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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?

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.

> 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 the answer there the diminishing marginal utility of leisure?

With a flat time preference and a horizon of now and one period in the future, I maximize my total utility when "now" and "the future" look the same -- I work the same number of hours, consume the same amount of stuff, and have the same amount of leisure.

We don't *need* money in this model; we just need one good that can be stored (stuff that is consumed) and one good that can't. We could just as easily replace "interest" with "wine that gets nicer with age," only then the idea of the central bank setting wine-niceness-rates makes no sense. Leisure, on the other hand, cannot be banked.

Because interest is only paid on consumption of the products of labor and not the non-consumption of those?

> We could just as easily replace "interest" with "wine that gets nicer with age," only then the idea of the central bank setting wine-niceness-rates makes no sense. Leisure, on the other hand, cannot be banked.

Addendum to the above: this might also be a decent way of separating real from nominal shocks.

A real shock happens when wine doesn't get as nice with age and everybody knows about it. Production of wine vis a vis leisure will change, but it's probably still at the efficient frontier.

A nominal shock happens when wine doesn't get as nice with age, but it comes as a total surprise. Production *doesn't* adapt, which means that relative to how things could have gone there is a relative shortfall of net utility.

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! :D

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?

You get interest for forgoing something now for the promise of more of something (the same thing or a different thing) later.

The higher the interest rate on fruit the more you forgo fruit now for fruit tomorrow
The higher the interest rate on leisure the more you forgo leisure now for leisure tomorrow

In a model with money , both fruit and leisure can be exchanged for money, and then this money can be exchanged for the promise of more money in the future.

In a a model with no money then you can barter any combination of present leisure, present fruit, future leisure , future fruit against each other.

If the price for present v future transactions is controlled by the authorities and they get it wrong you will get a distortion.

Yep I got some Euler equations mixed around, but I think what you are getting at is displayed in figure 1 here:

http://web.cenet.org.cn/upfile/103912.pdf

Though there is more stuff going on in that model.

The standard New Keynesian model actually has two real interest rates: the nominal interest rate minus expected price inflation and the nominal interest rate minus expected wage inflation, which is apparent if you look at the first order conditions. Calling the former the consumption real interest rate (which I prefer to the name output real interest rate) and the latter the leisure real interest rate (following your terminology). The consumption real interest rate is relevant for intertemporal substitution of consumption, while the leisure real interest rate is what is relevant for intertemporal substitution of leisure. When the central bank sets the nominal interest rate "too high," desire current consumption decreases since the price of current consumption vs. future consumption rises. However, since prices are sticky, the current price level cannot fall sufficiently to create the increased expected inflation necessary to keep the consumption real interest rate at its natural rate. Thus, consumption and output fall. This fall in consumption demand, causes labor demand to fall. However, in the canonical New Keynesian model, wages are fully flexible, and so, the level of wages falls as a result of the decreased labor demand. This fall in the level of wages allows expected wage inflation to increase sufficiently such that the leisure real interest rate actually falls (because the level of wages is being forced to do some of the work that the price level cannot do). Thus, agents substitute current leisure for future leisure. The result is that consumption falls, while leisure increases (causing output supply to decrease sufficient such that the output market clears, which is assumed in the canonical New Keynesian model). The key is, therefore, that prices are sticky, but wages are flexible in the canonical New Keynesian model. This is my guess at an answer.

Sorry, I only read the first couple of posts before I wrote and posted mine... I see that you basically said what I did.

If prices and wages are sticky, I think that the result of the central bank picking a nominal interest rate that is "too high" will depend on whether prices or wages are more sticky. If prices are more sticky, a recession will result. (Same argument as before, but those wages that are able to adjust will have to fall by more to get the level of wages to fall sufficiently.) If wages are more sticky, a boom will result. (Wage inflation will not increase sufficiently to keep the leisure real interest rate from rising, so labor supply will increase. This will cause output supply to increases sufficiently such that the price level will fall sufficiently (those firms that are able to adjust prices will decrease prices by more than if prices were fully flexible) to create enough expected price inflation to get the consumption real interest rate to fall. This will increase consumption enough to clear the output market.) If both are equally sticky, then the consumption and leisure will be unaffected because the two previous effects will cancel out.

