Christopher Luxon likes a podium, it seems. The National Party leader so likes something to hold on to, somewhere to put his notes to while speaking to the media, that his offsider brought a music stand to Karaka School’s agricultural day when he visited the rural community for his daily media stand-up on Saturday.

He had been doing hero laps, shaking hands and getting well-wishes from locals for much of the bright, spring morning; stopping often to pet a lamb, or crouching down to talk to a child and ask whether they had won any ribbons, or if they got enough homework.

He took photos, joked and laughed, and made fun of himself, telling one family how he wears SPF75 on his face and head.

He then took questions from a small press pack, the last of which centred around his controversial tax plans, and whether he was being accountable by refusing to give more details about the policy.

Luxon’s centrepiece tax policy promises tax relief for every income bracket, to be partly funded by a new 15% levy on foreign-bought homes costing $2 million or more. But it has faced non-stop critique from economists, Labour and the Greens.

National’s estimates were reviewed and approved by Castalia, but the strategic advisory company hasn’t shown what that review was exactly. Three economists from across the political spectrum – Sam Warburton, Nick Goodall and Michael Reddell – reviewed National’s policy and on Tuesday said it fell $450m short a year.

Luxon has stood by his numbers, but the economists said Castalia has yet to show the full workings –a detailing of the method, assumptions and calculations, and the reasonableness of them, caveats with the analysis, and identification of variations to the method and assumptions that might be appropriate. “None of this appears in what is written up as Castalia’s review,” they wrote.

Luxon, behind the music stand, still would not give these details. “I’ve given you the answers. You may not like my answer, but I’ve given you them,” he said.

Luxon also wouldn’t give a ballpark figure for how many public servants might lose their jobs as a result of his party’s pledge to shave 8.5% off the total public service budget. This would be up to agency chief executives, he said. But his possible coalition partner, ACT leader David Seymour, has estimated about 15,000 jobs would go almost overnight if his party was in government.

Half an hour up the road in Māngere, Labour leader Chris Hipkins was preaching to the converted at the E Tū union’s campaign launch. Gospel singing rang out in the hall, after Pacific dancers and drummers welcomed him in. He came out swinging in a speech which re-treaded many of his main talking points about the dangers of a National-ACT government.

All major polls are showing a clear trend towards the right, despite criticism about National’s tax plan, and despite Labour announcing its main policies of scrapping GST from fresh and frozen fruit and vegetables, and free basic dental care for under-30s.

But when asked about the possible prospect that people simply do not care whether National’s numbers are sound, Hipkins retained his fighting spirit.

“Nobody has voted yet,” he said.