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.
Worthwhile Canadian Initiative 
Alright, I’ll be the first lackey – I’ll write out the explanation that jumped into my head, although I think I’m missing something.
Isn’t the usual story that consumption (of fruit) drops as the interest rate is too high, as the consumption path of the representative agent that maximises utility now requires substituting more consumption to future periods? Because the agent receives a higher return now – if the agent can save in the current period, the higher return provided in the current period facilitates higher consumption in future periods than otherwise would be possible if the central bank had not made the mistake.
The agent can’t do this by decreasing leisure (under what I would consider leisure to be in this model – an activity that is costless and provides no return). If the agent consumes in large amounts in the current period – a fall in the consumption of leisure in the current period – it is essentially forgoing the higher return offered by the central bank.
I read my comment twice, and I can tell I’m missing something. My answer smells like partial equilibrium thinking…
I’ll post this comment and think about it more.
Ben: your paragraph about the usual story sounds right to me. But why can’t we apply that same story to consumption of leisure instead? If I consume less leisure (work more hours) today, I can save the extra wages, earn interest, and spend it in the future by consuming more leisure (working fewer hours).
Isn’t it that a lower real interest rates causes households to want to a) consume less currently; and b) work more currently, so we simply have a disequilibrium where the lower amount prevails?
Nick E: was that a typo? Did you mean higher real interest rates?
Yes
Nick E: OK. I thought it was a typo. But it might also be a Freudian slip, where you anticipated my next question:
By “…we simply have a disequilibrium where the lower amount prevails…” you presumably mean the “short side rule”, i.e. : Q = min{Qs,Qd}. Actual quantity traded is whichever is less: quantity supplied, or quantity demanded. OK.
You have the first step in what I think is a good answer.
But here is my next question, just for you:
Start again in equilibrium. Now assume the central bank makes a mistake, and sets the interest rate too low for one period. Why does the NK model say this causes an increase in consumption of fruit? Why doesn’t the NK model say this causes an increase in the consumption of leisure?
Does it not do so? Again, I’d imagine lower rates would cause households to want to a) consume more currently, and b) work less currently (got that the right way round, now). So again we have a disequilibrium, presumably again with reduced output, but maybe the effect on working hours is less than on consumption, so the fall in output is less that way round?
Nick,
Interesting. So if labour markets were monopolistic and goods markets were competitive then would lower rates cause a recession?
That is probably just very naive but isn’t leisure the opposite of labor? Would that not suggest that when people work less to consume less, leisure automatically increases?
“Why don’t too high interest rates cause a boom in output and employment?”
I assume you know that the consumption Euler equation is not really backed by the data (http://noahpinionblog.blogspot.com/2014/01/the-equation-at-core-of-modern-macro.html) so the NK model has a big question mark there.
My take to your question is that the causality is the other way around: With high spending (=output) you have less saving but a higher demand for capital which will increase rates.
Nick E: your argument (that starting in equilibrium, if the central bank set either a higher or a lower interest rate, the result would be a fall in output) makes logical sense to me. But that is not what the NK model says will happen.
Anon: Thanks!
Was that a typo? Did you mean to say “monopsonistic”?
Odie: Yes. Leisure is the opposite of labour (in the NK model). So when the central bank sets the interest rate too high, so people want to consume less leisure, why doesn’t consumption of leisure decrease and the amount of labour increase?
Yes, I read Noah’s post. But those correlations alone tell us nothing. It depends on the source of the shock. Noah is implicitly assuming the shocks to real interest rates are random and exogenous. That is very unlikely, unless the central bank plays dice with interest rates.
Nick, the answer clearly depends on whether wages are sticky or not. In the canonical model prices are sticky, wages are perfectly flexible so the labour market clears.
In this case the answer is straightforward I think, the fall in consumption demand leads to a fall in labour demand (meaning the labour demand curve shifts). This moves us along the labour supply curve to a new, lower, real wage.
So, people consume more leisure because it has gotten relatively cheaper.
BTW, I think this is also the expected result. The real interest rate is the relative price of current consumption, it is not the relative price of current leisure. If the real rate is too high it’s current consumption that is relativiely too expensive, not current leisure.