Alexander: "If both are equally sticky, then the consumption and leisure will be unaffected because the two previous effects will cancel out."

To keep it simple, assume both P and W are stuck for one period. And assume the labour market is perfectly competitive. Start in equilibrium.

Remember the "short side rule": Q=min{Qd,Qs}. Actual employment is whichever is less: labour demanded or labour supplied.

If the central bank raises the nominal interest rate, both real interest rates will rise, demand for fruit will fall, and we get a fall in employment. (Labour demanded falls because firms can't sell as much fruit, so we get an excess supply of labour.)

If the central bank cuts the nominal interest rate, both real interest rates will fall, demand for leisure will rise, and we get a fall in employment. (Labour supplied falls, so we get an excess demand for labour and an excess demand for fruit.)

I haven't followed all the conversation above, but my first thought is whether this would change by adding investment. You would think you'd reduce leisure too to work more to buy more leisure in the future now. But if there's no investment I don't see how demand for labor would increase and I'm wondering if that's part of the reason why only consumption adjusts.

All: let me sketch my answer:

First, there is money in the NK model, both as medium of account (prices are sticky in terms of money) and medium of exchange (there is a fruit market (strictly, n fruit markets) where money is exchanged for fruit, and a labour market where money is exchanged for labour). There is no market in which apples are traded for bananas. There is no market in which labour is traded for fruit. The absence of those barter markets is what makes it a monetary exchange economy.

Like Anon says above, though it's simpler to ignore commercial banks and assume everyone has an account at the central bank, which can have either a positive or negative balance, and where the central bank sets the rate of interest it pays on holdings of that money.

There are two real interest rates in the NK model: the real interest rate on fruit (nominal interest minus fruit price inflation); and the real interest rate on leisure (nominal interest minus wage inflation). Those two real interest rates move in opposite directions in the NK model when the central bank changes the nominal interest rate exogenously. That is why desired consumption of fruit and desired consumption of leisure move in opposite directions when the central bank changes the nominal interest rate.

It matters that the NK model assumes sticky prices and flexible wages.

It matters that the NK model assumes monopoly power in the output market and perfect competition in the labour market.

For example, if you assume sticky wages and flexible prices, and monopsony power in the labour market, you get exactly the opposite results to the standard NK model. If the central bank raises the nominal rate the real leisure rate rises, so people demand less leisure, supply more labour, and employment rises. Firms would like to cut wages but can't. So profit-maximising firms hire more workers now that more are willing to work, because MPL > W/P, and cut prices to sell more fruit. And if the central bank cut the nominal interest rate, employment and output would fall, because labour supplied would fall, as agents demand more leisure.

In the standard NK model, if the central bank increases the nominal rate, the real rate on fruit rises, and the real rate on leisure falls. Because W is flexible and P is sticky.

And since there is monopoly power in the fruit market, so P > MC, firms always want to sell more fruit **at a given P** than they actually sell. If we define "quantity supplied" as the quantity of fruit firms want to sell **at a given price**, there is always excess supply in a monopolistic market, even in full equilibrium. And if prices are sticky, which they are in the SR in the NK model, firms will choose to increase output when quantity demand increases and they can't change P. That would not happen if the output market were perfectly competitive, because firms would already be selling as much as they wanted to sell, and would simply ration customers if demand increased at given prices.

If we assume that both P and W are equally sticky, then the only way a cut in interest rate by the central bank would increase employment would be if you assume monopoly power (unions) in the labour market too, so there is always an excess supply of labour **at given W**, even in full equilibrium.

The "short side rule" says that Q = min{Qs;Qd}. Quantity actually bought-and-sold is whichever is less: quantity supplied; or quantity demanded. In a perfectly competitive market, in full equilibrium, Q=Qs=Qd. If the price is too high, Q will drop because Qd drops. If the price is too low, Q will drop because Qs will drop. We get a drop in Q if the central bank makes a mistake in either direction. But if there is monopoly power, so the price is "too high" initially, then Qs > Qd (at given P) even in full equilibrium. So Qd is what matters. And if there is monopsony power, so the price is "too low" initially, then Qs < Qd (at given P) even in full equilibrium. So Qs is what matters.

