Excess supply and monopolistic competition, once again

Why do firms so often seem to produce too much, or price too high, and have to sell off the excess at a reduced price?

You are a baker. You get up early and bake a batch of fresh bread. You set the price for the day. You aren't sure how much bread will be bought during the day. You can't bake more bread during the day, and you can't change the price either. At the end of the day, any unsold bread is no longer fresh, and has to be thrown (or given) away. What is the probability that you will have some bread left over?

The answer is surprisingly simple. The probability you will have some bread left over (an excess supply of bread?) is equal to: one divided by the elasticity of demand for your bread.

At one extreme, a pefectly competitive baker, facing a perfectly elastic demand curve, will almost never have bread left over. At the other extreme, as elasticity of demand approaches one (it can't go less than one for a profit-maximising firm, remember), a monopolistically competitive baker will almost always have bread left over.

 OK, I cheated a little, to get the answer that simple. I assumed a profit-maximising risk-neutral baker who knew the elasticity of demand for his bread, even if he was uncertain about how big the demand was. Then I took the limit of the solution as the uncertainty about the demand curve approached zero. It's qualitatively the same, but a bit less simple, otherwise.

This post is a follow-up to my earlier post on excess supply under monopolistic competition. The only difference is that in this post I have assumed the firm must decide how much to produce before observing demand. Putting both posts together, whether a firm chooses production before or after it observes demand, a monopolistically competitive firm is more likely to be willing and able to meet an unexpected increase in demand than a perfectly competitive firm.

Both posts are part of an ongoing conversation with Peter Dorman, about why there seems to be excess supply most of the time in market economies. This seems to make no sense if we believe the textbook competitive model, which says that in equilibrium firms are selling exactly as much as they want to sell. I am trying to convince Peter that the answer to this puzzle is to drop perfect competition and replace it with monopolistic competition. Peter's second post, in response, said that he would prefer to relax the assumption firms could adjust output after observing demand. And this post does that.

Peter also said that firms so often seemed to choose a price and quantity that seemed to be based on an over-optimistic forecast of demand. If they had known in advance what actual demand turned out to be, they would either have set a lower price, or produced a smaller quantity, or a bit of both. Let me see if my model can explain that too.

I was wondering how to construct a simple model to address Peter's points. And then I remembered I had already done it, over 20 years ago, with my Carleton colleague Vivek Dehejia. We built a macro model with monopolistically competitive firms, just like my baker, to show that business cycles would cause significant costs of wasted output, and would also reduce investment and long-run growth. (Most New Classical and New Keynesian models say that business cycles aren't very costly, because what you lose in recessions is almost compensated by what you gain in booms, and there's no effect on long-run growth.)

Our model's a bit complicated, even if you strip out the macro parts. Let me try to give you the intuition behind the results.

The baker has to decide on the price to set and on the quantity of loaves to bake.

Given the price, if the baker bakes one more loaf, it increases his total costs by MC (Marginal Cost). What does it do to his total revenue? The extra loaf adds nothing to revenue if he has unsold bread at the end of the day, but if he runs out of bread he can sell an extra loaf at price P. If U is the probability the baker has unsold bread at the end of the day, and so (1-U) is the probability he runs out of bread, the expected marginal revenue from producing one more loaf, given the price P, is (1-U)P. So he maximises expected profit by baking exactly enough loaves that (1-U)P=MC.

We can rearrange that equation to solve for U=(P-MC)/P.

Now the baker needs to set the price.

A normal firm with a downward-sloping demand curve, but no uncertainty, would choose a quantity where Marginal Revenue=MC. And since MR=(1-(1/e))P, where e is elasticty of demand, he sets a price where (P-MC)/P=(1/e).

But our baker is not a normal firm; he faces uncertain demand. Suppose he lowers the price just enough to increase expected quantity demanded by one percent, and also produces one percent more loaves. This would increase expected sales by one percent as well. Everything is proportional for a constant elasticity demand curve. But expected sales are less than quantity produced, and less than expected quantity demanded, since he sometimes has unsold bread, and sometimes runs out of bread. So if the baker cut price enough to increase quantity demanded by one loaf, and also produced one more loaf, expected sales won't rise by exactly one loaf. It only works exactly in percentages.

Never mind. To keep the math simple, let's just assume the variance of demand is small, so this approximation is good enough for our purposes. So our baker sets price almost like a normal firm. So the solution (in the limit, as variance of demand approaches zero) is nice and neat:

U = (P-MC)/P = (1/e)

The probability the baker will have unsold bread at the end of the day equals the percentage markup of price over marginal cost equals the inverse of the elasticity of his demand curve.

At one limit, as the baker becomes perfectly competitive, the price approaches MC, and he almost always sells out of bread. At the other limit, as the baker becomes more of a monopolist (the elasticity of demand approaches one), the price becomes much higher than MC, and the baker almost always has unsold bread.

