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Does marginal cost equal price?
A loyal and perhaps even addicted MR reader requests a discourse:
There is a best way to teach students that marginal cost curves slope up somewhere, when the common sense is that they are flat for practical purposes? It's difficult to reconcile that vision with the fact that firms don't change prices every time that they increase (decrease) production...
This one makes my head spin...
We're all taught that in a competitive industry price will equal marginal cost. Well, what is a competitive industry? There are lots of Chinese restaurants in or near Fairfax, and with a few noble exceptions they have more or less the same menu. Each could serve an extra diner at essentially zero marginal cost, yet the price of the food is not zero. Not even marginal meals are given away for free, except perhaps to the staff. If price is equal to marginal cost, we have to ask equal to which marginal cost? The marginal cost of one more Kung Pao Chicken? The marginal cost of being known for giving some meals away? The marginal cost of possibly setting off destructive price competition with rivals? The concept of marginal cost relies on a definition of time horizon, strategic assumptions, and the counterfactual against which real world action is being compared. Yikes.
Armen Alchian and Fischer Black are the guys to read on what cost really means (Buchanan and the Austrians only get you so far). If you really want to get dizzy read Lester Telser on when there is a core, and wonder whether the industry you have in mind meets his screwy but essentially correct standards for MC, AC, and no coherent equilibrium. It's not just the airlines. So when is price equal to marginal cost, average cost, or some blend of the two? And which definitions of average and marginal cost?
What about "reality"? Toss a bone to social frictions, then ask for some micro-studies of how "competitive" industries price in the short run. Use interviews and ethnography to supplement the formal models. In practical terms, you might end up with some understanding of a) why prices can be sticky in apparently competitive industries, and b) why few businessmen -- including high IQ types -- will admit to pricing at marginal cost or even understand what that means.
The bottom line: I'll say that MC is flat if truly all inputs are replicated. But that's never the case, so MC is usually zero under one set of counterfactuals and sloping upward dramatically under another set. That's not the end of the world, live with it.
The second bottom line: When it comes to teaching the students, just tell them that marginal cost slopes upward at some point. After all, sooner or later they all stop studying.
The third bottom line: #13 out of 50.
Posted by Tyler Cowen on March 5, 2007 at 06:59 AM in Economics | Permalink
Comments
There are no perfectly competitive industries as there is always some form of perceived product differentiation be it convenience, service or just random public rumor. This allows price to be greater somewhat that MC.
Further MC is often tricky to calculate so it’s less risky for businesses to price higher.
Posted by: David Young at Mar 5, 2007 8:01:27 AM
Maybe businessmen -- especially high IQ types -- just understand that if they ran their business via economic theory they would quickly go out of business. Unfortunately there's no such thing as ceteris paribus in the real world.
A family friend who was an economist had tried starting many small businesses on the side over the years. Every one failed, even the franchises which should have been a no brainer. However I knew of one economics professor that was very succesful starting and running several strip clubs.
Posted by: asiequana at Mar 5, 2007 9:04:13 AM
Study well:
1) "The Economics of Imperfect Competition" by Mrs.Joan Robinson,
2) Early articles of Sraffa and Harrod,
3) Read Jacob Viner's "Cost Curves and Supply Curves"
I hope you will get some, if not full, explanation.
And also you can check with Stigler's various articles.
Posted by: GVV at Mar 5, 2007 10:03:43 AM
lester telser...what a name. his parents must have been anagramists.
Posted by: jwass at Mar 5, 2007 10:46:31 AM
I agree. This is the "empty economic boxes" issue scrutinizing Marshall, eventually leading into the micro foundations of Post Keynesianism. It's tough, I have a hard time teaching Marginalist Marshallian neoclassical models to my intermediate micro class when only a handful will go to graduate school for economics, which seems like the only place in the universe where these assumptions are relevant. However, check out this econometric article:
Epple, D. & B.T. McCallum (2006). Simultaneous Equation Economometrics: The Missing Example. Economic Inquiry, 44:2 374-384.
The only empirically relevant supply curve I've seen...
Posted by: Ian at Mar 5, 2007 11:19:12 AM
re: "Each could serve an extra diner at essentially zero marginal cost, yet the price of the food is not zero."
What? Surely they have to pay something for the rice, etc. And then table space is scarce in principle, and in practice, Chinese take-out places I've been to tend to be pretty busy and often lack tables. Of course, maybe at the end of the day they've cooked some food they won't sell, which will spoil, but no doubt it wouldn't be worthwhile do engage in sophisticated bargaining with the last few meals in order to maximize returns, while trying not to undermine their normal market. Chinese fast food looks like a pretty competitive market to me.
Posted by: Nathan Smith at Mar 5, 2007 12:15:49 PM
Upward sloping marginal cost follows directly from the assumption of diminishing marginal returns to your variable factor(s). It's a three line proof. So if you want to tell me why marginal cost doesn't slope upward, tell me why marginal returns aren't diminishing.
