Government-subsidized public housing

Let's break this down into 2 parts:

Government-subsidized: Meaning that the government provides money to the person(s) running a particular enterprise for the purpose of making things easier for that one person or enterprise.

public housing: housing owned, controlled or heavily regulated by the government with certain goals (primarily providing a home for the extremely poor).

To call public housing government-subsidized is, in actuality, redundant. All public housing is, in some way or another subsidized.

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Speech Relevance

During 'A Time For Choosing', Reagan relays one of Johnson's ideas:
The President tells us he is now going to start building public housing units in the thousands where heretofore we have only built them in the hundreds. But FHA and the Veterans Administration tell us that they have 120,000 housing units they've taken back through mortgage foreclosures.
Johnson wanted to spend money to build thousands of housing units when the Federal government already controlled 120,000 through foreclosure. Reagan is simply pointing out a glaring waste of money.

In talking about the progressive income tax in 'Encroaching Control', Reagan says:
This is considered such a luxury and yet the New York Supreme Court has recently ruled that a man earning $14,000 a year is so poverty-stricken that he should be entitled to live in government-subsidized public housing.
I am still looking for the actual court case name, but I have found corroboration on a blog quoting a 1960 newsletter from the First National City Bank of New York (now known as CitiGroup).

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Source Links

Record of New York Supreme Court decision regarding housing