It's quite easy to modify the model to assume the baker can sell the unsold stale bread the next morning at a discount. If elasticity of demand is 2, and the baker can sell the stale bread at half price, he will now have stale bread to sell 75% of the time.

I don't know if this new model will satisfy Peter. But, if demand is not very elastic, it does explain why many firms will seem to have set prices that are too high, and/or produced too much output, compared to the price and output they would have chosen if they had known demand in advance. It will look like they were over-optimistic in their forecast of demand. It will look like excess supply.

And it can also explain why they would be so keen on marketing more generally. It's that gap between P and MC that does it. Having an unsold loaf is costly. But if it costs only MC to have an unsold loaf, and if the baker gets lucky and can sell it at a price P above MC, it's worth the risk. Marketing effort is also costly. But if it lets you sell an extra loaf at a price P above MC, it's worth it. And it's imperfect competition that puts P above MC.

It's not just bakers who have unsold bread. A salon may hire more hairdressers than it needs on average, and the labour of an idle hairdresser is as wasted as an unsold loaf. Gas stations have gas pumps sitting idle. Unsold bread is a metaphor for unemployment.

At other times, of course, the baker will run out of bread, the hairdressers are all busy, and there's a queue at the gas pumps.

Which is more common depends on the elasticity of demand. But we would never see unsold bread, idle hairdressers, or idle gas pumps, under perfect competition.

Comments

[Just visiting from Macleans]

I'm a coffee and muffin person - necessary staples when sitting down to read the daily paper. One coffee shop that I used to frequent sold 1/2 price day old muffins. I couldn't tell the difference - so I'd always buy a day old and save 60 cents. If there were no day olds, I'd buy a fresh one. So, in my case, the day olds were cannibalizing their higher margin fresh muffin sales. Say the muffins cost $0.10 for ingredients and sell for $1.20. On a half price muffin, they make 60 cents (the 10 cents is a sunk cost). So, they are losing 60 cents every time they sell me a day old.

The other option is to throw the excess muffins into the garbage, give them to a food bank (larger operations do this), or to pig farmers as feed.

Opportunity cost - if it costs $0.10 to make a muffin, and you sell it for $1.20, then your break even is 12 muffins. In other words, to avoid stock out (assuming the customer doesn't substitute for a different product that you make) at the margin, you can throw out 11 muffins, sell the twelfth, and be profit neutral - at the same time keeping your customer satisfied - so they return for repeat business.

The analysis is a bit different for perishable goods because they have a limited shelf life and hunger demand is restored daily.

Aside - Tim Horton's shops(Canada's ubiquitous donut franchiser) all used to have bakers on site, and at the end of the day, you'd see workers throwing bags and bags of surplus donuts into the dumpster behind the store. So, a few years ago, they went to central baking facilities, and shipping to stores frozen donuts. Of course this caused a general uproar at the time from donut aficionados - but the cops etc. finally accepted the new reality. So, they solved the inventory problem by adding freezers as buffers. And the franchises didn't need ovens, bakers etc - major operational savings. I don't recall donuts dropping in price as a result, though.

[Nick Rowe]

JVFM: "If there were no day olds, I'd buy a fresh one."

On what percentage of the days were there day-olds left over?

[Nick Rowe]

My guess is that Tim's has a very elastic demand curve (compared to Starbucks or whatever). So my little model predicts that Tim's will price with a small markup over marginal cost, and will often have queues of customers (like running out of bread or doughnuts), and will rarely have excess supply.

[Just visiting from Macleans]

On what percentage of the days were there day-olds left over?

Well, depends what time you got there, but I'd say generally more than 50% of the time at the place I frequented. Mind you it was a shop that had a certain "natural food" waste not want not philosophy - so that may explain the unprofitable selling of excess supply.

Tim Horton's in certain parts of the country can be considered a monopoly of sorts (Ont and eastern Canada - less so in Western Canada where Robin's donuts has a presence - don't know about Quebec) - and so the lower limit on price is set somewhat by its competitors - say Country Style, Coffee Time - who don't have enough franchises to take advantage of economies of scale operations. But, as a Canadian institution (frequently used for political photo ops with a "double double") it can charge a premium.

[Phil]

If I were a baker, I'd always bake too much in order to avoid disappointing customers. Once they realize that I'm out of bread more than my competition, they'll stop coming to avoid that risk.

However, if I'm the only baker in town, I might be more willing to run out. And, if there's a competitor right next door to me, I might also be more willing to run out, because my customers won't avoid me if there's an easy alternative supply on the days I'm out.

But if I'm Loblaws, and the nearest supermarket is (say) five minutes away, I'm not going to alienate my customers to gain an extra few dollars of expected profit on bread.

