The USSR fell apart in 1991 with a GDP of around $10,000 per capita PPP, and has reached about $30,000 per capita PPP today after stagnating throughout the 1990s.
I wonder whether it was communism that caused the USSR to fall apart? The communist ideology, as it was practiced in the USSR, included a centrally planned command economy and the lack of civil and political freedoms that was entailed under the Soviets. Perhaps those things caused the failure of the USSR (although the lack of political freedoms hasn't stopped the PRC).
On the other hand, perhaps competing with the US, with its head-start advantage from the get-go was what wore out the economy and caused the political union to fail in the end. The US had an economic advantage from the beginning, in 1917, when the Soviets took over Tsarist Russia. The cold war was expensive, what with the space program and the nuclear arsenal the USSR built up and all the other costs of competing.
What do we know about the cause of the fall of the USSR and whether it can be attributed to the socialist system or to competition with a competitor who was economically and technologically more advanced from the beginning?
Repost of an older answer I wrote on the subject:
PART I
Gorbachev's reforms are ultimately responsible for the Soviet collapse, which saw the end of Soviet superpower status, a massive reduction in the Soviet military's size and strength, the unilateral evacuation of all territories in Central and Eastern Europe occupied at great human cost in the Second World War, and a rapidly declining economy fragmented into fifteen separate states. Much of the argument that the Soviet political system and economy needed reform needed change to avoid collapse came directly from him - the phrase "Era of Stagnation" to describe the Brezhnev years is actually a piece of Gorbachev's rhetoric.
However there seems to be a strong case (made by Stephen Kotkin in Armageddon Averted), that while the Soviet economy was growing at ever slower rates, and increasingly unable to close the ever-present gap in living standards between the USSR and the West, probably could have continued to muddle on - there was no imminent danger of political and economic collapse in 1985.
It's also important to note that Gorbachev's reforms did not cause the collapse of the USSR on purpose, and Gorbachev was always committed to maintaining the union in some reformed shape under an economic system that was still socialist. However, his reforms both began to pick apart the centralized economy without really creating new institutions, which caused severe economic disruptions, and his political reforms unleashed new political movements outside his control, while all of these reforms antagonized more hardline members of the nomenklatura (party establishment). Ultimately he lost control of the situation.
The Soviet system was highly-centralized and governed in a top-down approach, and it was Gorbachev who put reforms into motion and also removed members of the Soviet government and Communist party who opposed reforms.
Gorbachev's period tends to get divided into roughly three periods: a period of reform, a period of transformation, and a period of collapse.
The period of reform lasted roughly from 1985 to 1988, in which Gorbachev and his supporters in the government (notably Eduard Shevardnadze, Gorbachev's foreign minister and the future President of Georgi, and Aleksandr Yakovlev, Gorbachev's ally on the Politburo and the intellectual driver of reforms) tried a mixture of moderate reforms and moral suasion to revitalize the Soviet economy as it was, echoing Khrushchev's reforms of 20 years previous. While the goal was a revitalization of Soviet society and the economy, there was a very strong focus on morality: this period notably featured the anti-alcoholism/prohibition campaign, and very public campaigns against corruption (Dmitry Furman called this a "sort of Marxist Protestantism").
When these efforts did not secure the results that Gorbachev and his reformers desired, more far-reaching reforms were pursued in the 1988-1990 period. This is when Gorbachev made massive changes to Soviet foreign policy, such as withdrawing from Afghanistan in 1989, announcing unilateral cuts to military spending and forces at the UN in 1988, and more or less cutting the USSR's Eastern European satellite states in 1989. On the domestic sphere, this is when Gorbachev pushed through major political changes to the Soviet system, pushing through a new Congress of People's Deputies to be filled through semi-free elections, removing the Communist Party's monopoly of power and creating the office of President of the USSR for himself in 1990. This is also the period when glasnost ("openness", ie the lifting of censorship) took off, and these all were largely attempts to establish a new base of support for continued reforms once it became clear to Gorbachev that most of the Communist Party was uninterested in this.
These reforms ushered in the 1990-1991 chaos, at which point Gorbachev essentially lost control. Falling oil prices and the crackdown on alcohol sales (which were a massive part of the Soviet budget), plus Gorbachev's loosening of management and sales restrictions on state firms while maintaining most of their subsidies, plus plans for importing of new Western machine tools and technology to revitalize the economy, seriously destabilized the Soviet budget, and caused the government to turn to the printing presses to cover ever increasing deficits.
People rarely name a single cause for the collapse; Wikipedia alone lists 25 contributing factors, and the Cold War is just one of them. I'll try to show how complicated the situation really was.
