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Tesla executives have highlighted a range of efficiency and cost improvements they said had put the company on track to launch a far cheaper electric vehicle, potentially allowing it to tap a big new market as it faces greater competition from rival carmakers.

The headway being made towards what it called a “next generation platform” for a cheaper vehicle dominated discussion at Tesla’s first-ever investor day, which was held at its gigafactory in Texas on Wednesday.

Lars Moravy, head of vehicle engineering, said the “large-volume” vehicle would be produced at a number of the company’s plants, including a new facility in Mexico that was disclosed by the country’s president earlier this week and confirmed by Tesla on Wednesday.

Tesla chief executive Elon Musk said that “affordability” was the main barrier to it reaching a far bigger market. Before recent price cuts for its electric vehicles, he said, “we weren’t sure about what the price elasticity of demand was for Tesla”.

“We found that even small changes in price have a big impact on demand — very big,” Musk added.

In the first apparent confirmation that the round of price cuts has helped to revive demand after a weak start to the year, Tom Zhu, head of Tesla’s China’s operations, said lower prices there had an immediate impact, with the company increasing its market share in the country.

“After [the price cuts] we generated huge demand, more than we can produce really,” said Zhu, who was also put in charge of Tesla’s productions facilities around the world at the start of this year.

Read more about Tesla’s investor day here.