[Nick Rowe]

Phil: that's a good point. It's not in my model.

I'm trying to think how to build it in. The cost to a customer if the baker runs out is the customer's foregone consumer's surplus. The expected cost will equal the total consumer's surplus, times the probability (1-U) of running out, times the fraction of customers who can't buy the bread but want to. And that expected cost needs to be included as part of the "full price" that a customer pays for the bread. And since quantity demanded (or number of customers) depends on that "full price", demand will be higher for a firm that never runs out, even for a given posted price. So that would mean that firms would have excess bread more frequently than my model would predict.

However, since I took the solution to my model in the limit as the variance of demand approached zero, I don't think (but I'm not 100% sure) this would affect my U=(1/e) result. Because the fraction of customers who were unable to buy bread would also approach zero in the limit.

[Greg]

> we would never see ... idle hairdressers, or idle gas pumps, under perfect competition.

If so, no one would get any hair cuts or gas. Queue length grows to infinity if server utilisation is always 1.

[Nick Rowe]

Greg: that's not what it means. It means they adjust output (hire just enough servers) so that there's almost always a queue.

[Just visiting from Macleans]

http://www.youtube.com/watch?v=7j5xbbQDTRM

[Just visiting from Macleans]

But if I'm Loblaws, and the nearest supermarket is (say) five minutes away, I'm not going to alienate my customers to gain an extra few dollars of expected profit on bread.

Are you talking price, or supply? Nevertheless, depending upon where you live, a good chance the supermarket you switch to is also "Loblaws":

When grocery shopping in Canada, it's hard to escape the long arm of Loblaw. Loblaw Companies Ltd. is the market share leader among Canadian supermarket operators. Its corporate, franchised, and affiliated banners (22 in all) fly over more than 1,440 stores nationwide. Trade names include Loblaws, Atlantic SaveEasy, Extra Foods, Fortinos, No Frills, Provigo, Your Independent Grocer, T&T, and Zehrs Markets, to name a few. Its stores offer more than 8,000 private-label products, including its signature President's Choice brand, as well as traditional and organic grocery fare. Loblaw is also Canada's largest wholesale food distributor. Loblaw Companies is a subsidiary of Canada's George Weston.

http://www.hoovers.com/loblaw/--ID__43534--/freeuk-co-factsheet.xhtml

[Just visiting from Macleans]

Btw, bread is a lousy example for "monopolistic" competition. My nephew needs to eat gluten free bread. There is limited supply available, so his mother was looking to purchase an automatic breadmaker, and had a long recipe list. Coincidently, over the course of three weeks, on the route I routinely cycle, two people had set out perfectly operational breadmakers at the side of the road for someone to pick them up (a passing fad apparently just like pasta makers, cappuccino makers, ice cream makers). So, I ended up trying them out before passing them on. Three cups of flour, pinch of salt, sugar, water, yeast, butter, milk powder - it took all of two minutes, set the timer,press the button, and I have fresh steaming bread when I woke up in the morning.

Throw in a cup of raisins when it beeps at 10 minutes and a whole different experience.

[Jon]

At other times, of course, the baker will run out of bread, the hairdressers are all busy, and there's a queue at the gas pumps.

You see now, I'm willing to pay the baker a premium so that when I show up, there is bread. Ditto at a store.

I realize that these people sell things, but they also sell a service.

[Nick Rowe]

Hmmm. Maybe I should keep my eyes peeled for a breadmaker. (I would never buy one, but like bicycles and a lot of things, if you wait long enough you can pick up less fashionable things for free.)

Jon: Yep. If you had zero transportation costs (including time) you wouldn't be bothered if one store ran out, because you would just go to the next. But it's those same non-zero transportation costs that make the individual store's demand curve slope down, finite elasticity, and monopolistic competition.

[Just visiting from Macleans]

But it's those same non-zero transportation costs that make the individual store's demand curve slope down, finite elasticity, and monopolistic competition.

7-11, Mac's Milk, convenience store around the corner. Non monopolistic competition.

[Frances Woolley]

Just visiting - totally digressing from the point of Nick's post - the Tim Horton's example is really interesting. The central plant that makes Tim Horton's doughnuts is owned and controlled by the Tim Horton's corporations. The individual franchises are essentially independent operations owned by individual franchisees. The franchisees are required to buy the ready-made Tim Horton's doughnuts - at a price so high that they make very little profit on their individual doughnut sales.

So I suspect the motivation for centralization there was partly a desire to avoid stale doughnuts - but mostly a desire to keep profits in the hands of the parent corporation rather than individual franchisees.

[Just visiting from Macleans]

So I suspect the motivation for centralization there was partly a desire to avoid stale doughnuts - but mostly a desire to keep profits in the hands of the parent corporation rather than individual franchisees.