Daniel: it wouldn't change if you added investment. Even though it is true that adding investment means you break the link between consumption of leisure and consumption of fruit. If the central bank raises interest rates, you would get a fall in both consumption of fruit and investment, and get an even bigger increase in consumption of leisure.

Nick,

"And if there is monopsony power, so the price is "too low" initially, then Qs < Qd (at given P) even in full equilibrium."

So you are saying that *any* kind of monopsony (labour or goods) would tend to reverse the sign of the elasticity of intertemporal substitution? And the relative amount of wage vs price stickiness also reverses the sign. So for example, a labour monopsonistic high sticky wage economy would be similar (in this regard) to the standard NK model?

If so, it's unusual in the sense that for most other variables in the economy we wouldn't think of a goods monopoly and a labour monopsony as having offsetting effects in GE.

Anon: I'm not 100% sure.

Take a simple example, where we consolidate the labour and output markets. Self-employed hairdressers. P and W are the same thing. Assume sticky P. Start in full equilibrium.

If the market for haircuts is perfectly competitive, an increase in R reduces Y, and a decrease in R also reduces Y.

If the market for haircuts is monopolistic, we get the standard NK result. (This is Larry Ball's old model of yeoman farmers). Increase in R reduces Y, and decrease in R increases Y.

If the market for haircuts is monopsonistic, we get the opposite results. Increase in R increases Y, and decrease in R reduces Y.

Now back to the regular case where we have both a labour market and an output market. If one is monopolistic and the other is monopsonistic, and if both P and W are sticky, then I *think* we get the same results (qualitatively) as when both are competitive. Starting in full equilibrium, either an increase in R or a decrease in R will reduce Y. Because one will reduce demand for output, and the other will reduce the supply of labour, and either of those two would reduce Y.

Yep, I think that's right. Full equilibrium Y would be lower than in a competitive economy, of course. But the effect of changes in R on Y would be qualitatively the same as in a competitive economy.

I'm not 100% sure about the *any* amount of P and W stickiness bit. That does seem a bit strange. It probably doesn't hold if W is close to being flexible, and P is much stickier. But I can't quite figure it out. I expect that's where you need math!

OK, I think that if W wasn't perfectly flexible, but was still flexible enough that the real rate of interest on leisure fell when the central bank increase the nominal rate, you would get standard NK results (qualitatively).

I *think* that if W is not a jump variable (which seems a reasonable assumption), then the mere absence of monopoly power in the labour market would be sufficient to reverse the sign of the impact effect of an decrease in R. Because W/P will not jump, and the real rate on leisure will fall, so labour supplied will fall, so employment will fall.

But I am having serious doubts about stability. Will firms want to raise P and W or lower them??

[edited to fix typos NR]

"Desired consumption of fruit and desired consumption of leisure move in opposite directions when the central bank changes the nominal interest rate."

Perhaps I'm thinking about this wrong but won't they move in the same direction ?

Assume I'm working 40 hours a week and get $100 of which I save $20 and spend $80 on fruit. The CB raises the nominal interest rate. I want to save more so I'll consume less fruit. But won't I also want to work more (consume less leisure) since each unit of leisure I give up is now worth more future fruit?

I can see that the result will be increased supply of labor and reduced demand for fruit but this is precisely because my demand for both fruit and leisure has fallen. This (with perfectly;y flexible prices) will lead to both w and p falling and real interest rates moving in the same direction too.

Perhaps this changes when you have p and w with different degrees of stickiness ? (if p falls less than w then real w has fallen so I will value leisure more).

Nick,

I'm reading you. Not commenting only because I can't figure it out. I need a mathematical model, but that's not so simple. Maybe Adam P will deliver us the truth in his drive-by shooting style. I'm more than willing to take a bullet for enlightenment.

Um,

I'm afraid Nick, has played a trick, for his question is Keynes' parable of the banana!