And this story clearly does not require the existence of money.
Because interest is only paid on consumption of the products of labor and not the non-consumption of those?
Adam P: Welcome back!
“Nick, the answer clearly depends on whether wages are sticky or not. In the canonical model prices are sticky, wages are perfectly flexible so the labour market clears.”
I agree. That is part of the answer.
And there are two real interest rates:
1. The nominal interest rate minus price inflation (call it the “output real interest rate”).
2. The nominal interest rate minus wage inflation (call it the “leisure real interest rate”)
And the two real interest rates respond differently, depending on whether prices and/or wages are sticky.
Not a student obviously – but does it have something to do with asymmetry in the relationship to production?
Leisure isn’t produced – you’re talking more Rideau Canal skating, not a trip to Monaco.
The interest rate effect requires a linkage between something and production – i.e. consumption not leisure?
Higher rates encourage delayed gratification in terms of consumption – with the effect on leisure being determined as a residual of the interest rate linkage between consumption and production.
Total guess of course. Probably useless.
I am not sure I understand the model. If there is no investment or tradeable assets, then how do you move consumption into the future? What does it mean for the central bank to set an interest rate in this context. The way it could make sense is if the fruit is put in a storage bin and the central bank magically turns it into (1+r) times the amount of fruit in the next period. If that’s true, then higher than expected int rates would mean the central bank will produce more fruit next period to put in the storage bin. This essentially raises the marginal value of working as opposed to leisure. Most likely leisure would go down depending on the utility function, income/subs effects. It’s hard to see implications of this as it is partial eqbm model though, that is unless one can show how the central bank magically creates fruit.
Yeah I am thoroughly confused. I don’t know really know anything about these kinds model but I have trouble figuring out why the interest rate even matters in your world. Here’s a few thoughts/questions…
1. Are there markets where agents can trade a fruit for a debt contract? I’m thinking here of a Lucas model I remember where even if individuals are identical you still need an interest rate that guarantees they don’t want to trade, otherwise an accidental bump to the interest rate creates a glut of people offering consumption goods and not enough wanting to consume them!
2. Are individuals heterogenous?
3. IF there is no heterogeneity and no market for good-debt trades, why should there be an Euler equation here? There just doesn’t appear to be a link between today and tomorrow in your set up. What am I missing?
Deniz: “If there is no investment or tradeable assets, then how do you move consumption into the future?”
In aggregate, agents can’t. One individual can do it, provided he can find some other individual who wants to do it the other way. But what if all individuals want to move consumption into the future?
“What does it mean for the central bank to set an interest rate in this context. The way it could make sense is if the fruit is put in a storage bin and the central bank magically turns it into (1+r) times the amount of fruit in the next period.”
Good question. But that is not what the central bank is doing in NK models. The central bank does not buy fruit, and has no storage technology.
One question: When there is no investment how can consumption be forwarded into the future? Without investment I don’t see how interest rates even matter.
Ed:
1. Good questions. What is that other asset/debt contract? Who issues it? And what markets actually exist in this model? Who trades what in each market?
2 and 3. The simplest NK model assumes all individuals are identical. Each firm has a monopoly on the production of one variety of fruit. Each individual wants to consume all varieties. Symmetric model, with Dixit-Stiglitz preferences. Assume identical agents.
Back later.
Nick,
“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.”
Why would the representative agent want to consume less this period? Central bank sets the interest rate they will lend at too high and no one borrows at that interest rate. How does representative agent gain anything by substituting leisure for consumption?
“Good question. But that is not what the central bank is doing in NK models. The central bank does not buy fruit, and has no storage technology.”
Then I am not sure what it is that you are trying to model or ask here. The nice thing about ‘fancy maths’ is that it helps clarify all these implicit assumptions. Perhaps you should list them first. Suppose, as you say, there are heterogenous time preferences, then there’ll be trade. The interest rate will be the rate at which people trade fruit over time with each other. If the central bank sets a rate too high, this would be equivalent to a price floor. Borrowers will be scarce and those who cant lend will be forced to consume. So, consumption this period would then go up.
