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 
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:
Click to access 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:
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.