WASHINGTON — Consumers paid more for a range of goods and services last month, and unemployment benefit applications jumped last week to the highest level in three months. The latest data offered a picture of an economy facing inflationary pressures and a depressed job market.

The Consumer Price Index rose 0.4 percent in August, the Labor Department said today. That followed a 0.5 percent increase in July. Excluding volatile food and energy costs, core prices increased 0.2 percent.

Prices for food, energy, and apartment rents, and clothing all increased.

Separately, the Labor Department said applications for unemployment benefits rose 11,000 to 428,000 last week. The four-week average, a less volatile measure, rose for the fourth straight week to 419,500, the highest level in eight weeks.

Applications need to fall below 375,000 to indicate that hiring is increasing enough to lower the unemployment rate. They haven’t been below that level since February.

“One bad week means nothing, but claims have been nudging higher since … early August. We await the next few weeks’ numbers with interest, and a degree of trepidation,” said Ian Shepherdson, chief U.S. economist for High Frequency Economics.

A third report from the Federal Reserve said manufacturing was mostly weak outside of strong auto production. Factory output rose 0.5 percent in August, after increasing 0.6 percent in July.

Most of the gain came from a 2.6 percent increase from autos and related products. The second straight month of increases in auto production was evidence that supply chain disruptions stemming from the Japan earthquake are easing.

The data suggest the economy isn’t improving much after it barely grew in the first six months of the year and employers pulled back on hiring.

At the same time, consumers are being hit with higher prices for basic necessities. That has reduced consumers’ purchasing power, cut into their ability to spend on other items and weakened the economy further.

For the 12 months that ended in August, core prices surged 2 percent, the biggest year-over-year increase in nearly three years. That’s at the high end of the Federal Reserve’s informal inflation target. It could limit the central bank’s ability to take further steps to try to revive the economy.

Food prices rose 0.5 percent in August, the biggest increase since March. That was partly because of higher prices for cereals and dairy products.

Food prices are likely to keep rising because an unusually hot summer damaged this year’s corn harvest. Corn is used in everything from cereals to animal feed to sodas. It takes about six months for changes in corn prices to filter down to grocery store shelves.

Among the factors driving up the core index were rental costs. They rose 0.4 percent, the most in nearly three years. Many Americans have been renting rather than buying homes, pushing up rents.

Clothing costs rose 1.1 percent, extending a string of increases that stem partly from steep rises in cotton prices earlier this year. Airline fares rose 1.1 percent, the most since March.

There are signs that core consumer prices could level off soon. Cotton prices have come down by nearly half from the spring, and clothing costs are expected to follow.

And new-car prices rose earlier this year because of supply shortages caused by Japan’s March 11 earthquake. New-car prices were unchanged in August for the second straight month.

“Core inflation will remain at or above the Fed’s implicit two percent target until at least the middle of next year,” said Paul Ashworth, chief U.S. economist for Capital Economics.

Fed Chairman Ben Bernanke acknowledged last week that rising commodity prices had pushed up inflation this year but said it was likely to moderate in coming months.