"In the story Keynes envisions a simple economy that produces and consumes only bananas and in which “ripe” bananas keep only for a week or two. There is a thrift campaign in that closed economy to increase saving with no corresponding increase in investment in bananas. With the same amount of bananas being produced as before the thrift campaign, savings will lower demand, causing the price to fall. This might seem desirable, Keynes points out, for it may increase saving and reduce the cost of living. However, if wages have not changed along with the falling price, the cost of production becomes greater than the revenue represented by the price and businesses will lose an amount of money equal to the saving rate. The consequence is that businesses need to cut costs by lowering wages or by firing workers, and this only makes matters worse. As the overall income level falls, this pushes the economy into a deeper recession. Keynes argued that the best way out of the economic downturn is for the central bank to pump more money into the economy to increase investment." (Encyclopedia.com)

Thanks to Min, for us Paleo-Keynesians, it is leisure, not idleness, watching these angels dance.

TMF: There are four goods: present C, future C, present L, future L

Let i be the nominal interest rate:

Trade off between present C and future C, relative price i - price inflation

Trade-off between present L and future L, relative price i - wage inflation

Trade off between present C and present L, relative price W/P

etc.

Anon: Are you following the bit with self-employed hairdressers, where there is monopsony?

Ron: Yep, but we shouldn't be surprised if the New Keynesian model is in some respects similar to what Keynes said. But there is a difference between the thrift campaign in that example and the central bank increasing interest rates in my example. (And the encyclopedia bit you quoted gets the national income accounting wrong.)

A highly simplified version of this story appears to be

- start in equilibrium
- CB increases the rate it offers on money
- This makes fruit and leisure less desirable
- wages are flexible and prices sticky so wages fall and so does qty of fruit sold until we get a new equilibrium at a much lower level of fruit production
- at this point real wages are expected to grow and prices fall in the next period.
- this means the real rates on labor and fruit go in opposite directions.

Its that last bit that worries me. Wouldn't that create arbitrage opportunities in the futures markets for labor and fruit ? People could borrow at the going rate, buy future labor from workers at attractive prices and still sell at a profit in the future. I think this would cause the price of future labor to fall. The same thing would happen with fruit future but in reverse. This would bring real interest rates on money, labor and fruit into line (assuming no expected productivity changes). I'm not sure how this fits in but it seems to complicate the story.

This might be a silly question, but why are you applying the "short-side rule"? New Keynesian models assume that both the labor and output markets clear. Non-trivially applying the "short-side rule" would imply contradicting the market clearing assumptions of New Keynesian models. Also, what are we assuming about the price level and the level of wages once the central bank realizes its mistake in the second period. To get expected wage inflation to rise, we need current wages to fall relative to future wages sufficiently. We have established that current wages will fall, but we have not established that future wages won't fall to offset this fall in current wages. Won't this depend on whether or not the central bank is targeting wage inflation?

Alexander: On the short-side rule:

Think micro for a minute. Compare two firms. One is perfectly competitive, the second is a monopoly. Start in full flexible price equilibrium, then fix the price by law. Then suppose demand increases. Will the firm increase output?

The perfectly competitive firm will not increase output, since it was already selling as much as it wanted to, where P=MC. Its profits will fall if it increases output.

The monopoly will increase output, since P > MC, and it will increase profit if it increases output.

In an important sense, a monopoly always has "excess supply" at existing prices.

"New Keynesian models assume that both the labor and output markets clear."

Labour market clearing -- yes.

Output market clearing -- certainly not. What even does "output market clearing" mean for a monopolistically competitive firm with sticky prices?

"Also, what are we assuming about the price level and the level of wages once the central bank realizes its mistake in the second period."

We are assuming that both P and W are not higher than they were before the central bank made the mistake. If the CB adopts price level path targeting (or wage level path targeting) P and W will be exactly the same as they were before the shock. With inflation targeting they would both be lower. (Everything relative to trend, of course).

"we shouldn't be surprised if the New Keynesian model is in some respects similar to what Keynes said."

Or at least not VERY surprised...

W.P. Yep!

OK, what was your answer to the brain-teaser?

I think output market clearing in a New Keynesian model means that the desired level of the Dixit-Stiglitz consumption aggregator equals the desire level of the Dixit-Stiglitz output aggregator and that desired consumption and output of each of the monopolistically-competively produced goods are equal. However, I get your point that monopolistically competitive firms do not have a supply curve and that p>mc for monopolistically competitive firms, and so, they will choose to increase their output supplied in response to an increase in demand, over some range, as a second best response if they are not allowed to increase their prices by as much as they would like. I think we were thinking of output market clearing differently.