The comments are fascinating…
my 2 cents… Consumption would have to be interest rate dependent. If interest rates are raised, someone expects extra cost and lowers consumption. Likewise, someone expects extra return and raises consumption. Since there is no investment, I assume no savings. All income is put toward consumption, which would not change on balance. In the aggregate people are as free as before to enjoy their leisure. Yet, some may work harder to earn back their extra cost, while some work less from their interest rate boon.
The puzzle looks like a balance sheet issue between equals within the institutions of a somewhat closed commune style economy. Are there employer-employee relationships implied in the puzzle? Who is the implied representative agent?
Alright let me make a fool of myself.
Interest rate shocks are somewhat confusing to me, since I generally think of monetary policy as endogenous. Of course you can model it as partially exogenous, but I don’t have a good story of what goes on in that case. By monetary policy we of course mean an interest rate feedback rule a la Taylor. There is no money often times in these models. I think you can get the picture that NK models are kind of weird/interesting just by sticking to preference shocks and tech shocks.
First, you ask whether monetary policy is set according to inflation and output relative to the flexible price equilibrium or inflation and output relative to the steady state. I like to think about the former. In that case the monetary authority is trying to undo the effects of Calvo staggered pricing. Calvo pricing is a two edge sword. It allows monetary policy to be potent, but it is also what the monetary authority is trying to correct. In some sense you could say the monetary authority’s job is to make the world look like an RBC model. That is not strictly speaking true, since NK models incorporate monopolistic competition, etc which are not generally included in RBC models. There is more to it than just the Calvo pricing and sometimes monetary policy might be able to fix other things, but that is what is very important in the basic model. Overall, it at least helps me to think about what is going on.
Alright, on to preference shocks, meaning people become impatient and want to consume more today. Prices cannot increase enough with the Calvo pricing, so people consume too much, and don’t take enough leisure. The monetary authority sees that inflation is up (the Calvo fairy touched a few producers and allowed them to increase prices), and relative to the flexible price equilibrium output is too high (also high relative to the steady state). If everyone could have increased prices, there would have been less consumption (though still some). According to the Taylor rule interest rates would increase for both reasons, inflation, and too much output relative to the flexible price equilibrium.
Tech shocks are more interesting. A tech shock allows for more production today and more consumption, but prices cannot drop enough to reflect the full increase in productivity, (the Calvo fairy only touched a few people). Prices did drop so inflation is low or negative, but relative to the flexible price equilibrium output is actually too low even though output did in fact increase. Prices should have dropped a lot more, so there should be more consumption and output. The Taylor rule says drop the interest rates on both accounts to bring consumption forward before the tech shock runs out. Note that even without capital there is generally still a risk free bond or contingent claims in these models.
Now other variants of the Taylor rule might tell you something else. If you include growth rates of output or variations of output from the steady state, you might get the idea output is too high, which would tend for interest rate to increase counter acting some of the decrease in interest rates from the low inflation according to the Taylor rule once again. The question revolves around how do you get at the potential output changing.
@youngecon: if you like, assume there is a one-period shock to the rate of time preference, so agents become more patient. The central bank should cut the rate of interest, but it does not know about the shock, so leaves the rate of interest constant. This is equivalent to the central bank setting the rate of interest too high. Bu the time the central bank observes the lagged data on P and Y, and the Taylor Rule kicks in, it’s too late.
Deniz: ” The nice thing about ‘fancy maths’ is that it helps clarify all these implicit assumptions.”
I disagree. I think it is questions like this that clarify the implicit assumptions. Like, for example, whether barter is allowed.
Assume all agents have identical preferences. That is a very common assumption in NK models. So there will be no intertemporal trade in equilibrium. So how does the central bank setting the rate of interest too high screw things up? Good question.
“Assume all agents have identical preferences. That is a very common assumption in NK models. So there will be no intertemporal trade in equilibrium. So how does the central bank setting the rate of interest too high screw things up?”
So now, this is making no sense to me. No trade, no investments, no assets, right? So people either pick fruit or enjoy leisure. Interest rates are meaningless now, as there is nothing t pay interest on. So they will have no effect on consumption.
