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Dr. Rowe;

There is a college freshman error in your assumptions: The rational monopolist does not necessarily seek higher prices; he seeks higher profits, i. e,. a higher return on his capital. How does he achieve higher profits? - - - - by segmenting the market and exploiting the buyer's economic surplus.

While I can't say I have thought it through, the rational monopsonist is probably trying to do something similar -- perhaps the inverse(?),

Anyway what they may be trying to do -- and what happens to output -- has little to do with the money supply.

BigEd: Phew! I thought you were going to say I had made a hi skool math error, since I usually do.


The individual monopolist faces an imperfectly elastic demand curve, and sets a price above his marginal cost to maximise his profit (utility in this case).

The individual monopsonist faces an imperfectly elastic supply curve, and sets a price below his marginal benefit to maximise his profit (utility in this case).

To be fair, the monopsony-as-an-argument-for-minimum-wages argument is usually made explicitly as a micro/partial-equilibrium argument. Flexible prices and no income effects and all. The implicit assumption being that the minimum-wage sector is small relative to the rest of the economy, which it more or less is. (The argument is wrong for other reasons)

notsneaky: true. But isn't it the lowest paid and lowest skilled workers who usually get hit worst in a recession? If monopsony were prevalent among the lowest wage jobs and workers, their employment would expand in a recession, which is not what seems to happen.

Microeconomists and labour economists should not be allowed out unaccompanied by a macroeconomist. We should make macro a compulsory part of the curriculum, errr.

Nick - to follow on notsneaky's comments - what if the firm is a monopsonist w/r/t labor but a monopolist w/r/t the finished goods it produces (plausible if it owns IP or has increasing returns to scale)? In a recession, sales would go down, because prices are too high relative to the stock of money. This would shift the demand curve for labor, because the firm has less need for labor there is less demand for the product. In a vacuum, the "job openings" the monopsonist had in normal times due to setting a below mkt-clearing wage will be easier to fill as M decreases. However, the number of jobs the firm seeks to fill should decline with the demand for currently produced goods and services.
Just a story, but seems plausible as a story for some sectors of the economy.

In not an economist, so this may be completely off base.

I don't think that the mangoes in your model are a reasonable proxy for money. Mangoes have intrinsic value, money does not, so increasing M increases wealth in a way that increasing the money supply does not. If everyone in an economy suddenly had twice as much cash it would cause the value of money to be halved. This would apply even to the monopsonists' calculation of the optimal point on the supply curve.

Of course at the zlb that inflation would no longer be expected. But would the zlb affect your model in other ways as well?

louis: I actually published a paper with a model like that, many decades ago. But I can't for the life of me remember why I set it up that way.

I think it depends on whether wages or prices are stickier. With sticky P and flexible W, it works pretty much like the textbook model or my monopoly model here. With sticky W and flexible P, it works like my monopsony model here.

Andrew: not bad for a non-economist! What you say is roughly correct, but if M is a smallish part of the total economy, it doesn't make much difference whether it's paper or mangoes, because the change in wealth would be small either way, and I'm holding P fixed anyway for my short-run analysis. And it was simpler for me to set it up my way, because if M were paper money that is held to be spent again next period, rather than mangoes that get eaten at the end of the period, I would have needed a multi-period model.

I have a simple (cab driver) model of the labor market (and just the market):
Monopsony (one buyer -- ownership) should be balanced by monopoly (one seller -- labor union). The check (to the balances) is provided by the willingness of the (ultimate) consumer to pay.

I think progressive economists are mostly blind to the black hole of unopposed monopsony that the vast majority of not-collective bargaining Americans (not continental Europeans) have disappeared out of their sight into.

A $15 min wage would shift about 5% of income from the top 55% who now take 90% -- I would say marking the bottom 45%'s wages to market. If I'm right about the latter then -- given the tendency of people to keep wages they earn circulating among firms with similar wage structures -- any job losses will congregate mostly in the middle class (with concomitant job gains in the lower income class). :-0

Denis: assume monogamy. Suppose husbands could easily divorce wives, but wives could not easily divorce husbands (or vice versa). Husbands would then have more bargaining power than wives.

If a worker finds a better offer (say at higher wages), and his employer is unwilling to match it, he just gives one month's notice and accepts that better offer. No bad feelings. If an employer finds a better offer (say at lower wages), and his worker is unwilling to match it, can he usually just give the worker one month's notice, then replace the worker with the better offer? No bad feelings??

I'm confused.

Take the standard NK model with monopolistic firms. Now suppose that they also have some monopsony power, i.e. they perceive inverse labor supply curve w(n).