Alexander: we are on the same page. (Should I edit your comment to delete that "desire" in the second line and replace it with "actual"? Because I think that was a typo.)

Normally. "market clearing" means; Qd=Q=Qs.

Here, in the output market, we have Qd=Q only.

Ok, I finally had some time to really think through the model and what should be happening. Sorry if the outcome may not quite fit with the NK model. First, households start saving (S) so consumption drops (C* = C – S). Without investment the only place to save is at the central bank (or equivalent: cash). If the central bank lends those savings out again (loans equal savings) then C* = C and not much has changed (but: household savings = firms debt). However, as the central bank has set the interest rate too high (as per assumption) savings > loans. Thus, S – loans > 0 and therefore C* < C. (The CBs “mistake” was then to not set the interest rate that S = loans resulting in savings being held as unproductive money balances.) Since C* is the only income of firms, they are faced with a reduction in sales (delta sales = C*- C). Unwilling to borrow the difference at the CB's interest rate they have to cut expenses = total wages W (Does not really change anything if we add profits here as they would also be income to the households). Two options:
1. With sticky wages firms have to lay-off employees.
2. With flexible wages, firms can reduce individual wages to maintain full employment.
In both cases W becomes W* which equals C and C*, respectively.
In 1) output of fruit will decline (assuming max productivity per worker, if not case 2 applies) and C*/Q* = P; prices will remain unchanged.
In 2) output will stay the same; thus C*/Q = P*; prices will decline. If prices are sticky, firms will accumulate excess inventory.

That should be the immediate outcome but lest not forget that the CB pays interest on the excess savings thereby increasing the money supply. The question then becomes when will the households use their savings plus interest income for consumption again. (Magnitude also matters here: At an interest rate of e. g. 5% households need 14 years to regain in interest payments what the economy had lost in income over one year due to money savings. That's a slow way to get out of a recession.)

I am sure Nick is shaking his head now ;-) but maybe he would not mind telling me where I am wrong.

Nick, O/T: I think I helped induce David Glasner into writing a post on Say's Law. You might be interested:
http://uneasymoney.com/2014/02/20/whos-afraid-of-says-law/

Odie: two mistakes:

1. Household income is the same as firms' revenues from the sale of fruit. Whether households receive that income in the form of wages or profits is immaterial.

2. Wages are perfectly flexible in this model, but it makes no difference to the level of employment **in this case** whether wages are fixed or flexible. If consumption of fruit drops, employment drops. If wages are fixed, that drop in employment means involuntary unemployment. If wages are flexible, wages fall to ensure the drop in labour supplied equals the drop in employment, so there is no involuntary unemployment. (But it would make a difference in the opposite case, where the central bank sets the rate of interest too low; if wages were fixed there would be no increase in employment or output, because labour supplied would not increase. Labour supplied would decrease, because of the cut in the rate of interest, so employment and output would fall.)

Tom: yep. I read it last night.

Odie: a third mistake: Net interest paid by the central bank is zero in this model. For every agent with a positive balance (green money) earning interest there is another agent with a negative balance (red money) paying interest. The net money stock is zero.

Nick Rowe,

James Randi once said that a magical change happens to PhD students at their graduation ceremonies, which makes them almost totally unable to say three short words: "I don't know".

I haven't graduated yet, so I'm quite at ease with saying that I don't know. I'm learning a lot from the discussion, though.

I think James Randi might have stolen that line from the (Canadian) Red Green show.

Really though, it's an open-ended question, masquerading as a closed-ended question, like all "Why?" questions. There are lots of different assumptions we could change in the simple NK model that would generate different results. There is no one right answer to a question like that.

I think it's been a good discussion too. The "short side rule" implicit in Nick Edmond's first comment, is one important lesson. We ought to learn that lesson in first year, when we draw a supply and demand curve, and then impose a binding price floor or a binding price ceiling. In both cases quantity drops. Because Qd drops with a price floor, and because Qs drops, with a price ceiling.

