What a great title—adopted by several works on Communist humour, just as Broken down by age and sex is popular among statisticians.
Ben Lewis’s Hammer and Tickle: a history of Communism told through Communist jokes  has many fine jokes, like this (p.214):
The government of the Union of Soviet Socialist Republics has announced with great regret that, following a long illness and without regaining consciousness, the General Secretary of the Central Committee of the Communist Party and the President of the highest Soviet, Comrade Leonid Brezhnev, has resumed his governmental duties.
A man was arrested for writing “Khrushchev is a moron” on a fence, and given 15 years in prison: 1 year for vandalism, and 14 years for disclosing state secrets.
Courtesy of Homeland, I’ve just noticed the fine metaphor for relations between the communist state and its employees:
We pretend to work, you pretend to pay us.
But Lewis is surely wrong that “For whatever reason the same phenomenon didn’t exist in the same way in South East Asia or China.” The Chinese have more such jokes than anyone, and it’s high time we had a volume of them in English: for starters, click here. One could compile a thick volume just of Li Peng jokes (preliminary offerings here and here).