Yes, that's the motivation. Franchise agreements usually dictate that the franchisees are required to pay fees, and purchase their supplies from the franchiser. So, as long as the profits of the franchisee are not negatively affected (through higher frozen donut costs - but less need to buy sugar, flour, sprinklings etc and manpower) the head office can capture all of the efficiencies. Win/indifference.

[Frances Woolley]

Just visiting: So, as long as the profits of the franchisee are not negatively affected (through higher frozen donut costs - but less need to buy sugar, flour, sprinklings etc and manpower) the head office can capture all of the efficiencies. Win/indifference.

No, I think given that head office can make the franchisees a take-it-or-leave it offer, the franchisee just has to suck it up, even if they are negatively effected. I don't know - it's one of the many areas of econ about which I'm woefully ignorant, and I couldn't actually find much econ analysis of the problem, though I'm sure there is lots.

[Just visiting from Macleans]

Don't bite the hand/piss off the hand that feeds you. It's a balance, no doubt. The franchises are on the front line, and hear the griping.

Do you remember the story of the Tim Horton's worker who was fired for giving out a free timbit to kids? It was a local franchise issue, but it gained national exposure. Works both ways. http://www.thestar.com/News/Ontario/article/422864

[Determinant]

The only reliable way to tell which grocery chain you are shopping at is to look at the house brand. President's Choice: Loblaw. Master Choice: Metro. Euquality: Sobey's.

[Just visiting from Macleans]

FW - Btw, the profitability of an existing franchise (with the costs etc for materials) is reflected in the purchase price of new franchises from head office- kinda like the NHL and entry fees.

[Frances Woolley]

JVFM - yes, it's an interesting problem - a corporation close to global saturation (MacDonalds) has very different incentives from one less well established. Head office has to balance the profits gained from selling new franchises at a higher one-off fee against the profits gained from charging a high price for ready-made donuts on an on-going basis. And if it switches strategy mid-stream, as Tim Horton's did when introducing frozen donuts, what does this do to credibility, reputation, etc?

[himaginary]

"So the solution (in the limit, as variance of demand approaches zero) is nice and neat: U = (P-MC)/P = (1/e)"

As MC is the increasing function of Q as shown in the graph of your previous post, I suppose you are referring to the particular point of MC here, which is MC=MC(Q*). As that is the point where MC equals *Marginal* Revenue, doesn't U represent some kind of marginal value? That is, isn't U the particular probability that additional bread remain unsold at Q=Q*? If that is the case, it seems wrong to apply U to the whole bread production.
And the expected revenue from that additional bread, (1-U)P, or (1-(1/e))P, is less than MC for Q larger than Q*, so it seems that the baker has no incentive to produce that additional bread.

"At the other limit, as the baker becomes more of a monopolist (the elasticity of demand approaches one), the price becomes much higher than MC, and the baker almost always has unsold bread."

This is the point Peter criticized as counter-intuitive and/or counterfactual. He wrote:
"From observers like Alec Nove and Janos Kornai, we have come to recognize that the prevalence of buyers’ markets is what distinguishes capitalism; in the state-managed systems of pre-1989 socialism, the seller was king."

And, of course, pre-1989 socialism almost never had unsold bread.

Plus, Tim Horton's episode JVFM introduced may serve as another counter-example. The company took a step closer to more of a monopolist in order to *reduce* unsold doughnuts.

[Nick Rowe]

himaginary: There are three quantities: quantity produced; quantity demanded; and quantity sold (which equals the lesser of quantity produced and quantity demanded). The relevant MC is the MC evaluated at quantity produced. The probability that there will be unsold bread, U, depends on: quantity produced; price; and the distribution of the shocks to demand. When I say U=(1/e) I am talking about what U will be when both price and quantity produced are at profit maximising levels chosen by the firm.

(And my solution, U=(P-MC)/P=(1/e), is only an approximation to that solution. It only holds exactly in the limit, as the variance of demand approaches zero, so that all three quantities converge. The full derivation and solution are in the paper I linked, but there is an ugly integral in the general solution which I didn't want to put into a blog post. That integral disappears in the limit.)

Yep. Under perfect competition you will never see unsold bread in my model. That's (one reason) why I reject perfect competition. It doesn't seem to fit the facts.

[Frances Woolley]

Nick: "A salon may hire more hairdressers than it needs on average...Unsold bread is a metaphor for unemployment."

Non-sequitur?

[Nick Rowe]

Frances: not a non-sequiter, but I should have expanded, to explain it more clearly. The idle hairdressers are unemployed, in one sense, even though they have a job. They aren't producing anything. If they were paid by the job, rather than by the hour, (or if they were self-employed), we would see them as unemployed whenever they weren't cutting hair.