A second lesson, that hasn't been brought out yet in discussion, is that the labour demand curve in the NK model, for a given P, is perfectly inelastic. It doesn't matter how much W drops; if firms can't sell extra output they won't hire extra workers. It's a Patinkin/Barro-Grossman constrained labour demand curve.

One of the duties of old guys like me is to teach some of these smart young NK whippersnappers some of the old lessons!

Hi Nick,

"So profit-maximising firms hire more workers now that more are willing to work, because MPL > W/P, and cut prices to sell more fruit" If firms are competitive, they charge a price equal to marginal cost (and even if they are monopolistic but flexible price setters they charge a price proportional to marginal cost. Marginal cost is usually increasing or at most constant with labour hired. If firms were to hire more labour they would increase prices. Of course this would make the real rate of fruit higher lowering further desired consumption so firms would not be able to sell and use the extra labour supply. Unemployment would appear in to senses, first more people would be willing to work but no new "jobs" would be added. Second jobs would be destroyed to cope with lower demand. If marginal cost was constant prices would remain constant and the job loss would be proportional to the nominal rate mistake. If there are increasing returns, the drop in consumption would be dampened by the fact that as consumption fall so do prices (due to marginal costs drops).

In fact we have two Euler equations one for fruit the other for labour (or leisure) both will be satisfied however, firms can easily not hire people willing to work but hardly can force sells of fruit that no one is willing to buy. The only solution is unemployment so that the labour market doesn't clear.

A very nice presentation about this topic: http://www.crei.cat/people/gali/jg2013_jeea.pdf

Nick,

"Net interest paid by the central bank is zero in this model. For every agent with a positive balance (green money) earning interest there is another agent with a negative balance (red money) paying interest. The net money stock is zero."

Sounds like someone is borrowing and someone is lending.

"Frank: And nobody borrows anyway."

Which is it?

Hi Roger:

I disagree.

Assume that prices are perfectly flexible, wages are sticky (assume stuck, for simplicity). Assume a monopsonistic labour market, and a perfectly competitive output market. In other words, I have made the exact opposite assumptions to the standard NK model.

Suppose the central bank sets the nominal interest rate too high for one period. Everybody know the central bank will get it right next period, and the economy will return to normal, at the same nominal wage.

P will jump down, and will be expected to rise next period, so that the real interest rate on consumption of fruit actually falls, despite the rise in the nominal rate, so demand for fruit will increase.

W will stay the same (by assumption it's stuck), so that the real interest rate on leisure will increase because the nominal rate has increased, so supply of labour will rise.

So when the central bank makes a mistake, and sets the nominal interest rate too high, we get an increase in output and employment.

You say: "If firms are competitive, they charge a price equal to marginal cost..."

If firms are competitive in the labour market, then marginal cost will equal W/MPL.

If firms are competitive in both the output market and the labour market, then firms will set a price equal to W/MPL.

If firms are competitive in the output market, but have monopsony power in the labour market, it is not true that firms will set a price equal to W/MPL.

In a monopsonistic labour market, it would be profitable for an individual firm to increase output and employment at the existing W and P, but they they face an upward sloping labour supply curve and know they would have to increase W to attract more labour. (Just like in the standard NK model, with monopolistic firms, it would be profitable for an individual firm to increase output and employment at the existing W and P, but they they face a downward sloping demand curve and know they would have to cut P to attract more customers.) But if W is fixed, so they can't cut W when labour supply increases, they will increase output and employment instead. (Just like in the standard NK model, with monopolistic firms, if P is fixed, so they can't increase P when demand increases, they will increase output and employment instead.)

I skimmed Gali's paper. It's a good one, but is not so good on providing the intuition, and showing what role the different assumptions are playing. Too much math and simulations.

Roger: Put it this way:

Only if prices are flexible will monopolistic firms set P as a markup over W/MPL. With sticky P that markup will vary over the business cycle. Like in the standard NK model.

Only if wages are flexible will monopsonistic firms set W as a markdown under PxMPL. With sticky W that markdown will vary over the business cycle. Like in my anti-NK model.

