Update: I sketch my own answer in the comments below.
This is a question for all students of New Keynesian macroeconomics. I mean "students" in the sense of "those who study", so that includes the profs too. It is a very basic question. There is no fancy math to fool you. If you cannot answer this question, then you do not understand the New Keynesian model. You have let the math fool you into thinking you understand it, just because you can solve the equations.
Assume the simplest NK model, with no investment, government, or foreigners. There is only consumption. But there are two sorts of consumption: there is consumption of produced goods (let's call it "fruit", with lots of different varieties of fruit); and there is consumption of leisure. Standard model.
Start in equilibrium. Now suppose the central bank makes a mistake, and sets the interest rate too high for one period. Intertemporal substitution of consumption kicks in. The representative agent wants to consume less this period, and so actual consumption drops.
Question: But why is it consumption of fruit that drops? Why isn't it consumption of leisure that drops? Why don't too high interest rates cause a boom in output and employment?
By the way: do you believe that nominal wages are sticky? And do you believe that employers have monopsony power, so an increase in the minimum wage could cause an increase in employment?
By the way: do you believe there is "money" in the New Keynesian model?
Macro is hard.
Update: I have an answer, but I'm not sure it's the only answer. I had to think about it, and I'm not sure I really understand it.