Does marginal cost equal price?

by on March 5, 2007 at 6:59 am in Economics | Permalink

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.

David Young March 5, 2007 at 8:01 am

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.

GVV March 5, 2007 at 10:03 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.

Ian March 5, 2007 at 11:19 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…

Don March 5, 2007 at 12:37 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.

joan March 5, 2007 at 12:40 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???

anon March 5, 2007 at 2:42 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.

anon March 5, 2007 at 3:49 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.

Person March 5, 2007 at 4:24 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.

Eric H March 5, 2007 at 5:21 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?

MBA prof March 5, 2007 at 5:52 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.

Ryan Miller March 6, 2007 at 6:15 pm

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.

Barkley Rosser March 10, 2007 at 1:34 pm

Even though the Chinese restaurants have similar menus, the
quality of the food varies. They are monopolistically
competitive.

paulie March 14, 2007 at 9:52 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.

tower defense May 10, 2009 at 1:12 am

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.

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