Posted by: Don at Mar 5, 2007 12:37:28 PM
Chinese fast food must be competitive, every metropolitan area I've lived in had what seemed like more than enough of them.
This past weekend I also learned that when a Chinese family moves to a small VT town with no Chinese restaurant they promptly open one and do very well (via a friend from VT).
Large Chinese restaurants with elaborate pacific islander decor and in-house comedy clubs are always packed with people (after lunch visit to Kowloons).
p.s. this blog makes me want to take economics classes to understand this stuff. Of course, I've got around 5 books on my 'to read list' because of this blog...
Posted by: Steve at Mar 5, 2007 12:37:50 PM
"There are lots of Chinese restaurants in or near Fairfax, and with a few noble exceptions they have more or less the same menu. Each could serve an extra diner at essentially zero marginal cost"
You should look at the marginal cost not for one meal but use units (say 20 or 30 meals) determined by the number of meals provided by the labor of one extra employee. For a large frim, the real world cost curves can look fairly smooth but for small frims the fact that labor comes in units of people matters. Quantum economics???
Posted by: joan at Mar 5, 2007 12:40:50 PM
Stupid question: how about just admitting that businesses price based on (expected) average cost, instead
of carving out all these epicycles? I'm just asking, is all.
Posted by: Person at Mar 5, 2007 1:34:36 PM
Person:
For single product firm, this is correct. However, multiple product firm will spread markup over marginal cost according to Ramsey rule i.e. price markup over marginal cost is in inverse proportion to the elasticity of demand.
Posted by: anon at Mar 5, 2007 2:42:19 PM
In response to Don's comment, marginal returns aren't diminishing because of external & internal economies [of scale] a la Marshall's Principles. Sraffa's criticism explains that this steers us away from the conception of perfect competition.
"Business men, who regard themselves as being subject to competitive conditions, would consider absurd the assertion that the limit to their production is to be found in the internal conditions of production in their firm, which do not permit of the production of a greater quantity without an increase in cost."
He says the chief trouble in increasing quantity supplied comes from selling more without reducing price, (movement along the downward-sloping demand curve) or incurring increased marketing expenses (shifting the demand curve up) to increase the willingness-to-pay of the market. Marketing expenses are not really a "cost-of-production," being extraneous from the conditions of production.
But, perhaps we can say that we have diminishing returns due to increasing opportunity cost of the variable factors employed?
Posted by: Ian at Mar 5, 2007 3:29:53 PM
Ian:
How exactly does this "steer us away" from perfect competition? Even when pricing at constant marginal cost, quantity supplied is obviously limited by the extent of the market.
Posted by: anon at Mar 5, 2007 3:49:42 PM
Economies of scale can give the firm market power. But, even monopolies are restricted by the demand schedule they face.
Posted by: Ian at Mar 5, 2007 4:16:20 PM
anon: If true, it still seems that any reference to marginal cost as a fundamental determinant of price
oversimplifies and under-explains.
Let me give a simple model of how production really works (apologies to those too familiar
with microeconomics):
A producer looks at the amount that will sell for each possible price (the demand curve for units he
produces, or Q = f(P)). He then chooses a production method. For each method there is a fixed and a marginal cost
(FC and MC). His profit R is price (P) times units sold Q minus MC*Q - FC. That is, R = P*Q - MC*Q - FC.
Each method has an optimum Q, found at dR/dQ = 0 (where increasing Q no longer increases profits).
But then, here's the catch: when he chooses a method, he is choosing an FC. That method determines MC. Then,
MC= f(FC). But MC can vary with Q. So MC(Q)=f(FC). That is, the relationship between marginal cost and
quantity varies with the choice of FC. So really, the cost due to MC should be:
sum(i=0 to Q) of MC(i).
Anyway, long story short, a producer is maximizing both over all production methods, and Q within that
production method. Even in a simple, ideal case, Q has to depend on more than MC of the last unit.
Posted by: Person at Mar 5, 2007 4:24:21 PM
Ian, there's a difference between marginal returns to variable factors and returns to scale. If it's your contention that marginal returns are increasing systematically in many industries -- well, that would lead to very few, very large firms in the industry, which is not observed in (for example) the Chinese restaurant market.
As to Tyler's assertion that the marginal cost of preparing another meal is zero: I'll be at his home expecting dinner at 6:30 tonight and every night thereafter. If the marginal cost really is zero, he won't mind at all.
Oh, and to respond to the question that prompted the original post: A firm that experiences any change in its cost structure will change its optimal quantity, while the prevailing price in the market is constant.
Posted by: Don at Mar 5, 2007 4:32:37 PM
You aren't paying for the food at a non-high-end-gourmet restaurant. You are paying not to have to prepare and clean it up. It's the same with paying for sex with a prostitute; you are paying for not having to have a relationship, not the sex.
If you want to figure the marginal cost of a restaurant meal, watch the busiest employee. That overworked waitress or prep cook who is right on the edge of not being able to serve or prepare one more meal - what is their time worth? The next one they hire to create some slack - how much do they cost?