Now based on three different assumptions we have: decrease in consumption, increase in consumption and no effect on consumption in the first period. We didn’t even get to the effect of leisure/production substitution yet!
Perhaps you should clarify first what an interest rate means for leisure loving pickers of frutopia.
Deniz: “Perhaps you should clarify first what an interest rate means for leisure loving pickers of frutopia.”
Yep. What does an interest rate mean in an NK model? That is one of the questions this post is about. WTF is really going on in NK models? What are the implicit assumptions?
Nick,
Actually, I meant monopoly labour supply. But I’ve rethought it, and I think the solution to your question is more general than the NK model. An agent optimizes intertemporal utility by having utility grow at the real rate (otherwise they will borrow/lend to smooth consumption further). So if the real rate is raised, consumption growth must also rise assuming utility is increasing in consumption. Given normal preferences, it makes sense that the new optimum is formed by reducing consumption/labour a bit right now and increasing both a bit tomorrow. (The utility loss is quadratic at the optimum, so it makes sense to do two half changes in opposite directions rather than one full change in one direction). So we get a recession.
“So how does the central bank setting the rate of interest too high screw things up? Good question.”
You have to find the Nash equilibrium. Lets say the bank raises the real rate, but no one changes their plans: consumption, production, prices and wages. Except me, an infinitesimal agent. I reduce my consumption and increase my production. That means all the rest of you end up in debt to me at a the new high rate of interest. In every transaction (labour and consumption) there is a debtor and a creditor and I just ran a surplus! If the rest of you don’t change your prices in response to the change in interest, you are allowing yourselves to be arbitraged by me. Once you all see what I’m doing, you will also rationally change your plans in accordance with the consumption Euler equation (the Nash equilibrium) and we will get an output gap (but without any actual lending taking place).
A lot of people seem to be confused about lending in the NK model in the above thread. You need to think of the NK model as a model of a competitive commercial banking system. Everyone has an account that can be in positive (deposit account) or negative (like a line of credit) balance. Whenever a transaction (goods or labour) occurs the buyer’s account is debited and the seller is credited. You can’t transact without incurring an entry into the central ledger. And all accounts earn the central banks policy rate.
If everybody is identical then nobody has any actual balance, but that doesn’t matter. At the margin each person can decide to run a surplus (deficit) and save (borrow). It is irrational not to let that choice effect one’s intertemporal consumption/leisure plans. It is only at equilibrium that no actual lending takes place, but the out-of-equilibrium arbitrage opportunities are critical for determining the equilibrium.
“1. The nominal interest rate minus price inflation (call it the “output real interest rate”)”
When you have a price then I guess you need money in the model?
Pure credit economy:
“A state of affairs in which money does not actually circulate at all, neither in the form of coin… nor in the form of notes, but where all domestic payments are effected by means of… bookkeeping transfers”
Wicksell (1898)
ht: Woodford (2003)
Okay I think I see what is going on.
Essentially, the bad monetary policy is causing extra welfare loss on account of sticky prices. You cause people to do something they wouldn’t otherwise.
Let me first point out that in my above post I was always referring to the nominal rate, you can work through what said and see what happens to the real rate etc.
Lets say there is an exogenous increase in nominal i. The model wants to go to the RBC monetary neutrality case, but can’t. What do I mean by that: if nominal i goes up, generally with neutrality prices would go up to keep the real rate constant. With Calvo pricing you won’t get all the inflation to keep the real constant, so the real must increase. This induces consumers to postpone consumption, and take leisure. Essentially the supply of labor has decreased increasing the nominal wage. In these simple models the monopolistic competitive firms set prices as a markup over marginal cost, with marginal cost being the nominal wage relative to productivity (constant returns to scale in labor is the production function). Therefore, with the nominal wage going up, prices increase for the producers with the ability to raise. We get the limited inflation that was postulated at the beginning. We have some sense of general equilibrium. The loss comes from the fact that you are introducing a wedge in the prices the induces the agents to doing something they wouldn’t otherwise. The loss is in utility terms. This is assuming a pretty standard Taylor, it could be different otherwise. I would have to think more on why.
