PUERTO ORDAZ, Venezuela—This country’s industrial capital was once known for steel and aluminum. Today, people come here for the silicone.

Stringent currency controls, which have slashed trade and closed plants in this city of 700,000, have created an unexpected new boom sector: plastic surgery. A shortage of dollars allows a foreigner to sell greenbacks on the black market for 130 times more local bolivars than the official rate, giving them a Miss Venezuela beauty treatment on a Cinderella budget.

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