Posted by: Eric H at Mar 5, 2007 5:21:41 PM
Don:
Chinese restaurants are obviously localized so it's not clear that market would become monopolistic, even if returns are increasing.
Posted by: anon at Mar 5, 2007 5:27:31 PM
As part of merger investigations for both the Justice Dept and FTC, we asked non merging firms whether they could double output at their same marginal cost. They invariably said "yes" unless they had hard capacity constraints like parking lots, cruise ships, or casino/hotels.
So now I think that the scope of firms are limited mostly by downward sloping demand curves rather than upward sloping MC curves. Motivate supply curves as useful tools describing aggregate behavior of sellers, not with price taking behavior.
Posted by: MBA prof at Mar 5, 2007 5:52:00 PM
"Each could serve an extra diner at essentially zero marginal cost, yet the price of the food is not zero."
Opportunity cost pricing. If one of your customers is willing to pay a positive price it would be stupid to sell your food for free to another customer. Or am I wrong?
Posted by: SteffenH at Mar 6, 2007 4:03:49 AM
I would just like to note that in cases where the marginal cost does seem to more nearly approach zero, bargaining toward that cost is seen to occur. In the not-very-good Chinese restaurant in South Station in Boston, for example, the marginal cost for food at the end of the day is low (earlier in the day there is an opportunity cost that someone later might pay more for it), the food is already made and in warming trays and will spoil, and the seating is food-court style, so there's little competition for that. At the end of the day they readily engage in bargaining with the only real constraint seeming to be that they don't want to encourage customers to wait until prices will be cheaper. I've had end of day meals there at 50% off a number of times.
Posted by: Ryan Miller at Mar 6, 2007 6:15:02 PM
Each could serve an extra diner at essentially zero marginal cost, yet the price of the food is not zero.
Err, am I missing the obvious, but doesn't the notion that they would do such a thing require price discrimination?
Surely it is inherent in the restaurant industry that they have to price as an offer to everyone who comes in. Folk want to know at least the price, given they may have to guess on quality.
Nor are restaurants like cinemas (where folk may also have to guess on quality), which can differentiate on tickets because they are selling a series of essentially pre-produced single products (particular films in particular sessions) with a relatively simple cost structure to customers with considerable capacity to shift times. Restaurants are selling a whole range of items with a somewhat complicated cost structure created at the time to customers who typically want to eat now. The transaction cost problems of price discriminating (apart from the odd lead item, like "happy hour" cheap drinks) would be prohibitive.
So, their pricing would have to work back from flat price-to-everyone-per-item, time limits (food goes off) and space limits (seating is limited). Various restaurants would face much the same problems, and the more competitive the local area restaurant-wise, the greater the custom-loss penalty from pricing above competitors. So prices end up being pretty similar.
Having had to price medieval feasts, you take you fixed costs (hall hire, etc), variable costs (food mainly, since labour is free) and then price hoping to get enough folk to at least cover your costs and maybe come out ahead. If the price looks "too high" for what you know of your customers, you re-jig what you are offering. More folk mean more profit, but you don't price the last seat in the hall at marginal cost=marginal price. You price at a "break even" point on the basis of a conservative estimate of attendees (where total cost=total revenue) and hope to do better thereby making gravy because your attendees are more than TC=TR so your fixed costs are already covered and the extra folk are more-than-paying their marginal cost.
Posted by: Lorenzo at Mar 8, 2007 6:13:37 AM
Even though the Chinese restaurants have similar menus, the
quality of the food varies. They are monopolistically
competitive.
Posted by: Barkley Rosser at Mar 10, 2007 1:34:20 PM
"Chinese restaurants are obviously localized..."
A statement of cost. Electricity production is obviously localized.
Posted by: rluser at Mar 12, 2007 3:29:07 AM
Our little chinese takeaway story has brought up some interesting parrels to the competitive market model which some of you have mentioned, I just want to clear up both the parrels and differences. For a truely competitive market, you have assume a number of things. one is that the price varies according to demand. thus, if marginal cost is less than the price of the meal, the price of the meal will drop. however, competitive market theory also assumes that every player has complete information, ie that both the buyer and seller know exactly how much that meal is worth at that point in time. this is extremely difficult to achieve of course. therefore, the chinese takeaway owners estimate the average marginal cost of a meal over the long term taking into account that in high demand periods their meals are worth more and at the end of each day, low demand periods, their food is worth less. by doing this estimation they are in fact trying to simplify the price to account for the changing demands and make life easy for both the customer and themselves. of course, a pure competitive market rarely exists, so our young takeaway owner is stuck in a tough situation but give him a break i reckon, if his prices stay steady then life is easier and none of us have to think or bargain nearly as much. so basically, noones getting any free food from the chinese takeaway, sorry guys.
Posted by: paulie at Mar 14, 2007 9:52:49 AM