There's unemployment on the job and unemployment off the job.

Once you start thinking about unemployment that way, the rate of unemployment gets much bigger. Firefighters and fire engines spend most of their time unemployed.

[Maxine Udall (girl economist)]

Or the baker may face heterogeneous demand, i.e., customers with inelastic preferences for fresh bread, and customers who are indifferent to freshness, but not to price (i.e., more price elastic). Then the excess bread could be a form of price discrimination (which could indicate that the baker has some market power at least among those who value freshness, but it's not clear to me that it is necessarily the case. It could be an example of a competitive market and a clever baker providing exactly what the market wants with no erosion of consumer surplus for either group of purchasers. It's then two market demand curves and two products.)

On the hairdresser example, I suspect that the reason for excess hairdressers is more the tendency for hairdresser demand to resemble a Poisson process. A salon can smooth the arrivals with scheduling, but there is still (apparently) money to be made from walk-ins, so the optimal number of hairdressers is derived from a mixture of demand distributions and could result in some idle hairdressers some of the time even in a perfectly competitive market.

[himaginary]

"It only holds exactly in the limit, as the variance of demand approaches zero, so that all three quantities converge."

But the solution we are currently interested in is the one with quantity demanded less than quantity produced. The problem as I perceive it is whether there is some equilibrium state under that condition. Maybe we have to dig into the ugly integral to answer that question.

Besides, if all three quantities converge, that means there is no unsold quantity, so it seems that U should be zero in that case.

[Just visiting from Macleans]

It could be an example of a competitive market and a clever baker providing exactly what the market wants with no erosion of consumer surplus for either group of purchasers. It's then two market demand curves and two products.)

This marketing strategy also falls under cannibalization, though in a positive sense. From wiki:

In marketing strategy, cannibalization refers to a reduction in sales volume, sales revenue, or market share of one product as a result of the introduction of a new product by the same producer.
While this may seem inherently negative, in the context of a carefully planned strategy, it can be effective, by ultimately growing the market, or better meeting consumer demands. Cannibalization is a key consideration in product portfolio analysis.
For example, when Coca Cola introduced Diet Coke, a similar product, this took sales away from the original Coke, but ultimately led to an expanded market for diet soft drinks...

http://en.wikipedia.org/wiki/Cannibalization#Marketing_Management_.28and_Retail.29

[Nathan Tankus]

do you really believe that firms in the real world set marginal price to marginal cost?

[Jon]

Nick writes:

If you had zero transportation costs (including time) you wouldn't be bothered if one store ran out, because you would just go to the next. But it's those same non-zero transportation costs that make the individual store's demand curve slope down, finite elasticity, and monopolistic competition.

Agreed. Retail outlets are almost always MC rather than PC. What's the debate about again? Some commentators here appear to disagree or do they?

[Nick Rowe]

Maxine: Hmmm. Yes. Price discrimination could provide an alternative explanation. Except, sometimes they do run out of bread, which fits the stochastic demand hypothesis better, I think.

For the salon, yes, modelling the demand function as a Poisson process would make more sense. Also for coffee at Tim Horton's, if the limit is the number of servers, rather than the amount of coffee brewed (they can always brew more).

himaginary: Think of it this way. Suppose e=2, so the firm sets price and production so that they will have unsold bread approximately 50% of the time, and an excess demand the other 50% of the time. As the variance gets smaller, the amount of unsold bread gets smaller, and the amount of excess demand gets smaller, but the probability of each stays at approximately 50%. In the limit, both the amount of unsold bread and the amount of excess demand approach zero.

Nathan: "do you really believe that firms in the real world set marginal price to marginal cost?"

The whole point of this post (and the previous one) was to argue that firms do *not* set *price* equal to marginal cost.

[Just visiting from Macleans]

What's the debate about again?

Bad bygones: good or bad?
-or-
Good bygones: bad or good?

[Nathan Tankus]

"The whole point of this post (and the previous one) was to argue that firms do *not* set *price* equal to marginal cost." oh i'm sorry i actually mis-wrote my question. stupid me. multi-tasking is sometimes terrible. i meant to ask "do you believe that firms in the real world would set marginal price to marginal cost if we could somehow remove the 'imperfections' in real world competition?" if not can we stop calling it imperfect competition and start calling is real competition or new keynesian competition? imperfect competition implies that something is wrong with the real world market that if only we fixed we would get all those great welfare maximizing benefits or perfect competition

[Nick Rowe]

Nathan: "imperfect competition" and "monopolistic competition" are just two different names for the same model. They aren't very good names, but they are the names we are used to using, so we are stuck with them.

The only practical "cures" I can think of for the "imperfections" of "imperfect competition" would be cures that are far worse than the disease. (E.g. let's force all the corner stores in Ottawa to locate in one central location to make them behave more like perfect competition. Let's force all the restaurants to serve exactly the same food.)

