NEW YORK (CNN/Money) - Rising gas and food prices might worry the nation's consumers most, but it's the price of everything else that will be closely watched this week by investors and policy makers at the Federal Reserve.

Government reports are due Thursday on the producer price index, a measure of wholesale prices, and Friday on the consumer price index, which measures retail prices.

So-called "core" PPI and CPI -- measures that exclude often volatile food and energy prices -- will be the most closely watched, to see if inflation is posing a great enough risk to prompt a interest rate hike by the Fed at its June meeting.

"This week's CPI will seal (the Fed's decision)," said Anthony Chan, chief economist at Banc One Investment Advisors. "If we get a number at consensus or a little above, that'll tip it towards a June increase."

Economists surveyed by Briefing.com forecast that the core CPI will be up 0.2 percent, in the April report. In March, core CPI rose by an unexpectedly large 0.4 percent. Meanwhile, a 0.3 percent increase in the overall CPI is forecast, following last month's 0.5 percent increase.

The core PPI is expected to be up by 0.2 percent, the same as the March increase. The overall PPI is forecast to rise 0.3 percent, following the 0.5 percent gain in March.

The strong April employment report last week convinced investors that a June rate increase is coming from the Fed, even if economists remain unconvinced the Fed will pull the trigger before the August meeting. The Chicago Board of Trade Fed funds futures, which indicates trader's expectations of Fed action, indicates an 88 percent chance of a Fed hike in June.

But that belief would quickly change if the inflation readings come in weaker than expected, according to economists. That would send the yield on treasury bonds plunging and bond prices higher. U.S. stocks would likely also rally on the news.

Bond prices would be driven down further and stocks could also head lower if inflation shows strength in these reports, especially in the core-CPI reading, as fears of the Fed tightening take even greater hold on the market.

"I think that (high inflation readings) would be almost the last straw to convince the Fed," said Ethan Harris, chief economist at Lehman Brothers.

"It doesn't convincingly prove there's acceleration of inflation. But right now markets are telling the Fed, 'You guys are losing your credibility,'" he said. "The Fed does take a look out of the corner of its eye at what market is saying."

The PPI will also be watched by investors Thursday, but mostly for clues of what Friday's CPI might be saying. Signs of inflation in wholesale prices are less of a concern to the Fed and investors if they aren't being passed onto consumers at the retail level.