By the time Orban became prime minister, medical tourism had become widely accepted by policymakers as unique tool for economic development. Its promise was almost magical: tourism for countries that had not been gifted with beaches or mountains, or had lacked the good sense millennia ago to preserve their abandoned stone structures for future sightseeing purposes.

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Unlike Orban, Batorfi’s patients from abroad typically saw him only once or twice, if ever. Much as luck had once placed a promising young parliamentarian into Batorfi’s dental chair years before the patient would make good in politics, a fortuitous connection had introduced Batorfi to the practice of medical tourism years before the phrase meant much of anything to anyone. In 2000, Batorfi told me, a Hungarian based in England had approached him with a proposal. If he could persuade Brits to take advantage of cheap Hungarian dental work, would the dentist share with him a cut of the new business?

Batorfi got a license to practice in the U.K. and rented an office in London. To his surprise, the patients started coming, adventurous types willing to confront the unfamiliar in search of prices that—even with all travel expenses included—typically fell below half of what they might pay in Bristol or Belfast. “In the beginning, that an English dentist would recommend a Hungarian dentist was unbelievable,” Batorfi marveled to me recently.

Recognizing that foreign customers would be most likely to travel for expensive treatments where they could realize the greatest savings, Batorfi got his masters in implantology, which includes some of oral surgery’s most complex procedures. Back in Budapest, he began setting his prices in British pounds and offering free chauffeur pickup at the airport. He bought advertisements in London media. “The proof of his work and competence are the more than 35,000 patients he has treated. Dr. Bartofi is honest and always ready to share his knowledge and expertise with his patients,” declared an ad Bartofi had placed in The Times. About a decade ago, Batorfi’s adviser Laszlo Szucs told me, Batorfi spent approximately $200,000 to acquire four of what his adviser Szucs calls “the Rolls-Royce of dental chairs.” Szucs claims that there are only four other existing versions of the same model, manufactured by the Japanese company Morita: one owned by Russian President Vladimir Putin, one by German Chancellor Angela Merkel, and two by a private Swedish clinic. (I could not confirm this independently.)

In 2010, medical tourism had already converted Bartofi’s business from a diverse family-oriented dental practice to a high-value oral-surgery outfit, and, with his patient and friend having become head of government, he and others close to him told me he began to contemplate whether the dominant market position he had assumed could be extrapolated into a type of national comparative advantage. A 2010 study by the country’s central tax bureau estimated that the 60,000 or so dental tourists who traveled to Hungary each year generated at least 65 billion forints (about $227 million) in revenue for dentists, with another 13 billion or so forints (about $45 million) in ancillary spending on hotels and restaurants. The sector had survived the 2009 global recession, and business showed little sign of slowing. After all, the peculiar dynamics that brought people to Batorfi’s London clinic for consultations and onward to Budapest for surgery—a British health system that made certain types of medical care scarce, or costly, or both—weren’t likely to yield anytime soon. “There are few things in which Hungary is in a leading position, and dental tourism is the one,” Batorfi says.