If that's what you are saying, I agree with you. So, I think, do nearly all economists.

[Nathan Tankus]

yeah that's pretty much what i'm saying. I think that the majority of the economics profession, by talking about real world competition as if it was somehow "imperfect" implying that it needed to be, and could be, fixed hurts the public discourse. on the other hand i don't think the majority of the economics profession agrees with this assessment of competition as evidenced by all the reforms (chili in the 1970's russia in the early 1990's, east asia in the late 1990's) egged on by large swaths of the economics profession.

[Just visiting from Macleans]

NR: as much as I like oranges, bananas and bread, how about looking at an industry with perishable goods that is a bit more relevant?

Say the airline industry or the hotel industry?

At one time, flight costs were fixed, and Air Canada, for example, would sell off empty seats at the last minute to qualified student stand-by at say 30% of reg price. Of course, if you tried this option, there was a good chance you could be sitting at the airport for a few days.

Then along came Westjet (modeled on SW Airlines) who optimized profit by changing price with time (book early, pay less, last minute - pay through the nose), load factor, etc. This was a departure from the Air Canada model (selling excess supply at a discount), and they became more profitable as a result. This required better information systems. Guess which model prevails today? Stand by no longer exists. No need to guess. Just go onto the Air Canada or Westjet sites and look at the range of prices depending upon when you are flying, how long to departure time, and how full the plane currently is.

Btw, charter flights to vacation spots are different - they don't risk cannibalizing from regularly scheduled flights, and since their costs are fixed, last min bucket shop fares are highly discounted. I once flew return from London England (20+ yrs ago) to Rhodes Greece for £39, one day's notice, the couple beside me paid £500+ each for a package.

[RSJ]

I'm still not happy! Let me try to suggest a somewhat different proposal.

Marginal costs are also U-shaped, not just average costs.

* Imagine if a baker baked only one donut. He still needs to heat the oven, and wait for it to bake. He cannot be making more donuts while the one in the oven is baking. Not to mention going to the store to buy all the ingredients for only a single donut. It would be a very expensive donut. Only if you assume that wages and material costs are fixed costs can you argue that MC is always rising.

As the baker decides to make two, he can batch them so once he is already heating the oven and mixing the dough, the marginal cost of making a second donut is lower. It requires less labor time. That marginal costs continues to fall until he full capacity, at which point the pan is filled with donuts and he is wasting no time waiting for the donuts to bake, as he readies a new pan as the one in the oven is baking. He is always busy.

* A restaurant that is half full has higher marginal costs than a restaurant that is full, with a lot of turnover. When the restaurant is half-full, the waiters are standing around but still getting paid. The cook is waiting for the orders to come and in and cannot batch process the food. Large ovens that need to be heated are filled with small portions of food, etc.

* Process engineers don't design factories so that workers are tripping over each other when the factory operates at full capacity. Full capacity is the most efficient mode of operation. Beyond full capacity, you need to start paying overtime, add weekend shifts, etc., and the marginal costs rise steeply. Then perhaps workers are forced to wait as more materials come in, or you need to pay extra to get emergency supplies of inputs.

So the MC curve slopes rapidly down starting at 1, then levels out at full capacity, Q_f, and then begins to rise steeply thereafter. We can approximate the inability to exceed capacity by too much as a vertical asymptote, so that Q_max > Q_f and MC(Q_max) = infinite.

Now the businessman planning his capital deployment has an expectation of the demand curve. He knows the foot traffic, what the going donut rate is, etc. He *buys* a certain MC curve by purchasing square footage, capital equipment, etc. He can operate with a small oven that can bake 300 donuts a day at full capacity, with a corresponding MC of 30 cents, or he can buy an enormous donut-plex in which he manufactures 100,000 donuts a day (at full capacity) with a MC(Q_f) = 5 cents. Or anything in between.

As Q_f goes up, the price of this cost curve also goes up, but MC(Q_f) falls and the demand curve slopes down. There will be a *strategic* equilibrium in which the donut maker buys an optimal amount of capacity to maximize his profits and at that level, he will operate always at full capacity, with *lowest* marginal cost, not the highest marginal cost.

If you then add a stochastic demand curve, then because the MC curve is steeper to the right of Q_f than to the left, the optimal amount of capacity to deploy would be greater than the expected quantity demanded.

But in all cases, the donut maker can sell more donuts if he would only lower his price. But if he did lower his price, then the strategic result would be that he would not be able to remain profitable, since his Total Costs, which include a return on capital would exceed his total revenues, even though his marginal costs would remain significantly lower than his marginal revenue.