I am being a very slow learner on this post because I still don't get this part:

"For example, if you assume sticky wages and flexible prices, and monopsony power in the labour market, you get exactly the opposite results to the standard NK model. If the central bank raises the nominal rate the real leisure rate rises, so people demand less leisure, supply more labour, and employment rises. Firms would like to cut wages but can't. So profit-maximising firms hire more workers now that more are willing to work, because MPL > W/P, and cut prices to sell more fruit. And if the central bank cut the nominal interest rate, employment and output would fall, because labour supplied would fall, as agents demand more leisure."


Its "profit-maximising firms hire more workers now that more are willing to work, because MPL > W/P, and cut prices to sell more fruit" in particular that is confusing me.


I seeing this from the perspective of a fruit-producer.

- I see the demand for my product fall (workers are saving more of their income)
- I lower prices as a result (and other things equal would reduce supply, right ?)
- All other fruit prices are lowering prices to so real P falls
- real W goes up (wages are sticky)
- but somehow despite reduced demand for my product at any given price and increased real wages I end up hiring more workers.


I'm thinking that the reason I hire more workers is because the real value of my profits has gone up a result of the falling price level. is that it ?
Perhaps this is just an example of "macro being hard", but I'm struggling to visualize the supply and demand curves that would deliver this result.


TMF: You missed this bit from my previous comment:

"P will jump down, and will be expected to rise next period, so that the real interest rate on consumption of fruit actually falls, despite the rise in the nominal rate, so demand for fruit will increase."

In the standard NK model, we have an exactly parallel explanation for why the demand for leisure increases:

W will jump down, and will be expected to rise next period, so that the real interest rate on consumption of leisure actually falls, despite the rise in the nominal rate, so demand for leisure will increase.

Lets say fruit is expected to rise in price by 10% between now and next period and the money rate of interest is 10%

To prevent arbitrage opportunities the fruit rate of interest would be 0% (I lend you fruit, and when I get it back next period I can sell it for a 10% profit, which is the same as if the loan had been in money).

But why will this make me consume more fruit in period 1 ? The return on fruit (expressed in money terms) is still higher than before (if the money rate has risen as assumed).

Am I mus-understanding what "real interest rate on consumption of fruit" means ?

Hi Nick,

I think I kind of get what you are saying, in the case of monopsonistic firms in the labour market but competitive in the fruit market, the price is not set by firms and wages are fixed (or sticky) so wages will remain more or less the same and the prices will adjust (by the power of the Walrasian auctioneer, just as in the standard NK model for wages) in order to clear the fruit market. But I don't see how we could scape from decreasing returns. If wages are fixed and prices are flexible we need a price increase in order to comply the labour demand condition, which would read something like w=(1/M)P*n^alfa. If firms are to higher more workers they need a higher and not a lower price. And I don't think that price stickiness would help for this. I hope that I'm more or less making sense since I haven't ever work with monopsony models.

TMF: Suppose initially there is no expected inflation, and nominal interest rate is 4%, so the real interest rate on fruit is 4% too. I am can swap 100 apples this year for 104 apples next year. Then the central bank increases the nominal rate of interest to 10%, the price of fruit jumps down instantly by 10%, so is expected to rise by 10% between now and next year. The real rate of interest on fruit has now fallen to 0%, so current demand for fruit increases. I can swap 100 apples this year for 100 apples next year.

If the real interest rate falls, I want to consume more now and save less now. The rward I get (in terms of extra fruit) for postponing consumption has fallen.

Sorry there is a higher that should be hire.

Roger: OK, assume diminishing MPL. Assume we are initially in full equilibrium. MPL > W/P, both in the NK model, and in my model.

In the NK model, if demand for output increases, firms increase L and Y, W/P rises, and MPL falls.

In my model, if supply of labour increases, firms increase L and Y, W/P rises, and MPL falls.

It's exactly the same. The only difference is that W/P rises because W rises in the NK model, and W/P rises because P falls in my model.

Let's switch this discussion to my new post.

Thanks Nick. I think I get it.

In effect as fruit is the only thing in the price index it's rate of interest IS the real rate and the money rate is the nominal rate.

