Raising the interest rate (i.e. making loans more expensive) is the measure taken if there is a belief that there is too much demand for goods by the population (Keynesian inflation theory) or too much money in circulation (Monetarist inflation theory). It’s taken in the hope that reducing the purchasing power of the population will slow the price increase down with falling demand. Which is why you had mainstream economists talking of say the need to increase unemployment (i.e. take people’s incomes away) and how wage increases are bad due to the supposed theory of the wage-price spiral.
Wage-Price spiral> “Wage-price spirals, at least defined as a sustained acceleration of prices and wages, are hard to find in the recent historical record. Of the 79 episodes identified with accelerating prices and wages going back to the 1960s, only a minority of them saw further acceleration after eight quarters. Moreover, sustained wage-price acceleration is even harder to find when looking at episodes similar to today, where real wages have significantly fallen. In those cases, nominal wages tended to catch-up to inflation to partially recover real wage losses, and growth rates tended to stabilize at a higher level than before the initial acceleration happened. Wage growth rates were eventually consistent with inflation and labor market tightness observed. This mechanism did not appear to lead to persistent acceleration dynamics that can be characterized as a wage-price spiral” (IMF, Nov/2022)
Cutting taxes is a measure taken with the hope that with reduced costs, private enterprises will scale up production and increase the amount of goods’ supply as compared to demand, lowering or at least stopping the increase in prices, as orthodox economists hold the thesis that excessive demand (as supposedly caused by the 2020 Covid Crisis) is responsible for the currently high inflation.
Nowadays, it’s commonly accepted in many studies, such as this recent one from New Zealand that a significant cause in the inflation is the desire for even higher profits compared to what they already had in years prior.
Lowering taxes in response to a stagnant economy in this case is, as I understand it, unlikely to affect inflation, but is rewarding a private sector that used the fuel and energy price crisis caused by the war in Ukraine to enrich itself even as those prices fell again, with more riches. Especially considering the currently stagnant economy, it’s placing hope on a sector that has already failed to deliver out of an ideological belief that the state is unable to do what the private sector can, as well as the support it gets from and how many politicians have personal relationships with the private sector.