Then it "appears" as though prices are sticky, in the sense that in the face of a downward shift in demand, prices are not adjusted lower. The prices may not be sticky at all, but they can't adjust downward in order for the market to clear, given a certain configuration of the MC curve and p.e.d. The only solution for the donut maker is to liquidate capital and substitute to a smaller scale operation, rather than to lower prices and/or produce fewer donuts given his current MC curve. No instantaneous adjustment in price will result in the donut maker becoming more profitable, even if he has excess capacity and unsold donuts.

[RSJ]

Terrible. If the baker bakes a second loaf, then the extra costs are negligible, therefore MC is smallest. I *did* confused AC and MC, yet again! Sorry. But I think that U-shaped (average) cost curves are still key somehow to generating excess capacity;.At least, until I am forced to retreat even form that assumption :)

[himaginary]

"As the variance gets smaller, the amount of unsold bread gets smaller, and the amount of excess demand gets smaller, but the probability of each stays at approximately 50%. In the limit, both the amount of unsold bread and the amount of excess demand approach zero."

I think I said essentially the same thing when I wrote in my first comment:
"...doesn't U represent some kind of marginal value? That is, isn't U the particular probability that additional bread remain unsold at Q=Q*?"

So, U in the limit seems to be meaningful only in the vicinity of Q*.

[Just visiting from Macleans]

Bread: Monopolistic pricing, or loss leader? Today's G&M:

Grocers feel the heat to lure recession-frayed consumers with bargains in an uncertain economy. Supermarkets trumpet promotions on an array of popular items, from bread to bananas, although still quietly bump up prices on other merchandise, sometimes by shrinking the packaging. In the third quarter, food prices dropped 1 per cent from a year earlier, according to market researcher Nielsen Co.

http://tinyurl.com/2ev8sqx

[kevin quinn]

This is tangential to the main point but is a response to Nathan's comment and Nick's response. If you look at the history of thinking about MC, it is striking how nasty the response was to its originators, Chamberlin and Robinson. Chamberlin claimed that there was too much variety under MC because each firm will produce in long-run equilibrium at a quantity at which unit costs are still falling - unit production costs won't be minimized. His critics ridiculed him: those higher production costs are the "costs of variety," they said. But they didn't bother to check and see whether there was any tendency for the sum of production costs and variety costs to be minimized, they just implied/asserted that they would be. In a simple location model with fixed costs, constant variable costs per unit, and constant travel costs per unit of distance, and people who have perfectly inelastic demand for the good,it is easy to show that there are twice as many firms as would be optimal! Limiting entry would raise prices, but profits would increase by more than travel costs rose. Would the cure be worse than the disease?

[Peter Dorman]

Hi Nick. I have a question about your model. It seems to me that the baker is uncertain about the demand curve. In that case, isn't the question whether he/she raises the price slightly at the margin and also produces an extra loaf (possible high demand curve) or remains at the status quo? You have the baker contemplating a reduction in the price in order to sell another loaf, but this, of course, is the decision the monopolistic competitor (or monopolist) faces vis-a-vis a known demand curve. Why bake the extra odd loaf, in case the demand curve turns out to be higher, and not add the extra odd cents to the price?

Aside from the technicalities, I still think there is a problem with the prediction inherent in your model. If you are right, as markets approach perfect competition (more competitors), we should expect to see something closer to neutrality in producer expectations of demand: ex post excess demand should arise about as often as ex post excess supply. My hunch, however, is that it is the opposite: in competitive markets excess supply is most severe and the consumer is king, while in monopolistic markets S and D are more balanced (at the higher monopoly prices) and the consumer is dirt.

I like, though, how Canadian discussions of this problem quickly get into doughnuts at Tim Horton....

[john c. halasz]

Peter Dorman:

I'm still no sure about the exact purport of your initial question, nor what the unsolved problem or mystery is supposed to be. But insofar as the logical fiction of "perfectly competitive markets" is realistically approached, as with agricultural commodities, (ignoring ag subsidies), or retail sales, (ignoring Walmart), then profit margins are low, ("no economic profits"), bankruptcy risks high, and price volatility is high. So, yes, excess supply might be frequent there, but at the cost profits and survival. The logical implication would seem to me to be that firms emerge at the intersection of several markets and survive, only insofar as they can in some degree reduce or exclude competitive pressures, and reducing transaction costs below prevailing market levels, by stabilizing, if not controlling, one or more of the relevant markets. On the other hand, if firms are "imperfectly" competitive, then, yes, supply would be lower and excess demand and thus prices higher, and profit margins more sustainable. But that's the opposite of the question you asked about the tendency of excess supply capacity to prevail over available demand macro-economically in advanced capitalist economies, no?