The Fed changes a nominal price, but some other nominal price can’t change, so relative prices change. The Fed has cause a distortion of behavior = bad.
Anon,
“You have to find the Nash equilibrium. Lets say the bank raises the real rate, but no one changes their plans: consumption, production, prices and wages. Except me, an infinitesimal agent. I reduce my consumption and increase my production. That means all the rest of you end up in debt to me at a the new high rate of interest.”
Don’t you have to assume that all debt contracts reset to the increased real rate set by the bank (assuming the central bank can in fact set a real rate)?
“Once you all see what I’m doing, you will also rationally change your plans in accordance with the consumption Euler equation (the Nash equilibrium) and we will get an output gap (but without any actual lending taking place).”
Why would I necessarily act rationally about the whole thing? I may want to stay out of debt to you and I may not want an output gap. And so if you raise your production by 5% and cut your consumption by 5%, why couldn’t I raise my production by 20% and raise my consumption by 10%?
Nick, are you going to eventually tell us your (potentially non-unique) answer at some point? The suspense is killing me! 😀
Okay, I’ll probably get this wrong because I do not have a PhD and I only took only one class dealing with NK models. I love a puzzle though, so I’ll risk the embarassment nonetheless. Here is my intuition:
1. Households always act to satisfy two considions: a)the return to saving an incremental amount must just equal the utility cost in terms of forgone consumption (i.e. the Euler equation) b) the utility cost of working an incremental unit of labour must just equal the utility benefit of consuming the proceeds of that work (e.g. the real wage, this is the labour supply equation).
2. When the interest rate mistake occurs, households will want to shift consumption into the future because the return to saving will be higher (i.e. satisfying condition a). This also causes the marginal utility of an incremental unit of consumption to have upward pressure(i.e. due to diminishing marginal utility, the household is hungrier from saving more, so the fruit tastes better). Condition b) then implies that household would want to supply more labour at the prevailing wages prior to the shock (i.e. since the fruit tastes better, the reward to working is enhanced).
3. Turning now to the goods market, at the prevailing prices, houses will demand less output today. Firms, unable to change prices, will tend to sell less stuff and will want to cut output.
4. Look at the labour market now: With firms cutting output, their demand for labour will be reduced. Household labour supply is increased though, so there will be downward pressure on wages.
So with all these competing forces, what will the general equilibrium behaviour be? Because the wage is assumed to be fully flexible, it will move to make everyone happy with their decisions. It will fall suffiently so that households are happy supplying the amount of labour that firms demand, which in turn will be driven by household desires to consume less today. Inflation expectations take care of satisfying intertemporal plans -households will expect that tomorrow, when firms reset prices, they will lower them such that even with the lower labour income, households will be able to buy more, yielding the desired timepath of consumption.
Pat M: Quoting myself (from my comment above):
And there are two real interest rates:
1. The nominal interest rate minus price inflation (call it the “output real interest rate”).
2. The nominal interest rate minus wage inflation (call it the “leisure real interest rate”)
Tell us what happens to both of those real interest rates.
Nick, I couldn’t help notice that Stephen Williamson referred to this book:
https://mitpress.mit.edu/books/big-ideas-macroeconomics
And it is supposedly written for the layman. I saw Glasner’s review. Have you read it? If so, do you recommend it for someone like me? Will it help me to understand these kinds of posts (and your previous one)? Or am I better off with wikipedia. Lol.
BTW, reading Williamson’s comments, I have to say that it’s a little shocking how some of you macro types talk to each other (specifically Williamson, Noah, Quiggin, Krugman, DeLong, etc.). Are you and Glasner outliers (on the good side) on the macro politeness distribution. Are you guys (in general) like this with each other when you meet face to face at conferences?
(even when you are harshly criticizing a fellow economist, I rarely sense the personal animus in you that I often do in some others: and BTW, my list above is FAR from complete, in either the polite or impolite categories)
Tom: I haven’t read it. I would suggest a macro textbook. Say Mankiw’s second year text. Good basic coverage of the field.
I’m not always as polite as I should be. Macroeconomists are better behaved in person, usually.