But this just means they prefer a higher markup over marginal cost when they can adjust their prices. If their price is sticky, output is demand determined and you get the usual effects.

You say, "Monopolists pick a point on the demand curve; so if prices are sticky, quantities traded are demand-determined. Monopsonists pick a point on the supply curve; so if prices are sticky, quantities traded are supply-determined."

In my example, it's the final good price that is sticky, so output is still demand determined. Firms are both monopolists and monopsonists.

But it seems you have something else in mind.

Nick: I think the missing dimension -- the most missed -- is the conception of the employees bargaining with the (ultimate) consumer. If Walmart could not "divorce" its employees for instance (combination of centralized bargaining and no replacement workers allowed), then, workers there could calculate that, at 7% labor costs, they could double their wages and only drive prices up 7%.

More practically, a $15 minimum wage should only add 3% to prices while adding 50% to Walmart's average wage -- at a small cost of business (and jobs); sounds like a good deal for the worker.

But, workers have to keep their eyes on the (ultimate) consumers.

Suppose competitor prices were about the same and the few percent price increase would not be matched all around. If that would cost too many jobs that would not be such a good deal. But it all goes back to the consumer.

Fast food wages could go up 50% and drive prices up maybe 15% -- but demand for food is somewhat inelastic (and 65% of McDonald's consumers come through the driver thru; not too poor). Again, the ultimate determinate would be consumer reaction to labor costs increase.

Actually, Nick, in your response to Denis, the answer seems to be yes, the firm can (and do) just give one months notice (or less) and some minimal severance pay and replace everyone. Even including in the severance agreement clauses prohibiting talking about the agreement or disparaging the company in the future, and requiring them to train their replacements. If they refuse, they're let go immediately with no severance pay. Lots of bad feelings, but no way to express them. Even if they could, would it matter?

Thanks for responding, here's another question. For monopoly you have the condition P > M/100 but for monpsony you have P < M/100. Why aren't they the same?

It's always hard/weird to mix non-perfect-competition and perfect competition in a general equilibrium model. In that case you do have to put the wealth effects in and it's going to depend on the elasticity of substitution between minimum-wage (unskilled) labor and non-minimum-wage (skilled) labor. Or the goods produced by each. How does the *relative* demand for minimum-wage goods and non-minimum-wage goods change in a recession?

Also, I think we talked about this before, if a "recession" in a monopsonistic market means a decrease in demand, then wouldn't employment and wages still fall because the MC curve is still upward sloping? Not as much as in a perfectly competitive market, but still in the same direction. I'm thinking of a downward shift in the MRP curve. Sorry if I'm repeating some previous disagreement again. (off the top of my head if I remember correctly the issue was whether the MC curve is flat or upward sloping)

jonathan: firms are a distraction. In the market for apples (or bananas) in my model, there are buyers and sellers of apples. If the individual sellers of apples face a downward-sloping demand curve for their apples, and if they set a price to pick a point on that demand curve, it's monopoly. If the individual buyers of apples face an upward-sloping supply curve of apples, and if they set a price to pick a point on that supply curve, it's monopsony.

In other words: is the price-quantity a point on the demand curve (monopoly) or on the supply curve (monopsony)?

notsneaky: "Also, I think we talked about this before, if a "recession" in a monopsonistic market means a decrease in demand,..."

It's not at all obvious what "recession" would mean in a monopsony. We associate "recession" with sellers wanting to sell more at existing prices. But in monopsony, it is buyers who always want to buy more at existing prices.


Fine. Call leisure apples and goods bananas. My example amounts to one set of agents (say, the alphas) having both monopoly and monopsony power. Thus they push up the price of the apples they sell, and push down the price of the bananas they buy, which amounts to the same thing.

I think it's plausible that there's one set of agents (firms = net buyers of labor) that have some monopoly and monopsony power over another set of agents (households = net sellers of labor). Which amount to the same thing.

That said, I need to think more about your example, because it does sound interesting (and look into this monetary overhang thing -- by the way, do you know of any good sources on how communist economies functioned? I think it's an interesting topic about which I know nothing. Comparative economic systems is yet another subject they don't have time to teach in graduate school these days).

jonathan: "Call leisure apples and goods bananas."

No. The apples the alphas eat themselves are leisure; the apples they sell to others are labour. The bananas the betas eat themselves are leisure; the bananas they sell to others are labour.

Or the alphas are plumbers, who have an endowment of 200 hours of time, which they can either consume themselves as leisure or home production; or sell to others as plumber's services. The betas are electricians.