But what's wrong with the answer for why excess supply potential and constrained demand tend to prevail macro-economically provided by scale effects in technically efficient capital intensive oligopolies as dominant "players" in such economies? If one has a factory that produces, say, 100 units per day, and one wants to meet perceived demand at 200 units per day, then one must build another such factory and double one's capital costs. But if one can scale up to a factory producing 1000 units per day, the technical efficiencies realized might drastically reduce average unit capital costs, while raising labor productivity and the unit costs of labor, if not materials. But, then again, building a factory capable of producing 1200 units per day (or with the ready capacity to expand to such with additional capital expenditure) might only cost, say, 10% more than 1000 units. Given the more or less long lead-time for setting up such a factory, and the still longer anticipated "life" of such a fixed cost investment, which will persist through a variety of demand conditions, and the high upfront costs and long amortization of the investment, large uncertainties prevail in such investment decisions. But given such uncertainty and high costs, and given the aim of securing a market-dominant position to withstand/exclude competitive pressures through lowered marginal and average costs, wouldn't the provision of extra cheap productive capacity be "rational"? From which would follow the whole Galbraithian apparatus of marketing and advertising to generate artificial, synthetic extra demand, ("life-styles!").

At any rate, restaurants or doughnuts are a poor test case, since they would involve low capital intensities, with high relative labor costs and volatile material input prices. And they are not a "leading" sector of the economy: the economy won't expand or contract because more or less doughnuts are produced and sold, but doughnut sales will increase or diminish with the expansion or contraction of the overall economy.

[john c. halasz]

Incidentally, "monopolistic competition" based on product differentiation (and also differential pricing schemes) would also be largely the effect of such large oligopolistic firms with joint production. Alfred Sloan and GM would be the classic pioneering instance.

[Nathan Tankus]

"If you look at the history of thinking about MC, it is striking how nasty the response was to its originators, Chamberlin and Robinson." maybe they are the originators in the marginalist tradition, but outside of that there are plenty of economists outside of that with innovative (and arguably better) theories of non-perfect competition pricing as old or older.Gardiner Means, michal kalecki philip andrews, hubert henderson are just post-keynesian price theorists who have well trodded this path. that's part of why it's quite frustrating to read this particular conversation about excess supply and monopolistic competition as if there is no theoretical (or statistical) precedent for it.

[himaginary]

Peter@05:38 PM November 15: "In that case, isn't the question whether he/she raises the price slightly at the margin and also produces an extra loaf (possible high demand curve) or remains at the status quo?"

I think that "he/she raises the price slightly at the margin and also produces an extra loaf" part can be decomposed in two parts:
A) he/she keeps the price and produces an extra loaf.
B) he/she raises the price slightly at the margin.

I think Nick's model addressed part A. In normal monopolistic competition settings, if you cut price by 1/e and produce an extra loaf, you can surely sell that loaf. What Nick's model shows is that if you keep the price and produce an extra loaf, you can sell that loaf at probability (1-(1/e)). From marginal revenue's point of view, both results are the same, i.e., you earn (1-(1/e))P. So, as long as it is less than marginal cost, you won't produce it.

[Just visiting from Macleans]

I thought Peter's argument boiled down to this (well for me at least) - to define a demand curve you need three things - P,Q and e. You can only pick two - P&Q. So, in trying to hit the demand line with unknown elasticity e, why do firms err on the overproduction side more then underproduction - ie a bias?

Maybe it's like putting in golf. If you don't strike the ball hard enough, you'll never even have a chance to get it into the hole, - so you hit past the hole, and hope you have picked the perfect line for it to drop.

And if you don't overproduce, you'll never really know definitively where one point on the demand line exists (ie you left some money on the table if you produce too little or err on the left side of the curve.)

I don't follow the (1-(1-e))P argument if you don't know e - which I think was also the point he was making.

[Just visiting from Macleans]

NR, was just flipping through December's ROB magazine, and this article made me chuckle. http://tinyurl.com/2duwufp

It was about Salman Khan who:

"could be a poster boy for elite education: He has three degrees from MIT and a Harvard MBA. A few years back, while working at a Boston hedge fund, Khan began tutoring his cousins in New Orleans by posting YouTube videos of himself talking over Microsoft Paint drawings. Soon, strangers were watching his lessons. In 2009, he quit his job to expand what he calls the Khan Academy, which includes 1,800 lessons on everything from finance to the French Revolution."

This response I found humorous:

Q: You also have a lot of basic finance videos. How come?

A: At the hedge fund, we had these junior analysts who were straight-A, 4.0, summa-cum-laude graduates from Harvard and Yale, and I would have to spend a month explaining why something is priced the way it is, how markets work, or even the basic mechanics of backlogs and inventory. I thought, “Hey, if these guys don’t know it, then few people probably do.” And it’s working. I got a letter from a banker who works in mortgage-backed securities thanking me for my explanation.