Caracas (AFP) - With global oil prices in a prolonged slump, late Venezuelan president Hugo Chavez's vision of "21st-century socialism" is in trouble both at home and abroad.

The movement Chavez founded risks losing control of the National Assembly in legislative elections Sunday, even as Venezuela's sway over its fellow Latin American nations dwindles under the late leftist firebrand's successor, Nicolas Maduro.

Chavez, who died of cancer in 2013, ruled Venezuela for 14 years with a mix of authoritarianism and charisma, using the oil giant's booming crude revenues to fund a populist economic model of lavish subsidies and social spending.

The first in a string of leftist leaders to surge to power in Latin America, Chavez also wielded outsize influence in the region by granting cut-rate oil exports to friendly governments, rallying them around his fiery diatribes against US "hegemony."

But as oil prices have plunged from more than $100 a barrel to an average of $46 this year, Venezuela's economy has sunk ever deeper into crisis and its "petro-diplomacy" has lost heft.

"The socially and internationally ambitious model that Hugo Chavez put in place in 1999 rests on oil exports," said Jean-Jacques Kourliandsky, a Latin America specialist at French international relations institute IRIS.

"Venezuela had built an active and innovative social policy with oil revenues. Oil also gave it unprecedented capacity for diplomatic influence," he told AFP.

"The brutal drop in oil prices has shaken those two pillars of the regime."

Venezuela has the world's largest proven oil reserves, but its citizens have for months faced severe shortages of basic goods, long lines at the supermarket and inflation that the government says is 85 percent -- but which independent analysts put in the triple digits.

Venezuelans' buying power has fallen 34 percent, to the lowest level in two decades, according to consulting firm Ecoanalitica.

That is fueling widespread frustration with Maduro, whose popularity has sunk to 22 percent, and with the "Chavista" movement, which risks losing the legislature Sunday for the first time since Chavez came to power.

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Polls show the opposition leading by as much as 35 percentage points.

"People are fed up. Inflation, scarcity, insecurity, violent crime. They're sick of it, especially the hard core of the 'Chavista' electorate, because inflation hits the poor worst of all," said Olivier Dabene, director of the Latin America observatory at French institute SciencesPo.

- 'Brutal adjustment' -

Venezuela relies on oil exports for 96 percent of its hard currency -- a shrinking money supply that it desperately needs to fund the imports on which its economy has grown dependent.

It has sought to plug the gap with a system of exchange rate controls, but that has put downward pressure on the bolivar currency, which is worth 140 times less on the black market than at the official exchange rate.

All that has put the country on track for a painful economic adjustment, analysts say.

But in a system where presidential power far outweighs the legislature's, an opposition win will not likely change Venezuela's economic woes, said Carlos Malamud of the Real Instituto Elcano think tank in Spain.

"Resolving the economic situation requires a brutal adjustment plan that will be strongly resisted by the working classes," he said.

"It's one thing to have a majority in parliament, but it's another to have a bearing on the economy, especially in such a strong presidential system."

Venezuela's influence in the region has meanwhile declined sharply under Maduro, who lacks not only Chavez's good economic fortune but his charisma.

"Venezuela no longer has Chavez's leadership nor a commodity worth $100 a barrel. That reduces its power and increases the willingness of regional leaders to speak out against (it)," said David Smilde of the Washington Office on Latin America.

The leftward tilt that Chavez spearheaded appears to be flagging in the region -- from Argentina, which elected a conservative new president last month, to Brazil, where impeachment proceedings have been opened against leftist President Dilma Rousseff, and Cuba, a close Venezuelan ally that has embarked on a historic rapprochement with the United States.

Venezuela "doesn't have the resources to buy influence anymore," said Malamud.