I spent 6 months teaching macro in Havana in the late 1990's. That's all I know about it. I may have read a few things, but I can't remember what. My memory is a mess. Oh, I remember now. I read my colleague Richard Carson's book on comparative systems. It was good, but I have little or nothing to compare it to.

Barro-Grossman 1971(?) has a simple model that includes a "repressed inflation" regime, that is the same as "monetary overhang" and my "monopsony" regime.

Monetary overhang was very obvious at that time in Havana. At the margin, there were no goods to buy with extra money, so no incentive to work to produce those goods, and so no goods to buy. The classic Barro-Grossman supply-side multiplier. The economy seemed on the brink of collapse, then they opened the semi-free markets, and everything seemed to change a bit for the better in just one week. So I was teaching them that sort of macro.

jonathan: though I expect you could augment the model by adding retailers of apples and bananas, and assuming they have both monopsony and monopoly power. What happens when M changes depends on whether wholesale or retail prices are stickier.

jonathan: here's my old post on "The anti-NK model". It takes the standard NK model, and inverts it, by assuming monopsony power in the labour market, and sticky wages. The key equation is the "Consumption of leisure Euler IS". If the CB raises the interest rate, employment rises.

jonathan: here's a neat way to model it. Add retailers to my model in this post. Assume retailers have both monopoly and monopsony power, so the retail price is above the wholesale price. That creates a vertical wedge between the AD and AS curves in my picture, just like a tax wedge. Start in full flexible price equilibrium. If both retail and wholesale prices are sticky, an increase in M will cause a movement down along the curves, but the wedge must stay vertical, so there is a fall in A and B. (But a decrease in M will also cause A and B to fall.) If one of the two prices is flexible, the wedge will shrink or grow when M changes.

Firms are just retailers, who buy labour power at the wholesale price, and sell congealed labour at the retail price ;-) (Sorry for the Marxian BS)

When I think of a "monopoly", I am looking from the outside and thinking that all the players in the monopoly are taking advantage of their monopoly position. "All the players" would include labor, owners and enablers.

"Monopsony" is more difficult. The thought here is that labor is disadvantaged because of the monopoly power of the employer, with the employer not fully passing the advantages of the monopoly to the workers. This perspective begins with the tact assumption that the existence of a monopoly is good because it provides benefits; the problem is that the benefits go to the wrong people (not the workers).

If we shift our perspective back to someone looking from the outside , there is no such thing as "monopsony", there is only "monopoly". Whether the advantages of monopoly go to workers or owners or enablers, is of no matter to the "victims" of monopoly behavior.

So how does this post apply to the total economy? I am still struggling to make that application.


In this model, do we assume that the mangoes are consumed? We do see that the apples and bananas are consumed, but what about the mangoes?

Is the condition
(for P < M/100)
for monopsony a typo? Shouldn't it still be ">"?

Roger: by the end of the period, all apples, bananas, and mangoes will be consumed. (Mangoes are first used as money, then eaten). It's a one-period model.

Andrew: It's not a typo.


Actually, I think there are two ways you can draw an analogy between your model and a production setup.

The first is what you described: households all have an endowment of a particular type of labor, and they want to consume their own labor (leisure), and also other peoples' labor (consumption). Then firms are just a mechanism that allows people to do that. Your model takes the case with two types of households, and abstracts from firms.

But there is a second way of drawing an analogy. Suppose that households are born with an endowment of labor, and another agent called firms are born with an endowment of consumption goods. Both agents like consumption and labor, with firms' preferences representing their production functions. Then households sell their labor to firms (on the labor market), and use their wages to buy consumption goods from firms (in the goods market).

Under this interpretation, if apples are labor and bananas are consumption, then alphas are households and betas are firms. And in the NK model, the price of apples is flexible and the apple market is competitive, while the price of bananas is sticky and betas have monopoly power in the banana market.

It's almost poetic to imagine firms as beasts born with an endowment of consumption goods, that they will part with for the pleasure of seeing workers slaving away at their jobs. But this is mathematically isomorphic to the usual story.

"The alphas choose B to maximise U = log(200-A) + log(B) + log(M+PA-PB) taking A as given."

How might the alphas come to this utilization? When the alphas trade, two distinct populations of alphas (each with a distinct utility) are formed. This is the result of two events:

1. a-landers travel to b-land and buy bananas, leaving extra mangoes (M) in b-land.

2. b-landers travel to a-land and buy apples, leaving behind mangoes (M).

Assume that there are many players which allows the trade to occur incrementally during the time period required for adjustment.