First of all, let's establish the timeline.
The Cold War was a long and complicated political game which had little to do with ideologies. It was a clash of two global empires. Both sides wanted to expand their political influence but avoid direct confrontation, because ever since the 1960s the nuclear arsenals were large enough to guarantee the "mutual assured destruction". This lead to a certain dynamic: the countries would try to de-escalate the confict, signing treaties and making amends, then someone would test the boundaries of the agreements, and sooner or later another crisis would be at hand. At this point the leaders would accuse each other of warmongering and a new phase would begin. The beginning of the 1980s saw such a "hot" phase. The USSR violated one of the previous agreements by invading Afganistan (the situation around that was complicated as well), after which the US immediately cancelled the ongoing work on another disarmament agreement and boycotted the Moscow Olympics; then in 1981 Reagan introduced anti-USSR sanctions for suppressing an insurrection in Poland and soon gave his famous speech about "the Empire of evil". It's important to note that on this iteration the US seemed to have an upper hand in the defense department: they started to heavily rely on cruise missiles, and Reagan famously declared a military space program named "star wars". Meanwhile the USSR was still stuggling economically after the 1970s era of stagnation.
Naturally, after just a few years a need for de-escalation arose again (and this time the USSR was heavily interested in it, given the circumstances - and the fact that Afganistan essentially became the Soviet Vietnam). As early as in 1984 there was talk of making peace and finding diplomatic solutions. For instance, here's an account of Margaret Thatcher's parlay with Gorbachev (yet to become the president):
"We were convinced that our system suited us best. The Soviet system no doubt suited them best. Accepting all this, it was essential in the interests of both peoples to try to diminish hostility and the level of armaments." (source)
As you can see, it's a clear beginning of another "thaw"... and it also shows how little ideology really mattered.
Now I have to say a few words about that ideology - communism itself. First of all, the regime was called "socialism": communism was believed to be the goal, the bright future of a perfect society (which would become reality if it weren't for those pesky Western imperialists and undesireable elements within society). But by the 1980s this ideology was a shell of its former self. Officials were still required to cite Marx and Lenin (Gorbachev's speech from 1987, in the middle of Perestroika, is riddled with quotes from them despite a pretty clear message about democracy). But people mostly perceived this as an empty ritual. The regime was more of a bureaucracy than anything else; mottoes didn't really matter that much.
What did matter, and that's where you're right in your assumptions, was planned economy. Earlier I mentioned an insurgence in Poland - it wasn't an isolated case. In fact there were two waves of political and economic crises in the Eastern Bloc, one in the 1970s and another one in the late 1980s. Economies were becoming increasingly inefficient, and markets had to be carefully reformed to make them more liberal. USSR itself wasn't an exception: it experienced shortages of most consumer items, and the industry was underperforming... and then, to top it off, in 1985 oil prices plummeted, and oil was as important for the USSR export as it is for the modern Russia.
So here we have a stage on which Gorbachev appeared - a liberal politician who already had a warm impression of Western countries and had to solve a diplomatic and economic crisis. That's pretty much why, after a somewhat traditional first year in power, he declared his "Perestroika" which included civil liberties and legalization of small business. Between 1985 and 1988 he repeatedly engaged in negotiations with Reagan, which lead to several agreements, including nuclear disarmament. In 1988, Reagan visited Moscow, and when asked about "the empire of evil" stated: "I was talking about another time, another era".
However, his economic reforms weren't as successful. By 1989 the internal crisis in the USSR was so drastic that ration stamps were introduced, and the national debt skyrocketed. With his peaceful initiatives and weak economy, Gorbachev was unable to maintain control over the Eastern Bloc, and in 1989 satellite countries underwent an entire wave of (mostly peaceful) revolutions. "Glasnost" played its role as well: once being vocal about one's disillusionment with communism became legal, people didn't hesitate to voice it.
I have to point it out - all of this happened before the fall of the USSR. It was a long process with lots of contributing factors - but it gained so much momentum that at a certain point there was no way to stop it. In 1991, when the Cold War was technically over, Gorbachev was faced with another wave of separatism and political infighting (and the economic crisis was also far from over): now that the Eastern Bloc was all but dismantled, the leaders of the republics of the USSR proper gathered to re-negotiate their status. Yeltsin, the head of the Russian Republic, was one of them - and he had a long-standing conflict with Gorbachev... Long story short (TOO LATE!), there was a couple of coups, and the whole union crumbled.
Gorbachev's interviews from those days show that during those negotiations he was still convinced the union would remain! So, as you can see, it was a long pocess spanning almost a decade, with dozens of contributing factors.