OK. Part of my answer:
Suppose we changed the standard NK assumptions:
Assume perfectly flexible prices, instead of sticky prices.
Assume sticky wages, instead of perfectly flexible wages.
Assume a monopsonistic labour market, instead of a perfectly competitive labour market.
Given those new assumptions, if the central bank set the interest rate too high, there would be an increase in output and employment.
Pat M,
“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?”
Because most debt contracts are not floating rate. Imagine an economic system where the central bank sets a nominal interest rate and immediately all previously incurred debt contracts are reset to that rate. In this economic system there is no timing arbitrage – I can’t borrow now when nominal interest rate is low and save later when nominal interest rate is high.
And so,
“When the interest rate mistake occurs, households will want to shift consumption into the future because the return to saving will be higher.”
The return to saving will be higher, but the cost of previously incurred debt will also be higher. And so why wouldn’t the increased return on saving be used to service existing debt? No consumption shifting would occur.
Frank: the simple NK model assumes there is only a one-period interest rate. And nobody borrows anyway. And it wouldn’t matter anyway. That is just another red herring, that will lead Pat M off the scent he is following well.
Stop now.
I rather expect that there is linguistic confusion here, that leisure and fruit are sufficiently different that it does not make much sense to speak of consumption as applying to both in the same way, and that two different meanings of consumption are thus being confused.
Now, if by leisure we mean something like going to the movies, then the two are similar enough that we should expect that a reduced desire to consume might affect both in the same way. We eat less fruit and go to fewer movies.
One difference is that the consumption of fruit involves the consumption of leisure, but not the other way around. I can “consume” leisure without eating fruit.
Nick Rowe: “Leisure is the opposite of labour (in the NK model).”
Here lies the root of the linguistic problem. Leisure is not the opposite of labour. Idleness is, to use the older term for not working. “Leisure” has connotations that cloud the mind. Would we really talk about “consuming” idleness? Idleness is not a good. It includes leisure (though they overlap) and rest, which are good, as well as boredom, which is bad. Being too idle is a problem in a way that having too much fruit is not. The confusion between leisure and idleness is the basis for the joke about the Great Vacation of the 1930s.
Nick, on the two rates:
The production rate: Nominal rate is up due to the mistake, expected price inflation is down. I forgot to add in my original comment that this would be due to the staggered price setting. That is, some firms would have been able to lower prices during the period that the mistake ocurred, but not enough to fully offset the reduced demand for consumption. These firms would be stuck with lower prices in the next period, causing firms that change their prices in the next period to want to match the lower price. So, the net effect would be that the expected real rate between the mistake period and the next one would go up.
The leisure rate: Nominal rate up, current period wages down. Next period, as a result of the lower price in the goods market and the desire among households to consume a bit more than in the mistake period, equilibrium in the goods market will be at a higher level of output. Labour demand will increase, wages should go up. So looks like positive wage inflation. My guess is that it will be just enough to keep the leisure rate constant.
I think this is leading toward the result that because wages are flexible, the leisure rate can adjust so that the time path of the household’s labour income is consistent with the household’s desired time path for consumption. The leisure rate is the flexible rate, so it does all the adjustment to achieve equilibrium.
…BTW Nick, it occurred to me that what you would call “good monetary policy” a hyperinflationist (or other doom & gloomer) might call “postponing the inevitable.” … Ha! And thanks for the Mankiw tip (I’m compiling a list of terms / concepts I need to learn under “Stuff Tom should learn” on my blog).
Pat M: very close, but not quite there.
Next period, the central bank fixes its mistake, and the economy returns to the natural rate of everything. Nominal wages have to fall enough this period, so they are expected to rise enough next period, to make the real rate of interest on leisure go down. So that people wish to consume more leisure this period. (Maybe it would be more complicated with a non-separable utility function.)
Important lesson: there are two real interest rates in the simple NK model, one for consumption of fruit, and one for consumption of leisure. Those two real interest rates move in opposite directions when the central bank sets the nominal rate too high and causes a recession. They move in opposite directions because prices are sticky but wages are perfectly flexible.
But what would happen to the model if both prices and wages were equally sticky?