Each player will have an interim utility. Let's follow it from the alpha side: Alphas travel to b-land to buy bananas. They take M on the trip and leave some quantity of M in b-land. The equation for alpha's utility when alphas leave b-land is:

Ua = log(200) + log(B) + log(M-PB).

The betas, who remain in b-land, will have a utility of

Ub = log(0) + log(200-B) + log(M+PB).

Correspondingly, the alphas who remain in a-land (but trade with b-landers) will have a utility of

Ua = log(200-A) + log(0) + log(M+PA).

Here is the problem: Still following the alphas, at the beginning of the adjusting period (but after one transaction for each player) we find two expressions for Ua:

Ua = log(200) + log(B) + log(M-PB) and Ua = log(200-A) + log(0) + log(M+PA).

Both equations are correct following ONE transaction by each player. The model has divided the population into two distinct groups. It takes a second transaction by each player to arrive at the quoted utility equation.

The requirement for a second transaction by each player introduces an element of time and the opportunity for decision making by each player prior to completing the second transaction. Monopoly pricing, the introduction of a money shock, or any other changed assumption will alter the goal of maximum utilization. We are brought back into the world of diverse definitions of maximum utility.

People argue for the minimum wage because of the difference in bargaining power between workers and firms. Trying to argue against this with yet another model that assumes equal monopsony for all goods (except money) misses the mark. Have the producers of bananas have much greater monopsony power than the producers of apples, and then see if a minimum ratio of the banana/apple price is a good idea for overall utility.

Roger: Are you sure you want to use log 0 = -infinity?

Nick: I think I get it now. I was confused by the Prisoners' Dilemma aspect of the model: if M >= 100P and the Alphas and Betas are all saints then they will agree to each sell 100 units, which maximizes both total and individual utility. But if they are the homo economicus of modelers' dreams, greed forces the solution to the Nash equilibrium, which actually provides less utility for everyone.

In fact the disparity between the cooperative and selfish solutions is greater for larger M. In other words greater wealth gives agents greater scope for selfishness.

Whereas in the monopoly case the buyer does not have complete freedom to set the quantity, the seller can cut him off at 100, making A=B=100 a Nash equilibrium.

Follow up questions:

1. Does this model suggest that monopsony is "worse" than monopoly? Or are there other examples where the reverse is true?

2. Perhaps the assumption of constant maximal greed that is built into the Nash equilibrium is unrealistic?

3. I'm still bothered that this model doesn't capture inflation. That increasing the money supply should lower the value of money seems so fundamental that it should be built into the model before anything else. In other words why I should I trust anything from a model that can't handle inflation? Or are you assuming ZLB conditions here? But in that case wouldn't you have to make other modifications, e.g. in the relative utilities of A/B versus M?

jonathan: I think I'm with you. And if alphas and betas had different monopoly/monopsony powers, then we need to keep Pa and Pb different. For example, if betas have monopoly power in the banana market, and monopsony power in the apple market, betas choose both Pa and Pb, and alphas choose both A and B. Shouldn't be too hard to solve.

rsj: I'm looking at which assumptions fit the macro facts.

Andrew: yep, it's Prisoners Dilemma, except at the competitive equilibrium.

1. I don't think so. Actually, my model suggests monopsony is worse than monopoly, because monopoly A and B never go to zero, but monopsony A and B can go to zero easily, if P is half of the competitive equilibrium value.

2. Depends on number of agents.

3. It's not meant to capture inflation. But it could be changed fairly easily to model how prices are set before M is revealed, to show how P depends on expected M. That would just be boring textbook, so I left it out.

Right, it's easier for a small number of agents to cooperate.

I thought rsj made a good point that this model assumes both groups have equal monopsony power, which seems very unrealistic.

Let me rephrase my question about inflation. You introduce this post as being about the effect of loosening monetary policy. But the M in the model represents personal cash holdings. Does loose monetary policy really mean that everyone's cash holdings go up? The ZLB hasn't had that effect on me.

I can't ague with Nick, of course. But I think the stronger argument against raising minimum wages (at least to a lefty like me) should be the low coincidence between earning minimum wage and being a member of a poor household. Stephen did a post on this way a few years ago (well, it may be many years ago now). It's his post that really changed my mind. I seem to remember him showing (with data, of course) that, if your objective was to help the poor, min wage increases where no better than randomly throwing money around.

So it turns out that minimum wage increases - at least in Canada (I suspect it might be different in the US) - is just not a great way to help poor households. Better to just give them money. Or at least stop clawing back benefits at 100+% marginal rates when they do manage to do better for themselves. Oh, and increase the WITB (why are the righties all over this!??).

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