is a similar situation in rationing.
The smart money is to issue ration coupons, but make it clear that
they are freely tradeable.
If one looks at it closely, the coupons are actually a form of money.

The major problem is that 'nanny' wants the poor to buy food and
clothing, while the 'poor' far prefer alcohol and cigarettes.
- and they'll get them - regardless.

By welfare you mean cash, well we have established that cash will get
people on a higher indifference curve than discount coupons.

It is possible that the person who told you that welfare is Pareto
inefficient was thinking of something else.

Working is a form of trading, welfare discourages work, therefore
paying people to explicitly not work, if work is available, is Pareto
inefficient as the employers are worse off as they do not benefit from
the labour.
Mind you, the 'poor' might far prefer watching Oprah to working ...

An off the wall alternative is to supply the 'poor' with high quality
illegal substances which they can then trade, we still have the
inefficiency of people not working, but we have the fairly
considerable benefit that one does not need to tax highly paid bond
brokers and give cash to the 'poor'.

Economic theory can be rather amusing.