Four increases have already been delivered this year, and the cash rate sits at 4.6%, the highest in fifteen years. On Tuesday the Reserve Bank of Australia is expected to make it five. Markets are pricing a move to 4.85%, and almost nobody on the economist circuit is arguing otherwise.

The case for another interest rate hike was made on Wednesday, when the Australian Bureau of Statistics reported that headline inflation had accelerated to 4.3% in the year to September. The bank's preferred underlying gauge, which strips out the most volatile prices, ran at 3.6%. The bank wants price growth back at 2.5%, and it is a long way from there.

What the September numbers showed

The pressure is broad, which is what makes it uncomfortable. As the Guardian reported, transport costs are up 8.7% over twelve months, driven largely by fuel prices that have climbed since the US and Israel went to conflict with Iran. Food rose 3.2%. Housing, the biggest single category in the index and the largest contributor to the annual rise, was up 5.2%, as builders passed on dearer materials and labour and electricity bills stayed high.

Central bankers have said for decades that a single oil shock can be looked through, and they have often been right. Fuel, though, doesn't stay in the petrol station. It travels through freight, groceries and construction, and by the time it shows up in rents and building quotes it has stopped looking temporary.

Andrew Hauser, the RBA's deputy governor, told a Senate estimates hearing the same day that the readings were too high. His larger worry was expectations. If households and businesses begin to assume prices will keep rising at this pace, they behave accordingly: wage claims firm up, firms reprice more often, and getting inflation back down gets harder. He called that a "nightmare" scenario. He also said it hadn't yet taken hold, which is a careful way of saying the bank is trying to act before it does.

A slowing economy, a stubborn price level

The other half of the picture is less comfortable still. Unemployment has been lifting. Household spending is subdued, the housing market has weakened, and the labour market has softened. Stephen Smith, a partner at Deloitte Access Economics who expects the increase next week, put the bind plainly: the economy is already slowing, yet the bank has little appetite to let expectations drift after so long above target.

Call it the classic central banker's squeeze. Raising the cash rate again lands on mortgage holders who have absorbed four increases in ten months, and on a government that has spent weeks arguing over who is to blame for the cost of living.

Josh Gilbert, a market analyst at eToro, described the situation as a "higher-for-longer" story. Anyone waiting for relief, he suggested, should bring patience. I'd go slightly further: the language that accompanies Tuesday's move will say more than its size. If the bank hints that five is the last of this cycle, markets will start pricing a plateau. If it doesn't, they'll start pricing a sixth.

Politics on the other side of the world

Canberra would have preferred a different calendar. Prime Minister Anthony Albanese flew out on Saturday for the Commonwealth leaders' gathering in Antigua and Barbuda, which means he will be overseas when the rate decision is announced, Guardian Australia noted. Analysts quoted there see the trip as a chance to reset a domestic debate that has been dominated by grant-funding controversies and price pressures. Monash University politics scholar Zareh Ghazarian, an associate professor, said the prime minister has "a lot of spot fires burning domestically."

Further travel follows over the coming weeks, with leaders' meetings scheduled in Turkey, the Philippines, China and the United States. A leader who spends November in meeting rooms abroad while mortgage repayments climb at home is taking a political risk, however sensible the diplomacy.

Treasurer Jim Chalmers has pointed the finger outward. He told reporters that the government accepts its part in the fight against inflation, but attributed the main pressure to dear oil and a private sector that is bouncing back, and he called the war in the Middle East disastrous for the cost of living around the world. Critics see it differently. They point to a mix of fuel costs, government spending and weak productivity, and the argument over how much weight each deserves hasn't been settled. It probably won't be before the next election.

What to watch

Tuesday's decision looks like a formality on price, so the real information will be in the accompanying statement and the forecasts. Three things matter: whether the bank revises its inflation path upward again, since officials have already warned that the outlook is worsening; whether it says anything about the softening labour market, which would suggest the tolerance for further tightening is thinning; and how markets read the gap between the 4.85% they expect and wherever the bank thinks the peak is.

Other central banks are working through the same oil-driven arithmetic, each with its own jobs and price data, and the Australian experience is an early indication of how stubborn that shock can be once it spreads. A fifth interest rate hike would leave Australian borrowers paying more than at any point in a decade and a half. Whether it is enough is a question the next few monthly inflation prints will answer, and the bank has made clear it isn't assuming the answer is yes.