So when an increase in the nominal rate causes fruit prices to fall by definition this will cause the real rate to start to fall as well if prices are expected to rise again next period.

Intuitively it seems possible that a 1% rise in nominal interest rates could cause a fall greater than that in the price index if prices are flexible. If prices are not flexible then this could never happen.

To finish the thought: If the price index falls by more than nominal rates have increased then real rates will move in the opposite direction to nominal rates and we will see the counter-intuitive results of the flexible price/sticky wage NK model (as long as prices are expected to bounce back next period).

TMF: yep. But with Calvo price-setting, the price level can't jump. It can only move continuously.

Nick, thanks for answering.

To 1): “1. Household income is the same as firms' revenues from the sale of fruit.”
If the firms borrow the savings back (as per your point 3) then firm spending = C* + loans + interest expense = household income = W* + interest income. Total household income remains unchanged, only the composition differs by the interest.

“Whether households receive that income in the form of wages or profits is immaterial.”
Was that not what I said (Odie:“Does not really change anything if we add profits here as they would also be income to the households.”)?

To 2): “Wages are perfectly flexible in this model, but it makes no difference to the level of employment **in this case** whether wages are fixed or flexible. If consumption of fruit drops, employment drops. If wages are fixed, that drop in employment means involuntary unemployment. If wages are flexible, wages fall to ensure the drop in labour supplied equals the drop in employment, so there is no involuntary unemployment.”
I am not sure I understand the flexible wages part. Do flexible wages mean people are “voluntary” working part-time? I always thought flexible wages meant people work full-time but just for less. Btw. If you assume that firms borrow the whole savings then the only reduction in W would be the interest expense (unless you assume they borrow it to have it sit in their CB account). Is there such an implicit assumption in the NK model that savings = loans?

“(But it would make a difference in the opposite case, where the central bank sets the rate of interest too low; if wages were fixed there would be no increase in employment or output, because labour supplied would not increase. Labour supplied would decrease, because of the cut in the rate of interest, so employment and output would fall.)”
Maybe I missed it but are we not assuming full employment so Labor supplied COULD not increase?

To 3): ”Net interest paid by the central bank is zero in this model. For every agent with a positive balance (green money) earning interest there is another agent with a negative balance (red money) paying interest. The net money stock is zero.”
If the CB is only setting interest rates and do the bookkeeping, interest can only be paid from borrowers to savers. As the households are the savers (per assumption due to consuming less) they will receive wages and interest income from the firms. The total will be the same but the question is if we assume a one period saving or multiple periods:

One period: Households save S, firms accumulate excess inventory of fruit (value S). Firms borrow S from households, pay Wages W* = W – interest. People stop saving next period, C* becomes C again. Firms either throw away some fruit or reduce prices to sell excess inventory. (Or: If W* means lower output but households spend their full income (W* + interest) then that excess could be reduced over time even with sticky prices.)

Multiple periods: Households decide to continuously save from their income (W* + interest). If firms keep their spending (W* + interest) constant by borrowing back the savings, total household income will be constant but W* will decline while interest income will rise (due to accumulation of savings = firm’s debt). C* will remain constant if propensity to save stays the same. With falling W* output should decline and prices will rise.

Thanks again, your model has helped me quite a bit understanding some points (although I am still not quite sure if I agree with the results of the NK model.)

Odie: "I am not sure I understand the flexible wages part. Do flexible wages mean people are “voluntary” working part-time?"

Yes. If the aggregate labour supply curve slopes up, which it does in the NK model.

The firms are not borrowing. There is no investment. If all agents are identical, nobody borrows or lends, or saves or dissaves, in equilibrium.

The contributors to this blog seem to be professional economists. I am not. I live in the UK. Ever since WW2 our economy has gone through booms and busts. The economic cycle. However the oscillations are amplified through time until we had the financial collapse of 2009. What is it about the economic system that causes these booms and busts? In your view. I have my own view. I have even published an e-book about it!

About the original Keynesian economics. The model was used by the UK government after WW2. However, Keynes said. I believe, that the exchange rate should be free floating. This was not the case back then. It was a matter of political pride to have a strong GBP linked to the Gold standard and then to the US dollar. Devaluation of the currency was cause for national shame.

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