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I would like to know what would be the response of variables in the Basic New Keynesian model but with flexible prices (ie not with Calvo pricing). For example I have troubles to see how having flexible prices will matter for a productivity shockk or for a decrease in interest rate of the central bank.

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I think what you are looking for is a standard RBC-model. Because the main step, going from RBC to New Keynesian, is to include Calvo pricing among other things. This is covered in many textbooks like Gali's, where he first introduces the RBC model and then moves on to the New Keynesian setup.

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As DoubleBass says basic New-Keysian model with fully flexible prices is RBC model, I'd just add that if you have already the set-up of Calvo and want to convert it to fully flexible prices you need to set the share of firms that cannot change prices to zero (i.e. if $\lambda$ is the share of firms that cannot change their prices in $t$ then set it to zero). And compute from there you responses.

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