Dairy farming in New Zealand was not always this sophisticated. But ever since a liberal but free-market government swept to power in 1984 and essentially canceled handouts to farmers — something that just about every other government in an advanced industrial nation has considered both politically and economically impossible — agriculture here has never been the same.

The farming community was devastated — but not for long. Today, agriculture remains the lifeblood of New Zealand’s economy. There are still more sheep and cows here than people, their meat, milk and wool providing the country with its biggest source of export earnings. Most farms are still owned by families, but their incomes have recovered and output has soared.

“Farming in New Zealand is now a cold, hard business,” said Mr. Lumsden, who at the time of the farming revolution was president of Federated Farmers in the Waikato region, the heart of New Zealand’s dairy country. “I think we have benefited hugely.”

New Zealand’s farmers are not the only ones convinced that eliminating subsidies, or at least sharply cutting them, is a good idea. As negotiators struggle to revive the failing global trade talks and Congress moves ahead on a new farm bill in the United States, New Zealand and Australia — which also cut subsidies but not as drastically — are being extolled by economists and advocates for poor countries as models for Americans and Europeans to follow.

“They went cold turkey and in the process it was very rough on their farming economy,” said Ray Goldberg, a retired professor of agriculture and business at Harvard Business School. “But they came out healthier and stronger. They proved it could be done.”